SEPTEMBER 2011 VOLUME 2 NUMBER 3

SEPTEMBER 2011 VOLUME 2 NUMBER 3

Journal Editorial Board
KRZYSZTOF WESOŁOWSKI, Editor-in-Chief
Poznan University of Technology
Piotrowo 3A, 60-965 Poznań, Poland
krzysztof.wesolowski@et.put.poznan.pl
ANNA PAWLACZYK, Secretary
Poznan University of Technology
Piotrowo 3A, 60-965 Poznań, Poland
anna.pawlaczyk@et.put.poznan.pl
ADRIAN LANGOWSKI, Technical Editor
Poznan University of Technology
Piotrowo 3A, 60-965 Poznań, Poland
adrian.langowski@et.put.poznan.pl
WOJCIECH BANDURSKI
Poznan University of Technology
ANNA DOMAŃSKA
Poznan University of Technology
MACIEJ STASIAK
Poznan University of Technology
HANNA BOGUCKA
Poznan University of Technology
MAREK DOMAŃSKI
Poznan University of Technology
RYSZARD STASIŃSKI
Poznan University of Technology
ANDRZEJ DOBROGOWSKI
Poznan University of Technology
WOJCIECH KABACIŃSKI
Poznan University of Technology
PAWEŁ SZULAKIEWICZ
Poznan University of Technology
Advisory Board
FLAVIO CANAVERO
Politecnico di Torino
Italy
TADEUSZ CZACHÓRSKI
Polish Academy of Science
Institute of Theretical and Applied
Informatics
Gliwice, Poland
PIERRE DUHAMEL
CNRS - Supélec
France
LAJOS HANZO
University of Southampton
UK
MICHAEL LOGOTHETIS
University of Patras
Greece
JÓZEF MODELSKI
Warsaw University of Technology
Poland
MACIEJ OGORZAŁEK
AGH Technical University
Jagiellonian University
Cracow, Poland
JOHN G. PROAKIS
University of California
San Diego, USA
RALF SCHÄFER
Fraunhofer Heinrich-Hertz-Institut
Berlin, Germany
Cover design Barbara Wesołowska
c○ Copyright by POZNAN UNIVERSITY OF TECHNOLOGY, Poznań, Poland, 2010
Edition based on ready-to-print materials submitted by authors
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ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS is a peer-reviewed journal published at Poznań University of Technology, Faculty
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SEPTEMBER 2011 VOLUME 2 NUMBER 3
Radio Communication Series:
Recent Advances in Teletraffic
Issue Editors: Grzegorz Danilewicz and Mariusz Głąbowski
Note from the Issue Editors
Grzegorz Danilewicz and Mariusz Głabowski ˛ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Algorithm for queueing networks with multi-rate traffic
Villy B. Iversen and King-Tim Ko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Retry Loss Models Supporting Elastic Traffic
Ioannis D. Moscholios, Vassilios G. Vasilakis, John S. Vardakas and Michael D. Logothetis . . . . . . . . . . . . 8
Damming the Torrent: Adjusting BitTorrent-like Peer-to-Peer Networks to Mobile and Wireless Environments
Philipp M. Eittenberger, Seungbae Kim, and Udo R. Krieger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Analysis of OBS Burst Assembly Queue with Renewal Input
Tomasz Hołyński and Muhammad Faisal Hayat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Scheduling and Capacity Estimation in LTE
Olav Østerbø . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Multi-Service Load Balancing in a Heterogeneous Network with Vertical Handover
Jie Xu, Yuming Jiang, Andrew Perkis and Elissar Khloussy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Resources Management and Services Personalization in Future Internet Applications
Paweł Światek, Piotr Rygielski and Adam Grzech . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Compact node-link formulations for the optimal single path MPLS Fast Reroute layout
Cezary Żukowski, Artur Tomaszewski, Michał Pióro, David Hock, Matthias Hartmann and Michael Menth . . . . 55
Enhancing Data Transmission Reliability with Multipath Multicast Rate Allocation
Matin Bagherpour, Mehrdad Alipour and Øivind Kure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Analytical Model for Virtual Link Provisioning in Service Overlay Networks
Piotr Krawiec, Andrzej Bęben and Jarosław Śliwiński . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Decisive Factors for Quality of Experience of OpenID Authentication Using EAP
Charlott Lorentzen, Markus Fiedler, and Peter Lorentzen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Agent based VoIP Application with Reputation Mechanisms
Grzegorz Oryńczak and Zbigniew Kotulski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011 1
Note from the Issue Editors
This volume of Advances in Electronics and Telecommunications contains
papers submitted for “The First European Teletraffic Seminar (ETS)” held
in Poznań, Poland, in February 2011. The ETS has come into being as an
extension to the Polish German Teletraffic Symposium, which was initiated
in 2000, and the Nordic Teletraffic Seminar, initiated in 1977, with kind
support of French Teletraffic Community. The European Teletraffic Seminar
is intended to maintain a regular series of international seminars providing
a forum for discussions related to the issues of teletraffic, a discipline
covering phenomena in control and transport of information within communications
and computer networks, for researchers, practitioners, young
scientists, and students.
Traffic theory and engineering have been an inseparable part of the
development of telecommunications and ICT infrastructure from their very
beginning. Teletraffic problems have changed substantially over the recent
years as a result of the shift in the telecommunications area towards integrated
digital networks, data services, Internet and mobile communications.
Each and every newly introduced network technology is followed by a
major increase in both the number and the complexity of problems that need
to be resolved by theoreticians and traffic engineers. No matter what these
developing changes may bring, the essential task for traffic theory remains
the same – to determine and evaluate the relationship between the quality of
service parameters, the parameters that determine the intensity of calls, and
the amount of resources demanded by such calls as well as the parameters
that describe available network resources. These relationships provide a
basis to develop engineering algorithms used for designing, analysis, and
optimization of systems and networks.
This issue of Advances in Electronics and Telecommunications contains
extended versions of selected ETS papers presenting a broad range of
teletraffic usage in modern telecommunications. The topics cover subjects related to teletraffic issues in next
generation and new generation networks, e.g. Future Internet architectures and technologies, operation of modern
telecommunication and computer networks; broadband and mobile communication systems; integration of a
broad spectrum of services; computer and communications systems applications; methods and tools for networks
and services modeling issues; networks and services planning; forecasting and management; performance
evaluation, etc. We believe that all articles presented in the journal clearly prove the importance and justify
the presence of traffic theory and engineering in providing solutions to problems we face in all modern networks,
telecommunications and computer networks alike, even (or especially) today when transmission offers high
bandwidth and switching is performed within extremely short time. We hope that readers will find the ETS
papers selected for this issue of Advances interesting, as we believe that teletraffic is equally important for
researchers and practitioners.
We would like to thank all the authors for their contributions to this issue of Advances in Electronics and
Telecommunications. Our thanks extend also to ETS’ Technical Programme Committee Chairs: Paul J. Kühn
and Michał Pióro, as well as to ETS’ General Conference Chairs: Prosper Chemouil, Markus Fiedler, Wojciech
Kabaciński, and Maciej Stasiak, whose involvement and commitment was critical to the successful completion
of the efforts to integrate European conferences focused on traffic theory and traffic engineering.
Grzegorz Danilewicz
Mariusz Głąbowski
Issue Editors

ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011 3
Algorithm for queueing networks with
multi-rate traffic
Villy B. Iversen and King-Tim Ko
Abstract—In this paper we present a new algorithm for
evaluatingqueueingnetworkswithmulti-ratetraffic.Thedetailed
state space of a node is evaluated by explicit formulæ. We
consider reversible nodes with multi-rate traffic and find the
state probabilities by taking advantage of local balance. Theory
of queueing networks in general, presumes that we have product
form betweenthenodes.Otherwise,wehave thestatespaceexplosion.
Even so, the detailed state space of each node may become
very large because there is no product form between chains
inside a node. A prerequisite for product form is reversibility
which implies that the arrival process and departure process
are identical processes, for example state-dependent Poisson
processes. This property is equivalent to reversibility. Due to
product form, an open network with multi-rate traffic is easy to
evaluate by convolution algorithms because the nodes behave as
independent nodes. For closed queueing networks with multiple
servers inevery nodeandmulti-rate services wemay applymultidimensional
convolution algorithm to aggregate the nodes so that
we endupwith twonodes, the aggregated node and asingle node,
for which we can calculate the detailed performance measures.
Index Terms—multi-rate traffic, queueingnetworks, reversibility,
insensitivity, product form, convolution algorithm
I. INTRODUCTION
IN 1957, J.R. Jackson who was working at production
planning and manufacturing systems, published a paper
[1] showing that a queueing network of M/M/n–nodes has
product form. Knowing the fundamental theorem of Burke
(1956 [2]) Jackson’s result is obvious. Historically, the first
paper on queueing systems in series was by another Jackson,
R.R.P. Jackson (1954 [3]).
The key point of Jackson’s theorem is that each node can
be considered to be independent of all other nodes, and that
the state probabilities are given by Erlang’s waiting time
modelM/M/n.Thissimplifiesthecalculationofthestate space
probabilities significantly. The proof of the theorem was given
byJacksonin1957byshowingthatthenodebalanceequations
are fulfilled under the assumption of statistical equilibrium.
Jackson’s first model thus only deals with open queueing
networks.
In Jackson’s second model (1963 [4]) the arrival intensity
from outside may depend on the current number of customers
in the network. Furthermore, the service rates may depend on
the number of customers k in the nodes. In this way, we can
model queueing networks which are either closed, open, or
mixed. In all three cases, the state probabilities have product
Villy B. Iversen is with Department of Photonic Engineering Technical
University of Denmark, 2800 Kongens Lyngby, Denmark. Email:
vbiv@fotonik.dtu.dk
King-Tim Ko is with Department of Electronic Engineering City University
of Hong Kong, Hong Kong. Email: eektko@cityu.edu.hk
form between nodes. The model by Gordon & Newell from
1967 which is often cited in the literature can be treated as a
special case of Jackson’s second model.
The theory of queueing networks assumes that a customer
samples a new service time in every node. This is a necessary
assumption for having product form. This assumption was
investigated by Kleinrock (1964 [5]) and it turns out to be
a good approximation in real life.
In 1975 the second model of Jackson was further generalizedbyBaskett,Chandy,MuntzandPalacios(1975[6])tosocalled
BCMP–networks. These authors showed that queueing
networks with K nodes and more than one type of customers
also have product form, provided that:
a) The customers are classified into N chains. Each chain
j ∈ N is in each node i ∈ K characterized by
its own mean service time s j i and routing probabilities
p ik , {i, k ∈ K}. A customer may change from one chain
to another chain with a certain probability after finishing
service at a node. If the queueing system of a node is
a classical M/M/n system (including M/M/1), then the
average service time in a node must be identical for all
chains.
b) Each node is a symmetric (= reversible) queueing system
mentioned below (Sec. II-B): for each chain a Poisson
arrival process implies a Poisson departure process.
BCMP–networks can be evaluated by the multi-dimensional
convolution algorithm for multi-server systems. The famous
MVA (mean value) algorithm by Lavenberg & Reiser [7]
is applicable only if all nodes are single server systems
or infinite server systems. This paper is based on models
of Kingman (1969 [8]) and Sutton (1980 [9]), which are
generalizations of Erlang’s approach based on the assumption
of statistical equilibrium. All derivations are mathematically
very simple. Similar models are dealt with by Bonald &
Proutière (2003 [10]) and Bonald & Virtamo (2005 [11]).
They also consider multi-rate queueing nodes, but only with
infinite buffer. They present expressions for the average flow
throughput. Serfozo (1999 [12]) presents the general theoretical
background.
Our approach is algorithmic and directed to engineering
applications. For open networks we achieve an algorithm
which is linear in both number of traffic streams and number
of channels and has a very small memory requirement
(Iversen, 2007 [13]). For loss (buffer-less) systems we obtain
an algorithm for BPP (Binomial–Poisson–Pascal) traffic with
individual performancemeasures for each stream. For systems
with buffers (finite or infinite) we obtain both mean virtual

4 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
· · ·
· · ·
.
✗ ✔
✗
x 1 −d 1 , x 2
x 1 , x 2
✖
..
.
✕
x 1 µ 1
✖
..
..
. .
. .
..
..
..
..
✔
. · · ·
.
✕· · ·
For type j customers the service rate in state
x = (x 1 , x 2 , . . . , x j , . . . , x N ) is reduced by a factor
g j (x). The reduction factors g j (x) are chosen so that we
maintain reversibility, and they can be specified for various
parts of the state transition diagram as follows, where (d) is
the only non-trivial case.
· · ·
· · ·
.
..
..
. ✗ ✔ λ 1
✗
x 1 −d 1 , x 2 −d 2 x 1 , x 2 −d 2
✖
.
✕
✖
..
λ 1
λ 2
x 2 µ 2 λ 2
x 2 µ 2
x 1 µ 1
..
.
..
.
..
.
..
.
✔
. · · ·
.
✕· · ·
Fig. 1. State-transition diagram for four neighboring states in a reversible
nodewith two multi-rate trafficstreams and infinite capacity. State x j denoters
that x j channels are occupied by type j calls. For type j with slot-size d j we
choose the service rate d j µ j .
waiting times, virtual mean queue lengths, and loss (overflow)
probability for each stream.
In this paper we derive explicit formulæ for detailed state
probabilities of multi-rate closed queueing networks.
II. REVERSIBLE MULTI-SERVER MULTI-SERVICE NODES
We consider a system with n servers (channels, bandwidth
units) and infinite queue. The system is offered N different
traffic streams. Customers of type j arrive to the system
according to a Poisson arrival process with intensity λ j . A
customer of type j attempts to occupy d j servers, and if all
these are obtained the service time is exponentially distributed
with intensity d j µ j (j = 1, 2, . . . , N) where the factor d j
only is chosen for convenience. Later we may choose µ j = µ
for all services, then the service rate in a state with a total
of x busy channels will be equal to x µ, independent of the
actual mix of services. The state of the system is defined
by x = (x 1 , x 2 , . . . , x j , . . . , x N ), where x j is the number
of channels and/or queueing positions occupied by type j
customers. Thus, the number of type j customers is equal
to x j /d j . If the total demand for channels is bigger than the
number of channels available, then the customers share the
capacity and queueing positions in some particular way which
is specified below. When the number of servers is infinite, we
get the state transition diagram shown for two traffic streams
in Fig. 1. This diagram is reversible and has a simple product
form solution.
However, the capacity is limited to n servers, so we have
to reduce the service rates in all states requiring more than
n servers (overload). In the following we illustrate the theory
for two services, but also mention the general case with N
different services.
A. Reduction factors
We consider a system with N traffic streams. Let:
x = (x 1 , x 2 , . . . , x j−1 , x j , x j+1 , . . . , x N )
x − d j = (x 1 , x 2 , . . . , x j−1 , x j − d j , x j+1 , . . . , x N )
(a) x i ≤ 0 : g j (x) = 0.
The reduction factors are undefined for these states for which
the state probabilities are zero. By choosing the value zero,
the recursion formulæ below are correctly initiated.
(b) x i ≥ 0 ∧ 0 < ∑ N
j=1 x i ≤ n : g j (x) = 1 .
Every call is allocated the capacity required and there is no
reduction.
(c) x j = 0 for all j ≠ i, x i ≥ n : g i (x) = n/x i
Along the axes we have a classical M/M/n–system with only
one service, and the calls share the capacity equally.
(d)Stateswith moretypesofcustomersin totalrequiringmore
than n channels. If possible, we want to choose g i (x 1 , x 2 ) so
that all capacity is used. This requirement implies:
N∑
x j · g j (x) = n ,
j=1
N∑
x j ≥ n . (1)
j=1
We consider states x where x =
∑ N
i=1 x i > n and
all capacity is used. We apply flow balance equations for
Kolmogorov cycles.
A necessary and sufficient condition for reversibility (Kingman,
1969 [8], Sutton, 1980 [9]) is that all two-dimensional
flow paths are in equilibrium. In total we may choose:
( ) N
=
2
N (N − 1)
2
different cycles and thus different balance equations.
We assume that we know the reduction factors for states
x − d j below state x. To find the N reduction factors in
state x = {x 1 , x 2 , . . . , x N } we need N independent equations.
Thus, we may choose Kolmogorov cycles for the twodimensional
planes {1, j}, (j = 2, 3, . . . , N) which yields
N −1 independent equations. Furthermore we have the normalization
equation (1) requiring that the total capacity used
during overload is n. We get the following flow balance
equations for j = 2, 3, . . . N:
or
g 1 (x) · g j (x − d 1 ) = g j (x) · g 1 (x − d j )
g j (x) = g 1 (x) · gj(x − d 1 )
, j = 2, 3, . . . , N . (2)
g 1 (x − d j )

INVERSEN AND KO: ALGORITHM FOR QUEUEING NETWORKS WITH MULTI-RATE TRAFFIC 5
The capacity normalization equations is (1):
n =
=
g 1 (x) =
N∑
x i · g i (x)
i=1
N∑
i=1
{
x i · g 1 (x) · gi(x }
− d 1 )
,
g 1 (x − d i )
n
N∑
{
x i · gi(x } . (3)
− d 1 )
g 1 (x − d i )
i=1
Thus, we find g 1 (x) from (3) and all other reduction factors
in state x from (2). As we know, all reduction factors for
global states x up to n where x = ∑ N
i=1 x i and all reduction
factors for states where only one service is active, then we can
calculate all reductionfactors recursively.This is equivalent to
calculating the relative state probabilities, and thus by global
normalization the normalized state probabilities.
For two traffic streams we get the reduction factors:
n
g 1 (x 1 , x 2 ) =
x 1 + x 2 · g2(x1−d1,x2)
g 2 (x 1 , x 2 ) =
g 1(x 1,x 2−d 2)
n
x 2 + x 1 · g1(x1,x2−d2)
g 2(x 1−d 1,x 2)
We always find a unique solution when the offered traffic is
less than the capacity. When we know the reduction factors, it
is easy to find the relative state probabilities by local balance
equations. Due to reversibility we have local balance for each
service. We get
λ j · p(x − d j ) = g j (x) x j µ j · p(x) , j = 1, . . . , N.
Thus, we can recursivelyfind all reductionfactorsand all state
probabilities expressed by state zero. By normalization, which
should be done in each step to ensure numerical accuracy, we
obtain the absolute state probabilitiesfor a single multi-rate n-
server node. From the state probabilities we find performance
measures as mean sojourn time and throughput.
For low and normal load, each connection will almost get
the required bandwidth as for proportional fair scheduling. It
can be shown by studying the reduction factors for increasing
load that if the system becomes highly overloaded, then in
the limit we get fair scheduling where all connections will
be allocated the same capacity independent of the required
slot-sizes.
B. Classical queueing networks as special cases
When all traffic streams have the same bandwidth demand
d j = 1, we get the following simple solution:
g j (x) =
n
∑ N
j=1 x ,
j
N∑
x j ≥ n , j = 1, 2, . . . , N. (4)
j=1
Thus, the service rates of all customers are reduced by the
same factor and during overload the customers share the capacity
equally. The state transition diagram can be interpreted
as modeling the following systems, illustrated by Fig. 2.
.
· · ·
· · ·
· · ·
· · ·
.
.
..
..
✗ ✔ λ 1 ✗
✔
. . · · ·
x 1 −d 1 , x 2
x 1 , x 2
.
.
✖ ✕
✖
✕· · ·
..
..
g 1 (x 1 , x 2 ) · x 1 µ 1
λ 2 g 2 (x 1 −d 1 , x 2 ) · x 2 µ 2
λ 2 g 2 (x 1 , x 2 ) · x 2 µ 2
g 1 (x 1 , x 2 −d 2 ) · x 1 µ 1
. .
..
..
..
✗ ✔ λ 1
✗
x 1 −d 1 , x 2 −d 2 x 1 , x 2 −d 2
✖
.
✕
✖
. .
.
..
..
.
.
..
.
.
..
..
.
.
..
.
✔
. · · ·
.
✕· · ·
Fig. 2. State-transition diagram for four neighboring states in a reversible
system with two multi-rate traffic streams.
C. Generalized processor sharing (GPS) system
In states (x 1 , x 2 ) below saturation (x 1 + x 2 ≤ n) every user
occupy one server. Above saturation all users share the available
capacity equally. The model is insensitive to the service
time distribution and each service may have individual mean
service time. This model is called the GPS = Generalized
Processor Sharing model. For states x 1 + x 2 > n, a customer
typeone wantsatotal service rate µ 1 , andacustomertype two
wants a service rate µ 2 . But the service rates of all customers
are reduced by the same factor n/(x 1 + x 2 ).
As a special case, the Σ j M j /G j /1–PS single-server system
with processor sharing (PS) is reversible and insensitive to the
service time distributions and each class may have individual
mean service times.
D. Classical multi-service multi-server system
In classical queueing, a customer always get one server for
exclusiveusage. Thento maintainreversibilityfor x 1 +x 2 > n
wehavetorequirethatallcustomershavethesameservicerate
µ j = µ, and thus the same exponentially distributed service
time. The mathematical proof will be give elsewhere. This
corresponds to an M/M/n system with total arrival rate λ =
∑
j λ j andservicerate µ.All customersinthesystemhavethe
same probability of being the next one departing, independent
of the call type.
The system M/G/∞ is reversible, as the departure process
is a Poisson process because it is a random translation of the
arrival process.
E. Σ j M j /G j /1–LCFS–PR single-server system
From the very nature of the model it is obvious that it is
reversible as we always follow the same path back to state
zero as away from state zero. It is insensitive to the service
time distribution and each service may have individual mean
service time.
In conclusion, multi-server queueing systems with more
classes of customers, all having bandwidth demand d j =

6 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
1, (j = 1, 2, . . . , N), will only be reversible when the system
is one of the following queueing system:
• M/G/n–GPS , (for n = 1 PS - Processor Sharing).
• M/G/1–LCFS–PR,
• M/M/n, including M/M/1 with same service time for all
customers.
These systems are also called symmetric queueing systems.
Reversibility implies that the departure processes are Poisson
processes for all classes. These systems make up the nodes
allowed in BCMP–queueing networks.
III. MULTI-RATE MULTI-SERVER QUEUEING NETWORKS
We now build a network of nodes of the above type. As in
ordinary queueing networks we have a routing matrix which
specifies the route followed by a given traffic stream, named
a chain.
Open Queueing Networks
These are easy to deal with. By solving the flow balance
equations(flow in = flow out for each node) for each chain we
find the load (offered traffic) of each node. We then find the
state probabilities of each node and due to product form we
easily get the state probabilities of the total queueing network.
Closed Queueing Networks
From the flow balance equations we first find the relative
load of each chain in each node. For a closed network we
aggregate the nodes by multi-dimensional convolutions, keeping
account of the number of customers in each chain in the
aggregated node. All nodes except the target node are aggregated
into one node. This aggregated node is convolved with
the target node for which we find the performance measures
during the convolution. The multi-dimensional convolution is
defined as follows:
p 1,2 (x 1 , x 2 , . . . , x N ) = p 1 ∗ p 2 =
∑x 1
∑x 2
i 1=0 i 2=0
. . .
x N
∑
i N =0
p 1 (x 1 −i 1 , x 2 −i 2 , . . . , x N −i N ) · p 2 (i 1 , i 2 , . . . , i N )
The parameter x j is given in numberof channels. Both x j and
i j belong to {0, d j , 2d j , . . . , d j S j }, where S j is the number
of customers in chain j, and j = 1, 2, . . . , N. By changing
the order of convolution we obtain the performance measures
for each node. The performance measures are for example
mean waiting time and mean queue length for each chain, and
carried traffic for each stream in the node.
IV. NUMERICAL EXAMPLE
The convolution algorithm for closed multi-rate queueing
networks has been inplemented in a master thesis project by
Iliakis & Kardaras (2007 [14]).
Let us consider a closed network with two nodes and
two types of customers, alternating between the two nodes
(a generalized machine-repair model). We have 10 type-1
customers each requesting one channel for service in a node.
The service time is 4 tu in node-1 and 1 tu in node-2 (tu =
time units). We have 5 type-2 customers each requesting two
channels for service in a node. The service time is 2 tu in
node-1 and 0.5 tu in node-2. Thus, the packet size (bandwidth
times mean service time) is the same for the two types.
The capacity is 20 channels in node-1 so that we never
experience delay. The sojourn time in node-1 is thus 4 tu,
respectively 2 tu. In node-2 we have 5 channels and infinite
queue. We find the sojourn times equal to 1.1929 tu, respectively
0.6990 tu. Thus, the virtual mean waiting time (increase
in sojourn time due to limited capacity) in node-2 is 0.1929
tu for type-1, and 0.1990 for type-2. The waiting times of the
two services are ofsame orderof size, but by allocatingbigger
bandwidth to a type of traffic we can reduce the sojourn time
(response time).
Limitations of the algorithm are the number of states in the
multi-dimensionalstate space of each node, and the numberof
operations required during the multi-dimensional convolution
of the nodes.
V. FUTURE WORK
The above model correspondsto a store-and-forwardpacket
switched network with bottlenecks and to models considered
in production systems. The model may be generalized in
several ways. We way reserve at fixed minimum bandwidth
to a certain type in each node this type visits, so that we have
an end-to-end dedicated path with a guaranteed bandwidth as
in ATM and MPLS networks. If the stream requires more
bandwidth than guaranteed, then it has to compete with other
streams in each node for additional bandwidth. The system
will still be reversible.
We may introduce an upper limit to the number of simultaneous
connections of each type in a node. Then we may
experience blocking in the nodes, and the system will only be
reversible if we include blocked calls in the departure process.
VI. CONCLUSIONS
The convolution algorithm for the closed multi-rate queueing
networks is a generalization of the classical convolution
algorithm for queueing networks and has similar limitations
in number of chains and customers in each chain.
REFERENCES
[1] J. R. Jackson, “Networks of waiting lines,” Operations Research, vol. 5,
pp. 518–521, 1957.
[2] P. J. Burke, “The output of a queueing system,” Operations Research,
vol. 4, pp. 699–704, 1956.
[3] R. R. P. Jackson, “Queueing systems with phase type service,” Operational
Research Quarterly, vol. 5, pp. 109–120, 1954.
[4] J. R. Jackson, “Jobshop–like queueing systems,” Management Science,
vol. 10, no. 1, pp. 131–142, 1963.
[5] L. Kleinrock, Communication nets: Stochastic message flow and delay.
McGraw–Hill, 1964, dover Publications 1972.
[6] F.Baskett, K.M.Chandy, R.R.Muntz, andF.G.Palacios, “Open, closed
and mixed networks of queues with different classes of customers,”
Journal of the ACM, pp. 248–260, Apr. 1975.
[7] S. S. Lavenberg and M. Reiser, “Mean–value analysis of closed multichain
queueing networks,” Journal of the Association for Computing
Machinery, vol. 27, pp. 313–322, 1980.
[8] J. F. C. Kingman, “Markov population processes,” J. Appl. Prob, vol. 6,
pp. 1–18, 1969.
[9] D. J.Sutton, “The application of reversible Markov population processes
to teletraffic,” A.T.R., vol. 13, pp. 3–8, 1980.

INVERSEN AND KO: ALGORITHM FOR QUEUEING NETWORKS WITH MULTI-RATE TRAFFIC 7
[10] T. Bonald and A. Proutière, “Insensitive bandwidth sharing in data
networks,” Queueing Systems, vol. 44, pp. 69–100, 2003.
[11] T. Bonald and J. Virtamo, “A recursive formula for multirate systems
with elastic traffic,” IEEE Commun. Lett., vol. 9, pp. 752–755, Aug.
2005.
[12] R. Serfozo, Introduction to Stochastic Networks. Springer, Applications
of Mathematics, 1999.
[13] V. B. Iversen, “Reversible fair scheduling: the teletraffic theory revisited,”
Springer Lecture Notes on Computer Science, vol. LNCS 4516,
pp. 1135–1148, 2007, 20th International Teletraffic Congress, Ottawa,
Canada.
[14] E. Iliakis and G. Kardaras, “Resource allocation in next generation
internet,” Master’s thesis, Technical University of Denmark, 2007.
Villy Bæk Iversen received the M.Sc. degree in electrical engineering in
1968 and the Ph.D. degree in teletraffic engineering in 1976, both from
The Technical University of Denmark, where he is associate professor at
Department of Photonics Engineering. He has worked in many developing
countries as an ITU-expert. He is Professor Honoris Causa at Beijing
University of Posts and Telecommunications, former vice-chairman of the
International Advisory Committee of the International Teletraffic Congresses,
and Danish member of IFIP TC6 (Digital Communication). His research
interests include stochastic modelling, communication systems, and teletraffic
engineering. He has published more than 150 papers and edited several
conference proceedings. He is editor of the Teletraffic Engineering Handbook.
King-Tim Ko received his B.Eng.(Hons) and Ph.D. degrees from The
University of Adelaide, Australia. He has worked several years with the
Telecom Australia Research Laboratories in Melbourne before joining the
Department of Electronic Engineering of the City University of Hong Kong
in 1986, and currently an Associate Professor of the same Department. In
research, he is interested in the performance evaluation of communication
networks and mobile networks.

8 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
Retry Loss Models Supporting Elastic Traffic
Ioannis D. Moscholios, Vassilios G. Vasilakis, John S. Vardakas and Michael D. Logothetis
Abstract—We consider a single-link loss system of fixed capacity,
which accommodates K service-classes of Poisson traffic with
elastic bandwidth-per-call requirements. When a new call cannot
be accepted in the system with its peak-bandwidth requirement,
it can retry one or more times (single and multi-retry loss
model, respectively) to be connected in the system with reduced
bandwidth requirement and increased service time, exponentially
distributed.Furthermore,ifitslast bandwidthrequirementisstill
higher than the available link bandwidth, it can be accepted in
the system by compressing not only the bandwidth of all inservice
calls (of all service-classes) but also its last bandwidth
requirement. The proposed model does not have a product form
solution and therefore we propose an approximate recursive
formula for the calculation of the link occupancy distribution
and consequently call blocking probabilities. The accuracy of
the proposed formula is verified by simulation and is found to
be quite satisfactory.
Index Terms—Markov chain, call blocking, recursive formula,
retry, elastic services
I. INTRODUCTION
MULTI-RATE loss models are extensively used in the
literature for the call-level QoS assessment of modern
telecom networks. This assessment is critical not only for
the bandwidth allocation among calls of different serviceclasses
but also for the avoidance of over-dimensioning of
a network. Despite of its importance, the call-level QoS
assessment remains an open issue, due to the existence of
elastictrafficinmoderntelecomnetworks.Bytheterm“elastic
traffic” we mean calls whose assigned bandwidth can be
compressed or expanded during their lifetime in the system.
Modeling elastic traffic at call-level can be based on the
classical Erlang Multirate Loss Model (EMLM) ([1], [2]])
which has been widely used in wired (e.g. [3], [4], [5], [6]),
wireless(e.g.[7],[8],[9],[10])andopticalnetworks(e.g.[11],
[12],[13],[14],[15])tomodelsystemsthataccommodatecalls
of differentservice-classeswith differenttrafficandbandwidth
requirements.
In the EMLM, calls of different service-classes arrive at a
link of capacity C, following a Poisson process, and compete
for the available link bandwidth under the complete sharing
policy (all calls compete for all bandwidth resources). If upon
arrival a call’s bandwidth requirement is not available, the call
Ioannis D. Moscholios is with Dept. of Telecommunications Science and
Technology, University of Peloponnese, 221 00 Tripolis, Greece. Email:
idm@uop.gr
Vassilios G. Vasilakis is with WCL, Dept. of Electrical and Computer
Engineering, University of Patras, 265 04 Patras, Greece. Email: vasilak@wcl.ee.upatras.gr
John S. Vardakas is with WCL, Dept. of Electrical and Computer
Engineering, University of Patras, 265 04 Patras, Greece. Email: jvardakas@wcl.ee.upatras.gr
Michael D. Logothetis is with WCL, Dept. of Electrical and Computer
Engineering, University of Patras, 265 04 Patras, Greece. Email: m-
logo@wcl.ee.upatras.gr
is blocked and lost. Otherwise, it remains in the system for
a generally distributed service time [1]. The analysis of the
EMLM shows that the steady state distribution of in-service
calls has a product form solution (PFS) [16]. Exploiting
this fact, an accurate recursive formula (known as Kaufman-
Roberts formula, KR formula) has been separately proposed
by Kaufman [1] and Roberts [2] which determines the link
occupancy distribution and simplifies the determination of
call blocking probabilities (CBP). In [17], [18], the EMLM
is extended to the retry models, in which blocked calls can
immediately reattempt (one or more times – single-retry loss
model (SRM) and multi-retry loss model (MRM), respectively)tobeconnectedbyrequiringlessbandwidthunits(b.u.),
while increasing their service time which is exponentially
distributed, so that the product (service time) by (bandwidth
percall)remainsconstant.Aretrycallisblockedandlostfrom
the system when its last bandwidth requirement is higher than
the available link bandwidth.
In this paper, we extend the models of [17], [18], by
incorporatingelastictraffic.Wenametheproposedsingle-retry
loss model, Extended SRM (E-SRM) and the multi-retry loss
model, Extended MRM (E-MRM). In the proposed models,
when a retry call attempts to be connected in the system and
its last bandwidth requirement is higher than the available link
bandwidth, the system accepts this call (contrary to [17], [18],
where this call is lost) by compressing not only the bandwidth
of all in-service calls (of all service-classes) but also the last
bandwidth requirement of the retry call. The corresponding
service times are increased so that the product (service time)
by (bandwidth per call) remains constant. On the other hand
when an in-service call, whose bandwidth is compressed,
departs from the system then the remaining in-service calls
(of all service-classes) expand their bandwidth. A retry call
is blocked and lost from the system when the compressed
bandwidth should be less than a minimum proportion (r min )
of its required last-bandwidth. Note that r min is common
for all service-classes. The compression/expansionmechanism
together with the existence of retrials destroys reversibility in
the proposed models and therefore no PFS exists. However,
we propose approximate recursive formula for the calculation
of the link occupancy distribution that simplifies the CBP
determination. Simulation results validate the accuracy of the
proposed formulas. In the case of no retrials for calls of all
service-classes, the proposed models coincide with the model
of [19] which has incorporated elastic traffic in the EMLM.
We name this model, Extended EMLM (E-EMLM).
The remainder of this paper is as follows: In Section II
we review the SRM, MRM and E-EMLM. In Section III,
we present the proposed E-SRM and E-MRM and provide
formulasforthe approximatecalculationofthe linkoccupancy
distribution and CBP. In Section IV, we present numerical and

MOSCHOLIOS et al.: RETRY LOSS MODELS SUPPORTING ELASTIC TRAFFIC 9
simulation results in order to validate the models’ accuracy.
We conclude in Section V.
II. REVIEW OF THE RETRY LOSS MODELS AND THE
E-EMLM
A. Review of the single and multi-retry loss models
Consider a link of capacity C b.u. that accommodates calls
of K service-classes. Let j be the occupied link bandwidth,
j = 0, 1, . . ., C. Calls of each service-class k (k = 1, . . ., K)
arrive in the link according to a Poisson process with rate λ k
and request b k b.u. If b k b.u. are available, a call of serviceclass
k remains in the system for an exponentially distributed
service-timewithmean µ −1
k
.Otherwise,thecallisblockedand
retries immediately to be connected in the system with “retry
parameters” (b kr , µ −1
kr ) where b kr < b k and µ −1
kr > µ−1 k
. The
SRM does not have a PFS and therefore the calculation of the
link occupancy distribution, G(j), is based on an approximate
recursive formula, [17], [18]:
⎧
1 for j=0
1
K∑
⎪⎨ j
α k b k G(j−b k )+
G(j)=
k=1
for j=1, . . . , C ,
K∑
+ 1 j
α kr b kr γ kr (j)G(j−b kr )
⎪⎩ k=1
0 otherwise
(1)
where α k = λ k µ −1
k , α kr = λ k µ −1
kr , γ kr(j) = 1 when j >
C −(b k − b kr ), otherwise γ kr (j) = 0.
Equation(1)isbasedontwo assumptions:1)theapplication
of Local Balance (LB), which exists only in PFS models and
2) the application of Migration Approximation (MA) which
assumes that the occupied link bandwidth from retry calls is
negligible when the link occupancy is below or equal to the
retry boundary, i.e. when j ≤ C − (b k − b kr ). The existence
of the MA in eq. (1) is expressed by the variable γ kr (j).
The final CBP of a service-class k, denoted as B kr , is the
probability of a call to be blocked with its retry bandwidth
requirement and is given by:
B kr =
C∑
G −1 G(j), (2)
j=C−b kr +1
where G = ∑ C
j=0
G(j) is the normalization constant and
b kr > 0.
In the MRM, a blocked call of service-class kcan have
multiple retrials with “retry parameters” (b krl , µ −1
kr l
) for l =
1, . . . , s(k), where b krs(k) < . . . < b kr1 < b k and µ −1
kr s(k)
>
. . . > µ −1
kr 1
> µ −1
k
. The MRM does not have a PFS and
therefore the calculation of the link occupancy distribution,
G(j), is based on an approximate recursive formula [18]:
⎧
1 for j = 0
1
K∑
⎪⎨ j
a k b k G(j−b k )+
k=1
G(j)= K∑
+ 1 s(k)
for j = 1, . . . , C ,
∑
j
a krl b krl γ krl
(j)G(j−b krl )
⎪⎩ k=1 l=1
0 otherwise
(3)
where: a krl = λ k µ −1
kr l
, γ krl (j) = 1, if C ≥ j > C − (b krl−1 −
b krl ), otherwise γ krl (j) = 0.
ThefinalCBP ofaservice-class k,denotedas B krs(k) ,isthe
probabilityof a call to be blockedwith its last retry bandwidth
requirement and is given by:
B krs(k) =
C∑
G −1 G(j), (4)
j=C−b krs(k) +1
where G = ∑ C
j=0 G(j) and b kr l
> 0 for l = 1, . . ., s(k).
B. Review of the E-EMLM
Consider again a link of capacity C b.u. that accommodates
Poisson arriving calls of K service-classes. A call of serviceclass
k (k = 1, . . ., K) arrives in the system with rate λ k and
requests b k b.u. (peak-bandwidth requirement). If j + b k ≤ C,
the call is accepted in the system with its peak-bandwidth
requirement and remains in the system for an exponentially
distributed service time with mean µ −1
k
. If T ≥ j + b k > C
the call is accepted in the system by compressing not only its
bandwidthrequirementbut also the bandwidthofall in-service
calls. The compressed bandwidth of the new service-class k
call is:
b ′ k = rb k = C j ′ b k, (5)
where r ≡ r(n) = C/j ′ , j ′ = j + b k = nb + b k and T
is the limit (in b.u.) up to which bandwidth compression is
permitted.
Similarly, the bandwidth of all in-service calls will be
compressed and become equal to b ′ i = C j
b ′ i for i = 1, . . ., K.
After the compression of both the new call and the in-service
callsthestateofthesystemis j = C.Theminimumbandwidth
that a call of service-class k (either new or in-service) can
tolerate is given by the expression:
b ′ k,min = r minb k = C T b k, (6)
where r min = C/T is the minimumproportionof the required
peak-bandwidth and is common for all service-classes.
Thismeansthatif uponarrivalofaservice-class k call, with
peak-bandwidth requirement b k b.u., we have j = j + b k > T
(or equivalently, j ′ > T or C/j ′ < r min ) then the call is
blocked and lost without further affecting the system.
After the bandwidth compression, calls increase their service
time so that the product (service time) by (bandwidth per
call) remains constant. Thus, due to bandwidth compression
calls of service-class k may remain in the system more than
µ −1
k
time units. Increasing the value of T, decreases r min and
increases the delay of calls of service-class k (compared to
the initial service time µ −1
k
). Therefore the value of T can be
chosen so that this delay remains within acceptable levels.
The compression/expansion of bandwidth destroys reversibility
in the E-EMLM and therefore no PFS exists.
However,in[19]anapproximaterecursiveformulaisproposed

10 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
which determines G(j)’s:
⎧
1 for j = 0
⎪⎨
1
K∑
G(j) =
min(j,C)
a k b k G(j − b k ) for j = 1, · · · , T ,
⎪⎩
k=1
0 otherwise
(7)
where α k = λ k µ −1
k .
Equation (7) is based on a reversible Markov chain which
approximates the bandwidth compression/expansion mechanism
of the E-EMLM, described above. The LB equations
of this Markov chain are of the form [19]:
λ k P (n − k ) = n kµ k φ k (n)P (n), (8)
where P (n) is the probability distribution of state n =
n 1 , n 2 , . . ., n k , . . ., n K ), P (n − k
) is the probability distribution
of state n − k
= (n 1, n 2 , . . . , n k−1 , n k − 1, n k+1 , . . . , n K ) and
φ k (n) is a state dependent factor which describes: i) the
compression factor of bandwidth and ii) the increase factor
of service time of service-class k calls in state n, so that
(service time) by (bandwidth per call) remains constant. In
other words, φ k (n) has the same role with r(n) in eq. (5) or
r min in eq. (6) but it may be different for each service-class.
It is apparent now why the model of eq. (7) approximates the
E-EMLM. The values of φ k (n) are given by:
⎧
⎪⎨ 1 , for nb ≤ C, n ∈ Ω
x(n
φ k (n) =
− k )
x(n)
, for C < nb ≤ T, n ∈ Ω , (9)
⎪⎩
0 , otherwise
where Ω = {n : 0 ≤ nb ≤ T and nb = ∑ K
k=1 n kb k .
In eq. (9), x(n) is a state multiplier, associated with state
n, whose values, are chosen so that eq. (8) holds, [19]:
⎧
1 , for nb ≤ C, n ∈ Ω
⎪⎨
1
K∑
x(n) =
C
n k b k x(n − k
⎪⎩
) , for C < nb ≤ T, n ∈ Ω .
k=1
0 , otherwise
(10)
Having determined the values of G(j)’s we can calculate CBP
according to the following formula:
B k =
T∑
G −1 G(j), (11)
j=T −b k +1
where G = ∑ T
j=0
G(j) is the normalization constant.
III. RETRY LOSS MODELS SUPPORTING ELASTIC TRAFFIC
A. The extended single-retry loss model
The proposed E-SRM is a non-PFS model that combines
the characteristics of the SRM and the E-EMLM. In order
to provide an approximate but recursive formula for the
calculation of the link occupancy distribution we present the
following simple example.
Consider a link of capacity C b.u. that accommodates
Poisson arriving calls of two service-classes with traffic
parameters: (λ 1 , µ −1
1 , b 1) f or the 1 st service-class and
(λ 2 , µ −1
2 , µ−1 2r , b 2, b 2r ) for the 2 nd service-class. Calls of the
2 nd service-class have “retry parameters” with b 2r < b 2 and
µ −1
2r
> µ −1
2 . Let T be the limit up to which bandwidth
compression is permitted for calls of both service-classes
Although the E-SRM is a non-PFS model we will use the
LB eq. (8), initially for calls of the 1 st service-class:
λ 1 P (n − 1 ) = n 1µ 1 φ 1 (n)P (n), (12)
for 1 ≤ nb ≤ T, where n = (n 1 , n 2 , n 2r ), n − 1 = (n 1 −
1, n 2 , n 2r ) with n 1 ≥ 1 and
⎧
⎪⎨ 1 , for nb ≤ C, n ∈ Ω
x(n
φ 1 (n) =
− 1 )
x(n)
, for C < nb ≤ T, n ∈ Ω (13)
⎪⎩
0 , otherwise
with nb = j = ∑ 2
k=1 (n kb k +n kr b kr ) = n 1 b 1 +n 2 b 2 +n 2r b 2r .
Based on eq. (13) and multiplying both sides of eq. (12)
with b 1 we have:
a 1 b 1 x(n)P (n − 1 ) = n 1b 1 x(n − 1 )P (n), (14)
where α 1 = λ 1 µ −1
1 and the values of x(n) are given by:
⎧
1 , for nb ≤ C, n ∈ Ω
⎪⎨ 1
K∑
x(n) = C
n k b k x(n − k )+
k=1
, for C < nb ≤ T, n ∈ Ω .
+n ⎪⎩ kr b kr x(n − kr )
0 , otherwise
(15)
To derive the corresponding LB equations of 2 nd serviceclass
calls consider that a call of the 2 nd service-class arrives
in the system when the occupied link bandwidth is j b.u. with
j = 0, 1, . . ., T. If j ≤ C − b 2 , the call will be accepted
in the system with b 2 b.u. If j > C − b 2 , the call will be
blocked with its b 2 requirement and will immediately try to
be connected in the system with b 2r < b 2 . We consider three
cases: 1) If j + b 2r ≤ C the retry call will be accepted in
the system with b 2r . 2) If j + b 2r > T the retry call will be
blocked and lost. 3) If C < j + b 2r ≤ T the retry call will be
accepted in the system by compressing not only its bandwidth
requirement b 2r but also the bandwidth of all in-service calls.
The compressed bandwidth of the retry call is b ′ 2r = rb′ 2r =
C
j
b ′ ′ 2r where r = C/j, j′ = j + b 2r = nb + b 2r . Similarly,
the bandwidth of all in-service calls will be compressed (by
the same factor) and become b ′ i = C j
b ′ i for i = 1, 2. After the
compression of both the new call and the in-service calls the
state of the system is j = C. The minimum bandwidth that
a call of the 2 nd service-class (either new or in-service) can
tolerate is: b ′ 2r,min = r minb 2r = C T b 2r.
Based on the previous discussion we consider the following
LB equations for calls of the 2 nd service-class:
a) λ 2 P (n − 2 ) = n 2µ 2 φ 2 (n)P (n), (16)
for 1 ≤ nb ≤ C, where n = (n 1 , n 2 , n 2r ), n − 2 = (n 1, n 2 −
1, n 2r ) with n 2 ≥ 1 and
⎧
⎪⎨ 1 , for nb ≤ C, n ∈ Ω
x(n
φ 2 (n) =
− 2 )
x(n)
, for C < nb ≤ T, n ∈ Ω . (17)
⎪⎩
0 , otherwise

MOSCHOLIOS et al.: RETRY LOSS MODELS SUPPORTING ELASTIC TRAFFIC 11
Based on eq. (17) and multiplying both sides of eq. (16)
with b 2 we have:
a 2 b 2 x(n)P (n − 2 ) = n 2b 2 x(n − 2 )P (n), (18)
for 1 ≤ nb ≤ C, where α 2 = λ 2 µ 2 −1 and the values of x(n)
are given by eq. (15).
b) λ 2 P (n − 2r ) = n 2rµ 2r φ 2r (n)P (n), (19)
for C − b 2 + b 2r < nb ≤ T, whereP (n − 2r ) is the probability
distribution of state n − 2r = (n 1, n 2 , n 2r − 1) and
⎧
⎪⎨ 1 , for nb ≤ C, n ∈ Ω
x(n
φ 2r (n) =
− 2r )
x(n)
, for C < nb ≤ T, n ∈ Ω . (20)
⎪⎩
0 , otherwise
Based on eq. (20) and multiplying both sides of eq. (19)
with b 2r we have:
a 2r b 2r x(n)P (n − 2r ) = n 2rb 2r x(n − 2r )P (n), (21)
for C − b 2 + b 2r < nb ≤ T, where α 2r = λ 2r µ −1
2r and the
values of x(n) are given by eq. (15).
Equations (14), (18) and (21) lead to the following system
of equations:
a 1 b 1 x(n)P (n − 1 ) + a 2b 2 x(n)P (n − 2 ) =
for 1≤ nb ≤ C − b 2 + b 2r ,
(n 1 b 1 x(n − 1 ) + n 2b 2 x(n − 2 ))P (n), (22)
a 1 b 1 x(n)P (n − 1 )+a 2b 2 x(n)P (n − 2 )+a 2rb 2r x(n)P (n − 2r )=
(n 1 b 1 x(n − 1 )+n 2b 2 x(n − 2 )+n 2rb 2r x(n − 2r ))P (n), (23)
for C − b 2 + b 2r < nb ≤ C,
a 1 b 1 x(n)P (n − 1 ) + a 2rb 2r x(n)P (n − 2r ) =
(n 1 b 1 x(n − 1 ) + n 2rb 2r x(n − 2r ))P (n) (24)
or C < nb ≤ T.
Equations (22)-(24) can be combined into one equation by
assuming that calls with b 2r are negligible when 1 ≤ nb ≤
C − b 2 + b 2r (MA) and calls with b 2 are negligible when
C < nb ≤ T:
a 1 b 1 x(n)P (n − 1 ) + a 2b 2 γ 2 (nb
nb)x(n)P (n − 2 )+
+a 2r b 2r γ 2r (nb
nb)x(n)P (n − 2r ) =
(n 1 b 1 x(n − 1 ) + n 2b 2 x(n − 2 ) + n 2rb 2r x(n − 2r ))P (n),(25)
where γ 2 (nb
nb) = 1 for 1 ≤ nb ≤ C, otherwise γ 2 (nb
nb) = 0
and γ 2r (nb
nb) = 1 for C − b 2 + b 2r < nb ≤ T, otherwise
γ 2r (nb
nb) = 0.
Note that the approximations introduced in eq. (25) are
similar to those introduced in the single- threshold model of
[18].
Since x(n) = 1, when 0 ≤ nb ≤ C, it is proved in [18]
that:
a 1 b 1 G(j − b 1 ) + a 2 b 2 G(j − b 2 )+
+a 2r b 2r γ 2r (j)G(j − b 2r ) = jG(j), (26)
for 1 ≤ j ≤ C and γ 2r (j) = 1 for C −b 2 +b 2r < j, otherwise
γ 2r (j) = 0.
Toproveeq.(26),theMAisneeded,whichassumesthatthe
population of retry calls of the 2 nd service-class is negligible
in states j ≤ C − b 2 + b 2r .
When C < nb ≤ T and based on eq. (15), eq. (25) can be
written as:
a 1 b 1 P (n − 1 ) + a 2rb 2r γ 2r (nb
nb)P (n − 2r ) = CP (n). (27)
To introduce the link occupancy distribution G(j) in eq.
(27) we sum both sides of eq. (27) over the set of states Ω j =
{n ∈ Ω |nb
= j}:
∑
a 1 b 1 P (n − 1 ) + a 2rb 2r γ 2r (nb
nb) ∑
P (n − 2r ) =
{n|nb
nb=j}
{n|nb
nb=j}
C ∑
P (n). (28)
{n|nb
nb=j}
Since by definition ∑ n∈Ω j
P (n) = G(j), eq. (28) is written
as:
a 1 b 1 G(j − b 1 ) + a 2r b 2r γ 2r (j)G(j − b 2r ) = CG(j), (29)
where γ 2r (j) = 1 for C < j ≤ T.
Thecombinationofeq.(26)andeq.(29)givesthefollowing
approximate recursive formula for the calculation of G(j)’s in
the case of two service-classes when only calls of the 2 nd
service-class have “retry parameters”:
G(j) =
1
min(j,C) [a 1b 1 G(j − b 1 ) + a 2 b 2 γ 2 (j)G(j − b 2 )+
+a 2r b 2r γ 2r (j)G(j − b 2r )] (30)
for 1 ≤ j ≤ T, where γ 2 (j) = 1 for 1 ≤ j ≤ C, otherwise
γ 2 (j) = 0 and γ 2r (j) = 1 for C −b 2 +b 2r < j ≤ T, otherwise
γ 2r (j) = 0.
In the case of K service-classes and assuming that all
service-classes may have “retry parameters”, eq. (30) takes
the general form:
⎧
1 , for j=0
K∑
1 ⎪⎨ min(j,C)
α k b k γ k (j)G(j−b k )+
G(j)=
k=1
, for j=1, . . . , T,
K∑
+ 1
min(j,C)
α kr b kr γ kr (j)G(j−b kr )
⎪⎩
k=1
0 , otherwise
(31)
where γ k (j) = 1 for 1 ≤ j ≤ C, otherwise γ k (j) = 0 and
γ kr (j) = 1 for C − b k + b kr < j ≤ T, otherwise γ kr (j) = 0.
The final CBP of a service-class k, B kr , is the probability
of a call to be blocked with its retry bandwidth requirement:
T∑
B kr = G −1 G(j), (32)
where G = ∑ T
b kr > 0.
j=0
j=T −b kr +1
B. The extended multi-retry loss model
G(j) is the normalization constant and
Similar to the MRM, in the E-MRM a blocked call of
service-class k can have more than one “retry parameters”
(b krl , µ −1
kr l
) for l = 1, . . ., s(k), where b krs(k) < ... <
b kr1 < b k and µ −1
kr s(k)
> ... > µ −1
kr 1
> µ −1
k
. The E-MRM

12 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
Fig. 1. CBP for the 1 st service-class.
Fig. 2. CBP for the 2 nd service-class.
does not have a PFS and therefore the calculation of the
occupancy distribution, G(j), is based on an approximate
recursive formula whose proof is similar to that of eq. (31):
⎧
(
1 ,for j=0
∑ K
1 ⎪⎨
a k b k γ k
(j)G(j−b k )+
min(j,C)
G(j)=
∑
+ K
⎪⎩ k=1
s(k)
∑
l=1
k=1
), for j=1, . . . , T,
a krl b krl γ krl
(j)G(j−b krl )
0 , otherwise
(33)
where: a krl = λ k µ −1
kr l
, γ k (j) = 1 for 1 ≤ j ≤ C, otherwise
γ k (j) = 0 and γ krl (j) = 1, if j > C − (b krl−1 − b krl ),
otherwise γ krl (j) = 0.
ThefinalCBP ofaservice-class k,denotedas B krs(k) ,isthe
probabilityof a call to be blocked with its last retry bandwidth
requirement and is given by:
B krs(k) =
T∑
G −1 G(j), (34)
j=T −b krs(k) +1
where G = ∑ T
j=0 G(j) and b krl > 0 for l = 1, . . ., s(k).
IV. EVALUATION
In this section, we present an application example and
compare the analytical CBP probabilities with those obtained
by simulation. The latter is based on SIMSCRIPT II.5 [20].
Simulation results are mean values of 7 runs with 95%
confidence interval. Since, the resultant reliability ranges of
the measurements are small enough we present only mean
values.
Consider a link of capacity C = 80 b.u. that accommodates
three service-classes of elastic calls which require b 1 = 1
b.u., b 2 = 2 b.u. and b 3 = 6 b.u., respectively. All calls
arrive in the system according to a Poisson process. The
call holding time is exponentially distributed with mean value
µ −1
1 = µ −1
2 = µ −1
3 = 1. The initial values of the offered
traffic-load are: α 1 = 20 erl, α 2 = 6 erl and α 3 = 2 erl.
Fig. 3. CBP for the 3 rd service-class (retry calls with b 3r2 ).
Calls of the 3 rd service-classmay retry two times with reduced
bandwidth requirement: b 3r1 = 5 b.u. and b 3r2 = 4 b.u. and
increased service time so that α 3 b 3 = a 3r1 b 3r1 = a 3r2 b 3r2 . In
the x-axis of all figures, we assume that α 3 remains constant
while α 1 , α 2 increase in steps of 1.0 and 0.5 erl, respectively.
The last value of α 1 = 26 erl while that of α 2 = 9 erl.
We consider three different values of T: a) T = C = 80
b.u., where no bandwidth compression takes place. In that
case,theproposedE-MRMgivesexactlythesameCBP results
with the MRM of [18], b) T = 82 b.u. where bandwidth
compression takes place and r min = C/T = 80/82 and c)
T = 84 b.u. where bandwidth compression takes place and
r min = C/T = 80/84.
In Fig. 1, we present the analytical and simulation CBP
results of the 1 st service-class for all values of T. Similar
results are presented in Fig. 2, for the 2 nd service-class and in
Fig. 3 for the 3 rd service-class (CBP of calls with b 3r2 ). All
figures presented herein show that: i) the model’s accuracy
is absolutely satisfactory compared to simulation and ii) the
increase of T above C results in a CBP decrease due to the

MOSCHOLIOS et al.: RETRY LOSS MODELS SUPPORTING ELASTIC TRAFFIC 13
existence of the compression mechanism.
V. CONCLUSION
We propose multirate loss models that support elastic traffic
under the assumption that Poisson arriving calls have the
ability, when blocked with their initial bandwidthrequirement,
to retry to be connected in the system one (E-SRM) or more
times(E-MRM)withreducedbandwidthandincreasedservice
time requirements. Furthermore, if a retry call is blocked
with its last bandwidth requirement, it can still be accepted
in the system by compressing not only the bandwidth of
all in-service calls (of all service-classes) but also its last
bandwidth requirement. The proposed models do not have
a PFS and therefore we propose approximate but recursive
formulasforthe CBP calculation.Simulation results verifythe
analytical results. As a future work, we will examine multirate
retry loss models that support both elastic and adaptive traffic
(e.g. adaptive video). Adaptive calls can tolerate bandwidth
compression, but their service time cannot be altered.
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of ON-OFF traffic sources with retrials under the complete sharing
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[9] D. Staehle and A. Mäder, “An Analytic Approximation of the Uplink
Capacity in aUMTSNetwork with Heterogeneous Traffic,”in Proc.18th
International Teletraffic Congress (ITC), Berlin, Sep. 2003, pp. 81–90.
[10] M. Głąbowski, M. Stasiak, A. Wiśniewski, and P. Zwierzykowski,
“Blocking Probability Calculation for Cellular Systems with WCDMA
Radio Interface Servicing PCT1 and PCT2 Multirate Traffic,” IEICE
Trans. Commun, vol. E92-B, pp. 1156–1165, Apr. 2009.
[11] A. Washington and H. Perros, “Call blocking probabilities in a trafficgroomed
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pp. 281–294, Jun. 2004.
[12] A. Sahasrabudhe and D. Manjunath, “Performance of optical burst
switched networks: A two moment analysis,” Computer Networks,
vol. 50, no. 18, pp. 3550–3563, Dec. 2006.
[13] J. Vardakas, V. Vassilakis, and M. Logothetis, “Blocking Analysis in Hybrid
TDM-WDM Passive Optical Networks,” in Proc. 5th Int. Working
Conference onPerformance Modelling and Evaluation ofHeterogeneous
Networks (HET-NETs 2008), Karlskrona, Sweden, Feb. 2008.
[14] K. Kuppuswamy and D. Lee, “An analytic approach to efficiently
computing call blocking probabilities for multiclass WDM networks,”
IEEE/ACM Trans. Netw., vol. 17, no. 2, pp. 658–670, Apr. 2009.
[15] J.S.Vardakas, I.D.Moscholios, M.D.Logothetis, andV.G.Stylianakis,
“An Analytical Approach for Dynamic Wavelength Allocation in WDM-
TDMA PONs Servicing ON-OFF Traffic,” IEEE/OSA J. Opt. Commun.
Netw., vol. 3, no. 4, pp. 347–358, Apr. 2011.
[16] K. W. Ross, Multiservice loss models for broadband telecommunication
networks. Springer, Berlin, 1995.
[17] J.S.Kaufman, “Blocking in aCompletely Shared Resource Environment
With State Dependent Resource and Residency Requirements,” in Proc.
IEEE INFOCOM’92, 1992, pp. 2224–2232.
[18] ——, “Blocking with retrials in a completely shared resource environment,”
Journal of Performance Evaluation, vol. 15, no. 2, pp. 99–113,
Jun. 1992.
[19] G. Stamatelos and V. Koukoulidis, “Reservation – Based Bandwidth
Allocation in a Radio ATM Network,” IEEE/ACM Trans. Netw., vol. 5,
no. 3, pp. 420–428, Jun. 1997.
[20] “Simscript II.5,” [online], http://www.simscript.com.
Ioannis D. Moscholios was born in Athens, Greece, in 1976. He received the
Dipl.-Eng. degree in Electrical & Computer Engineering from the University
of Patras, Patras, Greece, in 1999, the M.Sc. degree in Spacecraft Technology
& Satellite Communications from the University College London, UK, in
2000 and the Ph.D. degree in Electrical & Computer Engineering from the
University of Patras, in 2005. From 2005 to 2009 he was aResearch Associate
at the Wire Communications Laboratory, Dept. of Electrical & Computer
Engineering, University of Patras. Currently, he is a Lecturer in the Dept.
of Telecommunications Science and Technology, University of Peloponnese,
Greece. His research interests include simulation and performance analysis of
communication networks. He has published over 65 papers in international
journals/ conferences and has over 120 third-part citations. He is a member
of the Technical Chamber of Greece (TEE).
Vassilios G. Vassilakis was born in Sukhumi, Georgia, in 1978. He received
his Dipl.-Eng. degree in Computer Engineering & Informatics and PhD in
Electrical and Computer Engineering, both from the University of Patras,
Greece, in 2003 and 2011, respectively. Hi is involved in national research
and R&D projects. His main research interests are in the areas of teletraffic
engineering and QoS in wireless networks. He has published over 20 papers
in international journals/ conferences and has over 40 thirs-part citations. He
is a member of the Technical Chamber of Greece (TEE).
John S.Vardakas was born in Alexandria, Greece, in 1979. He received his
Dipl.-Eng. degree in Electrical & Computer Engineering from the Democritus
University of Thrace, Greece, in 2004. Since 2005 he is a Ph.D student at the
Wire Communications Laboratory, Department of Electrical and Computer
Engineering, University of Patras, Greece. His research interests include
teletraffic engineering in optical and wireless networks. He is a member of
the Optical Society of America (OSA) and the Technical Chamber of Greece
(TEE).
Michael D. Logothetis was born in Stenies, Andros, Greece, in 1959. He
received his Dipl.-Eng. degree and Doctorate in Electrical Engineering, both
from the University of Patras, Patras, Greece, in 1981 and 1990, respectively.
From 1982 to 1990, he was a Teaching and Research Assistant at the
Laboratory of Wire Communications, University of Patras, and participated in
many national and EU research programmes, dealing with telecommunication
networks, as well as with office automation. From 1991 to 1992 he was
Research Associate in NTT’s Telecommunication Networks Laboratories,
Tokyo, Japan. Afterwards, he was a Lecturer in the Dept. of Electrical &
Computer Engineering of the University of Patras, and recently he has been
elected Professor in the same Department. His research interests include
teletraffic theory and engineering, traffic/network control, simulation and
performance optimization of telecommunications networks. He has published
over 120 conference/journal papers and has over 220 third-part citations.
He has published a teletraffic book in Greek. He has organised the 5th
International Conference on Communications Systems, Networks and Digital
Signal Processing, CSNDSP 2006. He served/is serving on the Technical
Program Committee of several international conferences while he organizes
and chairs several technical sessions. He has become a Guest Editor in three
journals, while participates in the Editorial Board of journals. He is a member
of theIARIA (Fellow), IEEE(Senior), IEICE,ETRI,FITCEand the Technical
Chamber of Greece (TEE).

14 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
Damming the Torrent: Adjusting BitTorrent-like
Peer-to-Peer Networks to Mobile and Wireless
Environments
Philipp M. Eittenberger, Seungbae Kim, and Udo R. Krieger
Abstract—Mobile peer-to-peer (P2P) traffic is rapidly growing,
but present P2P applications are not specifically designed to
operate under mobile conditions. To assess the performance of
the prevalent file sharing application BitTorrent in a mobile
WiMAX network, we performed a measurement and analysis
campaign. In this study, we use the obtained measurement traces
to further investigate specific characteristics of this P2P network.
In particular, we analyze the distribution of its peer population
under mobile conditions and present a general classification
scheme for peer populations in BitTorrent-like P2P networks.
Further, we propose a simple heuristic to bound the outdegree
of BitTorrent-like P2P systems when operating in mobile
environments.
Index Terms—BitTorrent, P2P, Traffic Analysis, WiMAX.
I. INTRODUCTION
IN recent years P2P networks evolved to the dominant
source of traffic in the Internet [1]. Along with the evolution
of a new generation of wireless networks, like WiMAX and
3GPP LTE, a shift to an increased user mobility can be
witnessed. This development implies that users will have
more and more opportunities to use all their accustomed
applications wherever they are. Hence, mobile P2P traffic
will continue to grow rapidly in the next years (cf. [2]), but
current P2P networks have been designed to operate in wired
networks under stable conditions. Thereby, a growing need for
new traffic models supporting P2P applications in a mobile
environment and redesigned, mobility aware P2P protocols is
emerging.
Kim et al. [3] conducted several measurements in Korea
Telecom’s WiMAX network in Seoul, Korea, to investigate
the behavior of BitTorrent, one of the most popular P2P
file sharing networks under true mobile conditions. For this
purpose several measurements have been carried out while
driving by bus and by subway through Seoul at several days.
At each single measurement, a popular torrent with video
content has been chosen for download and all the packet
headers of the whole transmission have been captured. To
allow comparison, the same files have been downloaded under
static conditions in the WiMAX network and exemplary with
Manuscript received April 3, 2011.
Ph. M. Eittenberger and U. R. Krieger are with the Faculty of Information
Systems and Applied Computer Science, Otto-Friedrich University, Bamberg,
Germany (e-mail: philipp.eittenberger@uni-bamberg.de).
S. Kim was with the School of Computer Science and Engineering, Seoul
National University, Seoul, Korea. He is now with the Future Communications
Team, KAIST Institute for Information Technology Convergence, Daejeon,
Korea (e-mail: sbkim@itc.kaist.ac.kr).
a host in a campus network connected to the Internet by
an Ethernet link. In a WiMAX network disruptions occur
during hand-overs and the wireless link conditions fluctuate
due to signal fading. The main purpose of the measurement
campaign was to investigate the impact of mobile conditions
on the behavior of BitTorrent. In this paper we are extending
our previous results presented at the 1st European Teletraffic
Seminar (ETS2011) [4].
The outline of the paper is as follows. We start with a
discussion of related work in Section II. An introduction to
the BitTorrent network, its operational behavior and a presentation
of our measurement methodology follow in Section
III. Subsequently, we present a classification scheme for peer
populations in BitTorrent-like P2P systems and report the
results of our analysis in Section IV. We use our insights into
the BitTorrent peer population to propose a simple heuristic
to limit the number of open connections in Section V. Finally,
we conclude the paper with additional implications for the
adaption of BitTorrent-like systems to wireless networks.
II. RELATED WORK
Recently, several analytical models have been proposed to
yield a deeper understanding of the P2P data dissemination
among peers (e.g. [5] or [6]). Analytical models can provide
precious insights, but are typically based on unrealistic assumptions,
like global system knowledge. Therefore, we performed
a measurement campaign, to reveal the actual system
characteristics of the complex dissemination network of Bit-
Torrent and to yield novel insights, which can be incorporated
into new analytical models. Sen and Wang [7] performed a
large measurement campaign to analyze different P2P file
sharing networks. In their paper they tried to characterize
the peers of a particular mesh-pull P2P file sharing network.
To examine their distribution, they plotted the traffic volume,
duration of on-time and number of connections of the top 10
% of the investigated peer population on a log-log scale. From
the plot they concluded that the distribution is heavy-tailed, but
does not follow a power law. Subsequently, they concluded
“that P2P traffic does not obey power laws”. Despite the fact
that there can be found numerous other measurement studies
concerning the BitTorrent network (cf. [8] or [9] among many
others), the first study, which analyzed the performance of
such a file sharing network in a WiMAX environment under
true mobile conditions, was performed by Kim et al. [3]. In
this paper, we use the data traces obtained by Kim et al. to

EITTENBERGER et al.: DAMMING THE TORRENT 15
reveal deeper insights into the complex dissemination network
of BitTorrent. We investigate the data access patterns between
a single peer and the remote peer population, and show that
in this environment certain parts of the peer population can be
modeled by a power law distribution.
III. BITTORRENT
As already mentioned, BitTorrent is one of the most popular
P2P file sharing networks and itself a major source of the
Internet traffic nowadays. The protocol specification is publicly
available on the BitTorrent website [10]. Several distinct client
applications, which implement the protocol, are available.
Despite the fact that they differ in particular implementation
details, they are able to exchange data with each other.
BitTorrent is a representative of a mesh-pull P2P network, it
builds an overlay on top of the transport network based on a
mesh topology and the data dissemination is realized by a pull
mechanism, i.e. on request. To enable fast data dissemination,
BitTorrent uses the so called swarming technique, where each
shared file is divided into smaller parts, called chunks, and
then transmitted to (respectively received from) a multitude of
peers (the swarm).
A. BitTorrent Operations in Detail
A torrent is the set of peers collaborating to share a single
file. A peer can be in two different states, if the peer possesses
already the complete file and uploads it to other peers, then it is
called seeder. Otherwise, if it is still in the downloading phase,
it is called leecher. To join a torrent, a peer needs some metainformation
about it. This information is provided by a torrent
file, containing all the information necessary to download the
content, e.g. the number of chunks, hashes to verify their
correctness, the IP of the tracker server etc. Typically this
torrent file is retrieved from a website. Upon reception the
peer contacts the tracker server in the bootstrapping process,
which provides an initial list of the latest remote peers. The
peers of a torrent exchange messages to indicate the chunks
that they already possess.
Two vital optimization problems have to be solved to achieve a
high data throughput in a mesh-pull P2P network. At first, the
choice which pieces should be requested from other peers, and
subsequently, the selection which peers should be contacted for
the data. BitTorrent addresses the first problem with a rarestfirst
algorithm, i.e. each peer maintains a list of pieces, that
each of the remote peers has and builds an index of the pieces
with the least number of copies. The rarest pieces are then
requested from the remote peers. However, when a download
is almost completed, the peer does not use the rarest-first
algorithm; instead it sends requests for all of its missing pieces
to all of its remote peers to increase the throughput. This is
called end-game mode. The peer selection strategy is handled
by the so called choking algorithm. To encourage peers to
contribute their resources for the data dissemination, a tit-fortat
mechanism is implemented to impede free-riding, i.e. peers
not contributing data to the network should not be able to
achieve high download rates. Instead, this choking algorithm
provides sharing incentives by rewarding peers who contribute
data to the system. The algorithm determines the selection of
peers to exchange data with. Peers that upload data at high
rates are preferred. Once per choking period, usually every
ten seconds, a peer evaluates the transmission rates from all
the connected peers and selects a fixed number of the fastest
ones, depending on its upload capacity. It will only upload
data to these unchoked peers in this period. Data requests
from other peers are denied in this period, i.e. those peers
are choked. Another important part of the algorithm is the
optimistic unchoking behavior: every 30 seconds one peer is
randomly chosen and will be unchoked. This is meant to
explore new peers with even higher upload capacities and
as a side effect ensures data dissemination to low-capacity
peers. Once a leecher has finished the download and enters
the seeding state, it follows a different unchoke strategy. In
most of the implementations peers in seed state unchoke peers
with the highest download capacity to optimize the general
dissemination performance of the network and to maintain
high upload utilization.
B. Measurement of BitTorrent in a WiMax Network
The analyzed measurement traces have been captured in
March, 2010 in Seoul, Korea and were firstly presented in [3].
The measurements have been carried out on four different days
in parallel, i.e. on each day all the measurement runs started
at the same time, in four different scenarios, three WiMax
settings and one in a Ethernet environment. The throughput
of the WiMax network ranges from 30 to 50 Mbps, and a
base station typically covers a radius between 1 and 5 km.
Three laptops equipped with WiMax USB dongles where
used for the WiMax measurements and one desktop computer
for the reference Ethernet measurement. Vuze [11] was used
as the BitTorrent client in all measurement runs. For the
measurement some popular sitcoms served as torrents, which
had at least 300 seeds, with a file size ranging from 300 to 400
MB. An important fact to note is the over-provisioning with
seeding capacity in the measurement runs to ensure a high
data throughput. Of course, on each day the same torrent was
chosen to download in all four different settings. One WiMax
measurement was conducted stationary, i.e. the measurement
peer was located statically about 800 meters away from its
base station. Therefore, the signal strength was stable, but
not strong. For the next scenario one peer traveled about 12
km in a subway train through Seoul while conducting the
measurement. The duration was about 20 minutes. In the last
WiMax scenario the peer took a bus ride through Seoul, which
lasted about 30 minutes and the distance of the route was about
11 km. In both mobile scenarios the link quality fluctuated
highly and it even occurred that the WiMax connection was
completely lost due to hand-overs in between the base stations,
and thereby, the peer got a new IP address in some of the
measurement runs. An Ethernet measurement in a 100 Mbps
LAN was conducted on the university campus as a reference
to allow comparison. For a more detailed description, we refer
to Kim et al.’s study [3]. The main results of this study will
be also presented shortly. The WiMax peers suffer from poor
connectivity, the connections to the peers are less stable and

16 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
the connection duration is shorter as opposed to the reference
Ethernet measurement. In all WiMax settings the duration of
the file download took 4 to 5 times longer than in the Ethernet
measurement. The signaling traffic has been increased in all
WiMax measurements by a factor of 100 %. The mean of the
average download rates in the WiMax measurements ranges
from roughly 240 to 400 Kbps, as opposed to a mean of
1930 Kbps in the Ethernet runs. One reason for the poor
performance of BitTorrent in the WiMax network is certainly
the fluctuating signal strength, but the hand-overs in the mobile
measurements have a negative impact on the performance of
TCP transmissions too.
IV. CLASSIFICATION OF THE PEER POPULATION
A peer in a mesh-pull P2P network is typically connected
to more than a thousand different peers in just tens of
minutes. Hence, it is vital for the understanding of the inherent
hierarchical structure of a mesh-pull topology to explore the
preference relationship among the peer population. We have
shown in our previous work (cf. [12]) that it is possible to
classify the peer population of P2P streaming networks. In
this study we investigate the aggregated conversation model
of superimposed flows in inbound and outbound direction to
a home peer, i.e. the traffic volume generated by the superimposed
flows from and to the distinct feeder peers p i of the
dissemination flow graph G V . To clarify our terminology, we
regard a conversation as bidirectional data exchange between
two endpoints, in this case peers. A flow represents the directed
data transfer, which can be identified by the traffic direction,
the IPs of both peers, the port numbers of the used transport
protocol and a given time-out value to differentiate widely
disparate flows. A stream φ represents the aggregated set of
flows sent from one peer to another.
Using the captured data traces, it allows us to describe the
exchange of chunk sequences among the peers by appropriate
teletraffic models. We use the amount of exchanged traffic,
i.e. received and sent bytes, in all streams as a metric for
the further classification of the peer population. Since we are
interested in the contribution of each peer and the variance
among different peers’ contribution, it is a convenient choice
to rank all peers according to their contribution and then
identify those with high contributions. Therefore, we sort
each stream by the number of transferred bytes in descending
order. If we arrange the streams φ(p i , p j ) according to their
number of exchanged bytes on a log-log scale, where p j is
representing the home peer, i.e. the measurement host, and
p i , i ∈ {1, ...., n}, denotes the feeding peer population, we
can realize a hierarchy of the peer population. To clarify our
concept, we use the WiMax bus trace of March, 17 as an
example. By using the rank ordering technique, we plotted the
distribution of the incoming streams in Fig. 1. Several distinct
regions can be spotted in this distribution. The profitable
region consists of the top peers and it’s body resembles in
all captured WiMAX traces asymptotically a straight line. In
this example, the region ranges roughly from 4,000,000 bytes
to 10,000,000 bytes. The upper limit of this region is given
by the file size or for streaming P2P networks by the session
length. Top peers contribute the largest share of the total data
volume, i.e. most of the data is received in conversations with
these peers. In the exemplary trace this region consists of 29
peers, which sent 47.80 % of the total data volume.
The next region, ranging from 20,000 bytes to 4,000,000 bytes,
is called the productive region, because it is likely that the
streams do not only consist of signaling overhead, but also of
useful data. This means, that chunks have been transferred,
but the ratio of signaling overhead is worse than before.
This region is built by ordinary peers. In this trace the 129
ordinary peers sent 52.03 % of the total data volume. Thus,
99.84 % of the total data volume has been transferred by the
158 peers of the profitable and productive region. All other
streams below this region can be regarded as almost useless
for the operations of the P2P network due to their minimal
contribution towards the volume of useful data. They consist
mainly of signaling overhead, e.g. connection establishment
and maintenance. Hence, we call the next region unproductive,
which is inhabited by futile peers. The horizontal lines at the
end of this region mainly consist of unsuccessful connection
attempts. Out of the 2060 incoming streams 1902 streams lie in
the unproductive region. To investigate this inefficiency more
thoroughly, we visualize the intensity of the incoming streams,
i.e. the amount of bytes per 10 second intervals, with the help
of traffic analyzer Atheris [13] (see Fig. 3). The effects of the
hand-overs are clearly visible, precisely when the intensity
of the incoming streams tends towards zero. Also, due to
the end-game mode, at the end of the trace, the intensity
increases dramatically. When we visualize only the streams
of the unproductive region, see Fig. 4, one realizes that the
incoming streams of the unproductive region continue over
the whole trace. This is not a big problem, when BitTorrent
is operating in a wired environment, like Ethernet, but in a
WiMax scenario this can be a high burden for wireless access
points, especially when multiple clients use simultaneously a
BitTorrent-like application. For the adaption of the BitTorrent
protocol to a wireless environment, we recommend to intensify
the data exchange with peers in the profitable region and
restrict it to peers in the productive region, and thereby,
avoiding the many useless connections in the unproductive
region.
So far, we have explained our observations by one representative
trace, but to allow a comparison, we have additionally
plotted the distributions of the inbound and outbound streams
in all the gathered traces, see Fig. 5 and 6. Apart from the
Ethernet measurement on March 16, the bodies of all the
data access distributions have the same shape on the loglog
scale. We see very clearly the influence of the choking
algorithm on the head of the distributions in all Ethernet
measurements, but also in the outbound traffic distribution of
the WiMax traces. Very few peers, between three and six,
receive by far the biggest share of the data. Additionally, in the
Ethernet scenario only a few peers sent most of the data to the
measurement host. However, this pattern changes in all WiMax
traces and the head of the inbound data distribution becomes
flat. This implies that the received data volume is more evenly
distributed among the peer population. This change is due to
the limited upload capacity of the WiMax peers. They are

EITTENBERGER et al.: DAMMING THE TORRENT 17
Fig. 1. Inbound data distribution (bus trace of March, 17).
Fig. 2.
17).
Inbound data distribution in the profitable region (bus trace of March,
Fig. 3. Intensity of the complete inbound traffic (Bus trace of March, 17).
Fig. 4. Intensity of the inbound traffic in the unproductive region (Bus trace
of March, 17).
choked more often and rely mainly on the optimistic unchoke
behavior, in order to successfully complete their download.
Thereby, the download performance suffers in all WiMax
scenarios. We interpret the number of transferred bytes of
a stream φ(p i , p j ) as realization x i of an equivalent income
X i ∈ R of the home peer p j . Considering the overhead for
establishing and maintaining the connection to the feeded peer
p j as costs, only the connections with top peers are really
profitable. Thus, the main focus of interest is given by the
distribution of the top peers. Since the feeding peer population
of this region contributes the largest proportion (approx. 50
% in the exemplary bus trace of March, 17) of useful data
with the best signaling overhead ratio. The asymptotic straight
line of the profitable region on the log-log scale (see Fig. 2)
indicates that the head of the distribution follows a power law.
Thereby, we can use a generalized Pareto distribution to model
this region of the peer population with a random variable
X and its sample {x 1 , ..., x n }. We denote the distribution
function of this generalized Pareto model by
F (x) = 1 − (1 + k x − µ
σ )−1/k for k ≠ 0,
with µ ≤ x ≤ µ−σ/k for k < 0. To investigate the distribution
of the top peers, we set the minimum x min to the lower bound
of the profitable region, i.e. x min = 3, 981, 064 bytes. x min is
obtained with Clauset’s estimator (cf. [14]), which chooses
the value of ˆx min such that the probability distribution of
the measured data and the best-fit power law model is as
similar as possible above ˆx min . Hereby, we consider only the
flows from the top peers φ(p i , p j ), with p i , i ∈ {1, ...., n}
and n = 29, feeding the home peer p j . Using the transferred
amount of bytes x 1 ≤ x 2 ... ≤ x n , we can determine the
scaling parameter ˆα = 4.281707 by Newman’s estimate [15]
[ n
] −1
∑ x i
ˆα ≃ 1 + n ln
x min − 1 .
2
i=1
It is obvious that the Pareto model can only be applied for
the profitable region, since the distribution of the peers in the
productive region is not a straight line on the log-log plot,

18 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
Fig. 5.
Inbound data access distribution.
Fig. 6.
Outbound data access distribution.
but has a flat head and a steep tail. Such a rank distribution
indicates a Weibull distribution. The cumulative distribution
function (cdf) for the Weibull distribution is given by
F (x) = 1 − e −(xα)k for x ≥ 0,
where α is the scale parameter and k the shape parameter. Both
parameters are constant and in the analyzed trace α = 2259901
and k = 1.015688. To get the parameters, we used the maximum
likelihood estimation method. Since the shape parameter
k is close to 1, the increase of the data volume per peer
over time is fairly constant. Fig. 10 shows the cumulative
distribution function (cdf) of the received data volumes in
this region and the dotted lines show the fitted Pareto model.
Fig. 7-9 underline our observation, they show the empirical
cumulative distribution function (ecdf) of all other traces and
the fit to the Weibull distribution. The according parameters
for the fitted Weibull distribution are presented in Table I.
As a goodness-of-fit metric we use the Kolmogorov-Smirnov
test, which is the largest vertical distance between the fitted
and actual cumulative distribution functions, measured in
percentiles. For the bus trace we obtain a P-value of 0.9134 for
the Pareto model fit of the profitable region and a P-value of
0.9563 for the fitting of the productive region to the Weibull
distribution and regarding a significance level of α = 0.01
in both cases the null hypothesis can not be rejected. This
constitutes a strong indication that the observed sample data
obey a generalized Pareto respectively a Weibull distribution.
Regarding the distribution of the peers in the profitable and
productive region, the same observations can be made in all
the other captured WiMAX traces (cf. Table I regarding the
fit to the Weibull distribution).
V. CUTTING CONNECTIONS
Jelasity et al. [16] have shown how BitTorrent causes noticeable
problems through the sheer number of flows with ordinary
network equipment, i.e. normal Cisco routers. Wireless access
points have even less resources and when more and more
users start to use their accustomed applications in mobile
networks, the wireless infrastructure might encounter problems
tackling the quantity of flows caused by such P2P applications.
Therefore, we propose a small protocol adaption to prevent
overloading the wireless network infrastructure without
sacrificing performance. Inspired by Clauset’s estimator we
developed a simple heuristic to limit the open connections
of P2P clients when operating under mobile conditions. The
proposed Algorithm 1 can be used to limit the number of
contributing peers and thereby, reduce the load on the wireless
infrastructure, since the distribution of the top peers is quite
stable in all traces. Only very few peers enter respectively
leave this region after the process has stabilized, quite often
the ranking order of the top peers does not even change after
stabilization. We use again the Bus trace of March, 17 to
describe the idea of the proposed algorithm. Fig. 11 shows
the inbound data distribution at different points in time. When
the process is stable and shows a good fit to the Weibull
distribution, in this exemplary case after two minutes, we use
Clauset’s estimator to determine the cutting point (red line).
The cutting point identifies x min of the Pareto model and
the lowest part of the profitable region. Since the peer gets
most of the data from peers of this region, it is appropriate
to restrict data requests to such top peers without loosing too
much performance.
The algorithm needs initially only a vector with the amount
of contributed data volume of each peer and a threshold.

EITTENBERGER et al.: DAMMING THE TORRENT 19
TABLE I
WEIBULL FITTING PARAMETERS OF THE CAPTURED TRACES, ALONG WITH THE CORRESPONDING P-VALUES.
Trace n x min k α p
Bus trace
Static trace
Subway trace
15.03.2010 152 20000 1.009601 2,409,848 0.7195
16.03.2010 188 10000 1.111717 2,029,553 0.7479
17.03.2010 158 20000 1.015688 2,259,901 0.9563
18.03.2010 368 20000 0.9513743 1,431,563 0.7307
15.03.2010 137 100000 1.421969 2,812,421 0.9331
16.03.2010 105 100000 1.543955 3,752,800 0.7834
17.03.2010 110 100000 1.474172 3,539,219 0.8111
18.03.2010 195 100000 1.411851 2,983,383 0.8527
15.03.2010 166 300000 1.414346 2,235,072 0.63
16.03.2010 106 200000 1.608155 3,692,439 0.695
17.03.2010 205 20000 1.025806 1,746,502 0.9538
18.03.2010 200 200000 1.274519 2,823,105 0.8357
Fig. 7.
Ecdf of the inbound data distribution and the Weibull model fit (Bus traces).
Fig. 8.
Ecdf of the inbound data distribution and the Weibull model fit (Static traces).
Fig. 9.
Ecdf of the inbound data distribution and the Weibull model fit (Subway traces).

20 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
Fig. 10.
Cdf of the inbound data distribution in the profitable region.
Fig. 11. Inbound data distribution (bus trace of March, 17) with the cutting
points of Clauset’s estimator (red line).
The threshold determines the minimal data contribution of
a peer needed to be considered. The pseudo code is given
in Algorithm 1. The limit function returns a new vector
containing all values greater or equal the given threshold. The
algorithm estimates the scaling parameter α using maximumlikelihood
estimation and computes the Kolmogorov-Smirnov
distance D. The point where the measured data and the bestfit
power law model is as similar as possible, i.e. the distance
D is minimal, determines x min . When x min is computed,
a list of all peers with a greater or equal contribution is
returned. Subsequently, data requests should be restricted to
these peers. Thereby, the amount of open connections is
limited without loosing too much performance. The proposed
algorithm is scalable, since no global knowledge is required
and the computational overhead is manageable. However, the
main field of application is tied to environments with sufficient
seeding capacity. In the opposite case other measures are
needed but we leave this open to future work.
VI. CONCLUSION
To the best of our knowledge, this is the first study which
investigates the data access patterns of BitTorrent and tries to
fit the distribution of the feeding peer population to a model.
In our work we have additionally introduced a novel scheme
to classify the peer population of BitTorrent-like P2P networks
into different categories. We have shown that there are strong
indications that a particular part of the peer population obeys
a power law and that its distribution can be modeled by a
generalized Pareto model. Furthermore, when we investigated
the data distribution of the productive region, we found strong
indications that the part of the peer population, which contributes
nearly the complete data volume, can be modeled by
a Weibull distribution. The limitation of this study is the single
point of view regarding the measurements, but in future work
we plan to support our results with a distributed measurement
campaign. We have seen that the BitTorrent protocol and
especially the choking algorithm is not well adapted to the
fluctuating conditions in a WiMax environment. Therefore,
we propose following recommendations for the adaption of
BitTorrent-like systems to wireless networks. A very simple
part of the solution could be using another client instead of
Vuze. Iliofotou et al. [17] have shown that µTorrent achieves
on average a 16 % better download performance compared to
Vuze. One reason for the better performance might be the
limitation of the amount of open connections to peers by
µTorrent. In general, this might also be a good recommendation
in wireless scenarios, and thereby, not to overload the
base stations with too many open connections. To address this
problem we have developed a simple heuristic to restrict the
number of open connections. Another proposition would be
the usage of UDP instead of TCP as a transport protocol,
since especially TCP, as a connection oriented protocol, suffers
from the fluctuating link conditions and by the hand-overs
in a mobile wireless scenario. Finally, Lehrieder et al. [18]
investigated the positive effect of caches in a BitTorrent
network. As recommendation for network operators, supplying
a dedicated infrastructure with local caches to support the data
dissemination of BitTorrent-like networks can dramatically increase
the data throughput, but at the same time reduce the load
on the own infrastructure by reducing inter-domain traffic. This
proposal is very important with regard to the limited upload
capacity in a WiMax network, since the choking algorithm
is not well adapted to conditions of wireless networks and
the peers rely heavily on the optimistic unchoking behavior
to complete their download. Therefore, supplying a dedicated

EITTENBERGER et al.: DAMMING THE TORRENT 21
Algorithm 1 Cutting point algorithm
Require: ⃗x, x thres
Ensure: Process is stable.
sort(⃗x)
⃗y = ⃗x
⃗x = limit(x thres , ⃗x)
unique(⃗x)
n = size_of(⃗x)
for i = 1 to n do
x min = ⃗x i
⃗y = limit(x min , ⃗y)
o = size_of(⃗y)
/* Estimate α using MLE */
α = o/( ∑ o
l=1 (log( ⃗y l
x min
)))
/* Compute the KS-distance */
for j = 1 to o do
⃗z j = j/o
end for
for k = 1 to o do
⃗v k = 1 − ( xmin
⃗y k
) α
end for
⃗r i = max(abs(⃗v − ⃗z))
end for
/* Determine the minimal distance */
D = min(⃗r)
p = get_position(D, ⃗r)
x min = ⃗x p
return list of peers which sent more than x min bytes
infrastructure with local caches could foster the dissemination
performance of BitTorrent-like systems in wireless networks.
[6] G. Dán and N. Carlsson, “Dynamic Swarm Management for Improved
BitTorrent Performance,” in Proc. International Workshop on Peer-to-
Peer Systems (IPTPS ’09), 2009.
[7] S. Sen and J. Wang, “Analyzing peer-to-peer traffic across large networks,”
IEEE/ACM Transactions on Networking, vol. 12, no. 2, pp.
219–232, 2004.
[8] L. Guo, S. Chen, Z. Xiao, E. Tan, X. Ding, and X. Zhang, “Measurements,
analysis, and modeling of BitTorrent-like systems,” in IMC
’05: Proceedings of the 5th ACM SIGCOMM conference on Internet
Measurement. USENIX Association, 2005, pp. 35–48.
[9] A. R. Bharambe, C. Herley, and V. N. Padmanabhan, “Analyzing and
improving a BitTorrent networks performance mechanisms,” in 25th
IEEE International Conference on Computer Communications (INFO-
COM 2006). IEEE, 2006, pp. 1–12.
[10] Bittorrent. [Online]. Available: http://www.bittorrent.org/beps/bep_0003.
html
[11] Vuze. [Online]. Available: http://www.vuze.com/
[12] N. M. Markovich, A. Biernacki, P. M. Eittenberger, and U. R.
Krieger, “Integrated measurement and analysis of peer-to-peer traffic,” in
Wired/Wireless Internet Communications, 8th International Conference.
Springer, 2010, pp. 302–314.
[13] P. M. Eittenberger and U. Krieger, “Atheris: A first step towards a
unified peer-to-peer traffic measurement framework,” in 19th Euromicro
International Conference on Parallel, Distributed and Network-Based
Computing (PDP 2011). Euromicro, 2011.
[14] A. Clauset, C. R. Shalizi, and M. E. J. Newman, “Power-law distributions
in empirical data,” SIAM Reviews, 2007.
[15] M. E. J. Newman, “Power laws, pareto distributions and zipf’s law,”
Contemporary Physics, vol. 46, pp. 323–351, 2005.
[16] M. Jelasity, V. Bilicki, and M. Kasza, “Modeling network-level impacts
of p2p flows,” in 19th Euromicro International Conference on Parallel,
Distributed and Network-Based Computing (PDP 2011). Euromicro,
2011.
[17] M. Iliofotou, G. Siganos, X. Yang, and P. Rodriguez, “Comparing bittorrent
clients in the wild: the case of download speed,” in Proceedings
of the 9th international conference on Peer-to-peer systems(IPTPS’10).
USENIX Association, 2010.
[18] F. Lehrieder, G. Dán, T. Hoßfeld, S. Oechsner, and V. Singeorzan, “The
Impact of Caching on BitTorrent-like Peer-to-peer Systems,” in 10th
IEEE International Conference on Peer-to-Peer Computing 2010 - IEEE
P2P 2010, 2010, pp. 69–78.
ACKNOWLEDGMENT
The authors at Otto-Friedrich University acknowledge the
partial financial suppport by the ESF project COST IC0703.
REFERENCES
[1] Cisco Systems, “Cisco visual networking index: Forecast and methodology,
2009-2014,” White Paper, 2010.
[2] ——, “Cisco visual networking index: Global mobile data traffic forecast
update, 2009-2014,” White Paper, 2010.
[3] S. Kim, X. Wang, H. Kim, T. T. Kwon, and Y. Choi, “Measurement
and analysis of BitTorrent traffic in mobile WiMAX networks,” in 10th
IEEE International Conference on Peer-to-Peer Computing 2010 - IEEE
P2P 2010. IEEE, 2010, pp. 49–52.
[4] P. M. Eittenberger, U. Krieger, and S. Kim, “A classification scheme
for the peer population of bittorrent-like peer-to-peer networks.” in The
First European Teletraffic Seminar (ETS 2011), 2011.
[5] D. Qiu and R. Srikant, “Modeling and performance analysis of
bittorrent-like peer-to-peer networks,” in Proceedings of the 2004 conference
on Applications, technologies, architectures, and protocols for
computer communications (SIGCOMM ’04). ACM, 2004, pp. 367–378.
Philipp Eittenberger received the Diploma degree in information systems
from the Otto-Friedrich University, Bamberg, Germany, in 2010.
He is currently a Ph.D. candidate at the Communication Services, Telecommunication
Systems, and Computer Networks Group, Otto-Friedrich University,
Bamberg, Germany. His research areas include Internet traffic measurement
and analysis and peer-to-peer networks.
Seungbae Kim received the B.S. degree in computer science and engineering
from the Chung-Ang University, Seoul, Korea, in 2009, the M.S. degree in
computer science and engineering from Seoul National University, Seoul,
Korea, in 2011.
He is currently a research engineer at the Future Communications Team,
KAIST Institute for Information Technology Convergence, Daejeon, Korea.
His recent research areas include Internet traffic measurement and analysis,
peer-to-peer networks and content distribution networks.

22 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
Udo Krieger received the M.S. degree in applied mathematics and the
Ph.D. degree in computer science from the Technische Hochschule Darmstadt,
Germany.
In 1985 he joined the Research and Technology Center of Deutsche Telekom,
now called T-Nova Technology Center, in Darmstadt, Germany. He joined the
Otto-Friedrich-University, Bamberg, Germany in 2003, where he is currently
an associate professor. Udo Krieger has participated in the European research
projects COST 257, COST 279, COST IC0703 and EURESCOM P1112 and
has served on numerous technical program committees of ITC and IEEE
conferences including Infocom’98 and the European Conference on Universal
Multiservice Networks 2000. Currently, he serves on the editorial board of the
journal Computer Networks. His research interests include traffic management
of IP and wireless networks, teletraffic theory, and numerical solution methods
for Markov chains. He is a member of Gesellschaft fuer Informatik, Germany,
and IEEE.

ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011 23
Analysis of OBS Burst Assembly Queue with
Renewal Input
Tomasz Hołyński and Muhammad Faisal Hayat
Abstract—Ongoing research in Optical Burst Switching (OBS)
requires more in-depth studies both in theory and in practice
before the technology is realized. In OBS paradigm, traffic from
access networks is groomed at edge OBS nodes in the forms
of large chunks called bursts. This grooming called assembly is
crucial in analyzing the overall performance of OBS networks
as it affects the design of almost all major functions of OBS
nodes. The characteristics of assembled traffic and its effects
on OBS performance have been already extensively studied in
literature. In this work, the assembled traffic is studied using a
transform-based approach, since it is a natural way of analyzing
such processes where random variables are summed. The main
contribution of this paper is formulation of distributions of
burst length and burst inter-departure time in form of Laplace
transforms, which are valid for general independent lengths and
inter-arrival times of assembled packets. The results can be
subsequently inverted analytically or numerically to give full
densities or serve as moment generating functions for partial
characteristics. A simple method for the distribution of the
number of packets in a burst based on discrete Markov chain is
provided. Detailed analytical derivations with numerical results
are presented for Erlangian traffic and verified by simulations
to show good exactness of this approach.
Index Terms—Optical burst switching, burst assembly, hybrid
assembly, performance modelling, queueing theory, Laplace
transform
I. INTRODUCTION
THERE is an ever increasing demand for transmission
capacity due to increased popularity of new applications
requiring large amounts of data exchange. Dense wavelength
division multiplexing (DWDM) has promised to cater the
needs of future Internet backbones providing huge bandwidth
capacities. From the first generation of optical networks with
point to point connections, through the second generation with
DWDM ring networks, now we are heading towards the third
generation with flexible mesh topologies. Therefore, optical
networks demand a real change in transfer mode of data as the
established packet switching is not realizable in optical domain
in the near future with the current state of technology. Optical
circuit switching in the form of wavelength-routed networks
also cannot provide scalability required to achieve real flexible
mesh networks.
Optical burst switching has been proposed as a new
paradigm a few years back [1] in attempts to pave the
way for an all-optical backbone switching infrastructure. It
incorporates prospects of both coarse-grained optical circuit
switching and fine-grained optical packet switching and is
T. Hołyński and M.F. Hayat are with the Institute of Telecommunications,
Vienna University of Technology, Vienna, Austria, e-mail: {tomasz.holynski,
muhammad.faisal.hayat}@tuwien.ac.at
considered as implementable solution for future all-optical
networks.
Principles of OBS can be briefly summarized as follows.
The network is divided into two functional domains, the edge
and the core. At the edge, packetized traffic is buffered and
assembled into bursts consisting of many packets. As soon as a
burst is assembled, it is placed into a transmission queue and a
burst control packet is sent out of band over the network along
the path determined by a routing protocol. The burst control
packet configures switching connections in core nodes just for
the time of transmission of the incoming burst. Subsequently,
the burst is transmitted over the core without any nodal delays
and electronic conversion until it reaches an egress node where
disassembly finally takes place. Due to possibility of time
contention among different flows, bursts can be lost at the
core nodes.
The process of assembly results in a modified type of traffic,
a good understanding of which is crucial in practical engineering
of OBS networks as it affects many design parameters and
functions of OBS nodes at both edge and core [2], [3], [4].
From the viewpoint of performance evaluation, characteristics
of this traffic are the main input parameters for the theoretical
analysis of core switches (burst losses, optimization of fiber
delay lines). Therefore, it is important to dispose with at least
approximations of probability distributions of time intervals
between bursts and burst length. In a predominant number
of studies on OBS core (e.g. [5], [6], [7], [8], [9]) these
distributions are assumed to be negative exponential. While
this is true for the inter-burst times, due to superposition of
many independent flows, it is rather unrealistic when burst
length is considered.
Since OBS is still in a pre-deployment phase, one does not
know how large on average bursts should be and what degree
of variability in their length can be tolerated in practice. Long
bursts require more time to be assembled which results in
greater delays for single packets. Moreover, they will certainly
suffer higher losses and degrade performance of the upper
layers due to the need of reordering of the packets delivered
out of sequence [10]. On the other hand, shorter bursts,
generated at higher rate, will cause more control traffic and
unnecessarily load the network.
The analytical tools that can be used to analyze assembly
process are queueing theory, renewal theory or some complex
models which can be evaluated numerically. Analyzing the
assembly process with queueing theoretical approaches is not
straightforward as it does not fall under classical queueing
discipline. It is because an OBS assembly queue is not strictly
a queueing system with a server but it acts rather like a delay

24 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
element without a server and passes accumulated customers in
a batched manner when some criterion is met. Such behavior
may have an analogy but it is not completely mappable to
the batch service nor to gated vacation models. Therefore, we
devise a simple probabilistic technique based on observation of
the development of assembly of a single burst and determine
probabilities that the n-th packet will complete the burst.
Subsequently, referring to the trends from classical queueing
literature, for the distributions of interest we formulate the
solutions in the form of transforms.
Previous studies in this regard have analyzed the assembly
process in detail, with focus on the characteristics of assembled
burst lengths [11], [12], [13], the burst inter-departure
times [14], [13], its impact on different aspects of global
network performance, such as link-utilization and blocking
probability at intermediate nodes [3], [4], or a combination of
some of these aspects. However, to the best of our knowledge,
there is no study which have tried to analyzed this burstification
process with transform-based approach and general input
traffic conditions and only a few studies have paid attention to
the distribution of number of packets in burst and actual delay
distribution experienced by the packets especially for the most
favorite hybrid burst assembly. For example, Zapata et al. [15]
analyzed packet delays but only for non-hybrid mechanisms
and only average and maximum delays have been evaluated
but no other metrics, such as the variance, nor the actual delay
distribution. Rodrigo de Vega et al. [16] also analyzed the
packet delays and compute the delay of the first packet in the
burst, which is upper bound for a packet in burst but do not
mention the delay suffered by other packets in that burst and
they have also not extended their analysis for hybrid assembly.
Hernandez [17] used fixed packet lengths and Poisson arrivals
to find out delay distribution of each packet in a burst. To
our best knowledge, there is no study on the mentioned
probability distributions for general input and general packet
length. This work assumes this generality and aims at study
of two performance metrics that are most relevant for further
analysis of transmission queue and OBS core nodes, namely
burst length and inter-departure time in case of hybrid scheme.
At this stage of our development, we show exemplar solutions
where Erlang distributions of packet length and inter-arrival
time are assumed, mainly due to easiness of their transform
inversion. However, the method can be used also for more
complicated distributions, especially when powerful numerical
inversion techniques are applied [18], [19]. The study of the
delay of n-th packet can be also treated with this method.
The rest of paper is organized as follows. In Section II, the
OBS edge node architecture and burst assembly schemes are
briefly described. The analytical model for burst assembly is
presented in Section III. In Section IV numerical results with
simulations are discussed and Section V concludes the paper.
Fig. 1.
General architecture of an OBS edge node.
different destination/egress node. The classifier distributes the
incoming packets, with respect to each packet’s destination
address, into the respective queues of the burst assembly modules.
Based on the burst assembly technique, burst assembler
module then assembles bursts consisting of packets headed
for a specific egress node. After a burst has been aggregated,
the corresponding control packet is generated and sent on the
control channel. The assembled bursts wait for transmission
in the electronic transmission buffers called burst transmission
queues. The decision about scheduling a wavelength channel
and time on which a burst is going to be sent is taken by
the scheduling unit at the edge node. There are three main
schemes that have been categorized in literature for burst
assembly: time-based assembly, length-based assembly and
hybrid assembly.
In time-based assembly [11], after receiving the first packet
in an assembler queue, a timer is started. Packets are collected
in the queue until a defined time-out expires. The collected
packets are then assembled into a burst and sent to the
transmission buffer. The timer is restarted when a new packet
is received in the queue. Therefore in time assembly, bursts are
produced in periodic intervals from a single assembler queue,
however, their sizes may vary depending on the arrival rate. In
length-based assembly [14], [20], packets are collected until
the total length of packets exceeds a defined threshold. The
last packet that makes the total length equal or greater than
threshold triggers the assembly of packets into a burst. Therefore,
this kind of assembly generates bursts of approximately
equal lengths but variable inter-departures.
The two mentioned have are simple to implement but have
the following drawbacks. Monitoring only the time results
in undesirably long bursts in high-load scenario, whereas
II. OBS BURST ASSEMBLY
Typically, the edge node consists of a classifier, burst assemblers,
burst transmission queues, a routing and wavelength
assignment modules and schedulers as shown in Fig.1. Each
burst assembler module maintains one separate queue for each
Fig. 2.
Model of the hybrid assembly queue.

HOŁYŃSKI AND HAYAT: ANALYSIS OF OBS BURST ASSEMBLY QUEUE WITH RENEWAL INPUT 25
huge packet delays arise in length-based assembly under low
load condition. These problems are overcome with the hybrid
mechanism that takes into account both criteria. On arrival of
the first packet, the timer is started. The burst is assembled
on the basis of the time-out or length exceedance depending
upon which event happens first, as schematically presented in
Fig. 2. In this work, we have considered the hybrid assembly
as it encompasses the two other strategies as special cases.
III. ANALYTICAL MODELLING
In this section, we develop an analytical model for hybrid
assembly in which we consider a single assembly queue. In
the model, packets destined to this queue arrive from a renewal
process with general gap distribution and the lengths of packets
are general independent random variables. The analysis is
based on the observation of arrivals of subsequent packets
and summation of their lengths to find probability that the
aggregate of n packets exceeds one of the thresholds. Because
of the thresholds, the involved distributions and their Laplace
transforms (LT) are subjected to truncations from the right,
which are here indicated by an auxiliary operator [...] ∗ .
First, we find the probability mass function (pmf) of the
number of the packets in a burst and derive general Laplace
transforms of burst length and inter-departure time. Then we
proceeds with evaluations in case lengths and arrivals are
Erlang distributed. The quantities and notation used are listed
below.
Symbol
L
T A
l o
t o
f L (l)
f A (t)
ψ(s)
φ(s)
f L,n (l)
f A,n (t)
ψ n(s)
φ n(s)
[ψ(s)] ∗
q n
r n
a n, b n
p t
p l
π n
f BL (l)
f D (t)
f ex(l)
ψ BL (s)
φ D (s)
ψ ex(s)
φ A (s)
TABLE I
NOTATION USED IN THE ANALYSIS.
Description
packet length (random variable)
packet inter-arrival time (random variable)
length threshold
time threshold
probability distribution function of packet length
probability distribution function of inter-arrival time
Laplace transform of f L (l)
Laplace transform of f A (t)
pdf of the length of n aggregated packets
pdf of the time up to (n+1)th packet arrival
Laplace transform of f L,n (l)
Laplace transform of f A,n (t)
Laplace transform of a truncated pdf
prob. that n aggregated packets are shorter than l o
prob. that time up to (n+1)th packet arrival is less than t o
normalizing probabilities used for truncation of pdfs
prob. that a burst is assembled due to time criterion
prob. that a burst is assembled due to length criterion
pmf of the number of packets in a assembled burst
pdf of length of a assembled burst
pdf of burst inter-departure, LT: φ D (s)
pdf of the part of the burst part which exceeds l o
Laplace transform of f BL (l)
Laplace transform of f D (t)
Laplace transform of f ex(t)
Laplace transform of burst assembly time
the burst assembly is a regenerative process. This happens
due to the fact the timer is reset upon arrival of a first packet
making the past realizations irrelevant for the way the current
burst is completed. That means that analysis of assembly of
a single burst is sufficient for characterization of the whole
process.
The development of hybrid assembly can be followed with
the help of a discrete Markov chain shown in Fig. 3. The state
number represents the number of packets currently aggregated
and the absorbing state stands for the assembly completion.
Pmf of the number of packets in a burst π n
Starting with the state no 1 (first arrival and timer reset),
the transition probabilities can be explained by the following
narration (Fig. 4). The burst will consist of only one packet if
either its length exceeds l o (with probability P {L > l o }) or
the time up to the next packet arrival is greater than t o (with
probability P {T A > t o }), as shown in Fig. 4a. Since both
events are not disjoint, the probability of their union is
p 1 = P {L > l o } + P {T A > t o }
− P {L > l o }P {T A > t o }.
With the probability (1 − p 1 ), the burst will consist of at
least two packets. The same reasoning is repeated up to the
nth arrival, upon which one of the thresholds will be exceeded,
as depicted in Fig. 4b. Then, the probability π n that burst
comprises exactly n packets can be read out from the Markov
chain. Then
n−1
∏
π n = p n (1 − p i ), (1)
i=1
with p n expressed in general by
p n = (1 − q n ) + (1 − r n ) − (1 − q n )(1 − r n ), (2)
whereby the auxiliary probabilities q n and r n are calculated
by the following integrals
q n =
∫ l o
0
f L,n (l) dl, r n =
∫ t o
0
f A,n (t) dt. (3)
Derivation of the densities f A,n (t) and f L,n (l) requires summations
of independent random variables that are equivalent to
multiplications of their Laplace transforms. The summations
related with occurrence of the nth packet is done in such a way
that the length of the nth packet (or the inter-arrival between
the nth and (n+1)-th packet) is added to the already aggregated
A. Model for general independent traffic
First observation to be made is that under assumption of
stationary renewal input and independence of packet lengths,
Fig. 3.
Markov chain describing the assembly process

26 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
Fig. 5.
Description of hybrid burst assembly with Laplace transforms.
Fig. 6. Phase diagram for formulation of the Laplace transform of burst
length ψ BL (s).
Fig. 4. Examples of hybrid assembly with lengths and time thresholds: (a)
two possible realizations of assembly of a burst comprising one packet, (b)
assembly of a burst comprising n packets triggered by length exceedance.
portion (or elapsed time) which is truncated at l o (or t o ). Using
the Laplace transforms ψ(s) = L { f L (l) } , φ(s) = L { f A (t) } ,
φ n (s) = L { f A,n (t) } and ψ n (s) = L { f L,n (l) } the summation
can be expressed by the following recursive relations
ψ 1 (s) = ψ(s)
ψ n (s) = [ψ n−1 (s)] ∗ ψ(s) for n = 2, 3, ..., ∞ (4)
φ 1 (s) = φ(s)
φ n (s) = [φ n−1 (s)] ∗ φ(s) for n = 2, 3, ..., ∞, (5)
where the operator [...] ∗ denotes the fact that the Laplace
transform is calculated from the density truncated at l o or t o .
Understanding of Eq. 4 and 5 is supported by Fig. 5. Usage
of these relations can be greatly simplified by the observation
that [ψ n−1 (s)] ∗ = [ψ n−1 (s)] ∗ and [φ n−1 (s)] ∗ = [φ n−1 (s)] ∗
that leads to the non-recursive expressions
φ n (s) = [φ n−1 (s)] ∗ φ(s) for n = 1, 2, ..., ∞ (6)
ψ n (s) = [ψ n−1 (s)] ∗ ψ(s) for n = 1, 2, ..., ∞. (7)
Finally, calculation of the probabilities q n and r n requires either
analytical or numerical inversion of the transforms ψ n (s)
and φ n (s). Note that this operation needs to be performed only
on the intervals [0, l o ] or [0, t o ], respectively. Knowledge of the
probabilities q n and r n enables formulation of the transforms
of burst length and inter-departure time.
Laplace transform of burst length ψ BL (s)
Now, we are not interested in the probability for a concrete
number of packets but rather in finding the probabilities that
the assembly is completed by exceeding either of the length- or
time threshold. We observe that in the former case the length
is composed by a constant portion l o with transform e −slo and
a random exceeding part with transform ψ ex (s). In the latter
case, the burst is formed by sum of n packets with distribution
truncated at l o with the transform ψ n (s). Considering arrivals
of subsequent packets, we employ the probabilities q n and r n
to construct a phase diagram for the Laplace transform of burst
length shown in Fig. 6. The final result is a weighted sum of
all possible ways the diagram can be traversed:
∞∑
[
∏ n
ψ BL (s) = q i−1 r i−1
](1 − q n )ψ ex (s)e −slo
+
n=1
i=1
∞∑
[
∏ n
q i r i−1
](1 − r n )[ψ n (s)] ∗ , (8)
n=1
i=1
whereby we define q 0 = 1 and r 0 = 1. The transform ψ ex (s)
is not easy to derive from the original packet distribution, but
if a burst consists of many packets, it can be successfully
approximated by the well-known transform of residual lifetime
interpreted in the length domain
ψ ex (s) ≈ 1 − ψ (s)
. (9)
sE[L]
If the probability that the burst consists of few packets is
relatively small, the effect of this approximation negligible.
Moments of the burst length can be computed in the standard
way
E[BL k ] = (−1) k dk ψ BL (s)
ds k ∣
∣∣s=0
. (10)
Laplace transform of burst inter-departure time φ D (s)
The inter-departure time is equal to the sum of two periods:
the burst assembly time and the period separating the start
of the current timer and the departure of the previous burst.

HOŁYŃSKI AND HAYAT: ANALYSIS OF OBS BURST ASSEMBLY QUEUE WITH RENEWAL INPUT 27
where
φ A (s) =
∞∑
[
∏ n ]
q i−1 r i−1 (1 − q n )[φ n−1 (s)] ∗
n=1
i=1
Fig. 7. Phase diagram for formulation of the Laplace transform of burst
assembly time φ A (s).
∞∑
[
∏ n
+ q i r i−1
](1 − r n )e −sto , (13)
n=1 i=1
where again q 0 = 1 and r 0 = 1.
E[T k D] = (−1) k dk φ D (s)
ds k ∣
∣∣s=0
. (14)
All the above considerations are valid for general conditions.
Fig. 8.
Two possible realisations of burst inter-departure time.
B. Solutions for Erlangian traffic
In the sequel, packet length and inter-arrival time have
Erlang k and Erlang m densities, respectively.
(kε) k
( ) k kε
f L (l) =
(k − 1)! lk−1 e −kεl ψ(s) =
kε + s
( ) m
f A (t) = (mλ)m
mλ
(m − 1)! tm−1 e −mλt φ(s) =
,
mλ + s
where λ is the mean arrival rate and ε is reciprocal of the
mean packet length
λ = 1
E[T A ]
Calculation of the probabilities q n , r n , π n
ε = 1
E[L] . (15)
Formulation of the transform of the assembly time, φ A (s), is
very similar to that of burst length and is shown by Fig. 7.
If a n-packet-burst is completed due to length criterion, with
probability 1 − q n , its assembly time is a sum of n − 1 interarrival
times truncated at t o ( [φ n−1 (s)] ∗ ). A burst completed
due to timer expiry with probability 1 − r n , has obviously the
assembly time equal to the time threshold ( e −sto ). Duration of
the second period depends upon the fact whether the previous
burst departed due to length or time exceedance. In the former
case, the separating period is a full inter-arrival time, in the
latter it can be again approximated by residual life time
of T A ( [φ res (s)] ). Probabilities associated with both events
explained in Fig. 8 equal p l and p t , respectively.
p l =
p t =
∞∑
[
∏ n
q i−1 r i−1
](1 − q n )
n=1
i=1
∞∑
[
∏ n
q i r i−1
](1 − r n ).
n=1
i=1
Then the transform of burst inter-departure time is
(11)
[
]
φ D (s) = φ A (s) p l φ(s) + p t φ res (s) , (12)
Subsequent derivations are shown for the length, that is their
concern the probabilities q n . The procedure is identical for
time and r n . To start with, we express the density resulting
from addition of n − 1 Erlang k variables as
f L,n−1 (l) =
(kε)k(n−1)
(k(n − 1) − 1)! lk(n−1)−1 e −kεl . (16)
The Laplace transform of the truncated density f L,n−1 (l) can
be calculated as follows 1
∫ l o
[ψ n−1 (s)] ∗ =
0
1
a n−1
(kε) k(n−1)
(k(n − 1) − 1)! lk(n−1)−1 e −kεl e −sl dl
= 1 (kε) k(n−1)
(17)
a n−1 (kε + s) k(n−1)
[ (kε)
k(n−1)
k(n−1)−1
∑ (l o ) i ]
e −kεlo
−
e −slo ,
a n−1 i!(kε + s) k(n−1)−i
i=0
1 In this section, calculation of definite integrals of the type ∫ a
0 xn e −bx dx
is required. Applying multiple integrations by parts, one obtains
∫ a
0
x n e −bx dx = n!
b n+1 [
1 −
See for example [21] on page 670.
n∑ (ab) i ]
e −ab i!
i=0

28 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
where a n−1 is the normalizing factor needed due to truncation
at l o
∫ l o
(kε) k(n−1)
a n−1 =
(k(n − 1) − 1)! lk(n−1)−1 e −kεl dl
Then
0
k(n−1)−1
∑
= 1 −
i=0
(kεl o ) i
e −kεlo . (18)
i!
ψ n (s) = [ψ n−1 (s)] ∗ ψ(s) (19)
=
1 (kε) kn
a n−1 (kε + s) kn
−
[ (kε)
kn
k(n−1)−1
∑ (l o ) i ]
e −kεlo
i!(kε + s) kn−i e −slo
a n−1
i=0
To find the probability q n according to Eq. 3, the inversion
of ψ n (s) is needed on the interval [0, l o ]. By observing that
the second complicated term in Eq. 19 has no contribution to
the inversion below l o (due to the transform shift theorem),
we invert only the first one:
and finally
{ 1
f L,n (l) [0,lo] = L −1 (kε) kn }
a n−1 (kε + s) kn
1 (kε) kn
=
(kn − 1)! lkn−1 e −kεl (20)
a n−1
q n = 1 [
kn−1
∑
1 − e −kεlo
a n−1
i=0
(kεl o ) i
i!
]
. (21)
By identical procedure we find r n together with the associated
normalizing factor b n−1 .
r n = 1 [
mn−1
∑
1 − e −mλto
b n−1
i=0
(mλt o ) i ]
i!
(22)
inversion involving the shift property:
∞∑
[
∏ n
f BL (l) = q i−1 r i−1
](1 − q n )
n=1 i=1
[ k−1 ∑
j=0
ε [ kε(l − l
×
o
) ] ]
j
e −kε(l−l o ) u(l − l o )
j!
[
∞∑ [
∏ n ] ]
(1 − rn ) (kε) kn
+ q i r i−1
a n (kn − 1)! lkn−1 e −kεl ,
n=1
i=1
where u(l) is the unit step function.
Pdf of burst inter-departure time f D (t)
(24)
This derivation is done by analogy to that of the burst length
pdf, but because of the multiplication of transforms in Eq.12
the final inversion gives rather complicated expression, Eq. 25.
However, there is no practical need for detailed knowledge
of this function. Usually, in an edge node, output streams of
many assembly queues are merged before they are directed to
the transmission buffer(s). Since the single departure stream
is nearly renewal, we infer that the total departure process
tends to a Poisson process as the number of merged streams
increases.
This effect was proved in simulation where a number of
independent assembly queues fed by uncorrelated renewal
inputs was implemented. Fig. 10 shows the results for 10
queues with nearly negative exponential density irrespectively
of the type of packet inter-arrival density assumed.
IV. NUMERICAL EXAMPLES
Fig. 11 shows how the number of packets in a burst varies
when configuration of thresholds is changed in case of purely
Poisson traffic. The probability mass is symmetrically concentrated
around the mean. Fig. 12 depicts the situation when the
thresholds allow much more packets to be assembled. With
The pmf of the number of packets in a burst is now found by
Eq. 1 and 2.
Pdf of burst length f BL (l)
According to Eq. 8, this derivation involves the transforms
ψ ex (s) and [ψ n (s)] ∗ . The first one we approximate by the
transform of residual life which is:
ψ ex (s) ≈ 1 k
k∑
[ ] j+1
kε
(23)
(kε + s)
j=0
and the second we readily obtain from Eq. 17 substituting
n−1 by n. After insertion of the transforms into Eq. 8, we can
obtain the pdf of burst length by means of simple analytical
Fig. 9. Superposition of the departure streams from multiple assembly queues
in the edge node.

HOŁYŃSKI AND HAYAT: ANALYSIS OF OBS BURST ASSEMBLY QUEUE WITH RENEWAL INPUT 29
[
∑ ∞ [
∏ n
f D (t) = p l
n=1
i=1
[ 1 (mλ)
q i−1r i−1
](1−q mn
n)
b n−1 (mk−1)! tmn−1 e −mλt − (mλ)mn m(n−1)−1 ∑
b n−1
i=0
[ (λ)
m
] [
∑ ∞ [
∏ n
+ p l p t
(m−1)! e−mλ(t−to) u(t−t o) + p t q i−1r i−1
](1−q n)
n=1 i=1
m∑
[ 1
j=1
b n−1
t i ] ]
o
i!(mn−i−1)! (t−to)mn−i−1 e −mλ(t−to) u(t−t o)
(mλ) m(n−1)+j
(m(n−1) + j−1)! tm(n−1)+j−1 e −mλt (25)
−
(mλ)m(n−1)+j
mb n−1
m(n−1)−1 ∑
i=0
t i o e−mλto
i!(m(n−1) −i+j−1)! (t−to)m(n−1)−i+j−1 e −mλ(t−to) u(t−t o)
] ] m−1
+ p 2 t λ ∑
[ mλ(t−to) i
i=0
i!
]
e −mλ(t−to) u(t−t o)
Fig. 10. Simulation results of the superposition of inter-departures processes
from 10 independent assembly queues with thresholds l o=5 and t o=5 for
different distributions of packet inter-arrival times T A , whereby ε=1 and λ=1
Fig. 11. Pmf of the number of packets in a burst for various values of
thresholds. Packet lengths and inter-arrival times exponentially distributed
with ε=1 and λ=1.
decreasing variance of the input distributions, the analyzed
pmf tends to be more and more deterministic.
In Fig.13 density of burst length is plotted for various
settings. All three pdfs exhibit discontinuities at the point
equal to the length threshold. The parts of the curves below
l o represent realizations of assembly due to time-out expiry.
The smoothly decaying peaks, which are approximated by
mixtures residual lifetimes of Erlang distributions, are slightly
inexact compared to simulations in its initial region but this
error vanishes rather fast along the tail.
Fig. 14 presents densities for relatively high number of
packets collected. If l o = 50 and t o = 15, we have practically
only time-based assembly and expected manifestation of the
central limit theorem is observed regarding the pdf. In the
converse case, nearly no burst is smaller than l o resulting with
a sharp peak at this point.
Fig. 12. Pmf of the number of packets in a burst for Erlangian traffic (length
and time) with different coefficients of variation, ε =1, λ=1, t o=25, l o=25.
V. CONCLUSIONS
We have provided a nearly exact analysis of hybrid burst
assembly. Although the output traffic preserves the renewal
properties of the input, the distributions of interest turned out
to be complex functions of the involved parameters. Nevertheless,
they give an important insight into the characteristics of
the assembled traffic and could be approximated by simpler
tractable distributions. The presented results show mainly
that the assembled traffic is highly sensitive to the defined
thresholds and if their values are not properly adjusted, the
resulting large variances of lengths can severely degrade the
performance of OBS core nodes. Finally, the distribution of
burst length is very far from negative exponential as it is
commonly assumed in the literature of the subject.
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IEEE Commun. Lett., vol. 8, no. 1, pp. 119–121, 2004.
[6] M. Zukerman, E. W. Wong, Z. Rosberg, G. M. Lee, and H. L. Vu, “An
Accurate Model for Evaluating Blocking Probabilities in Multi-Class
OBS Systems,” IEEE Commun. Lett., vol. 8, no. 2, pp. 116–118, 2004.
[7] J. Teng and G. N. Rouskas, “Wavelength Selection in OBS Networks
Using Traffic Engineering and Priority-Based Concepts,” IEEE J. Sel.
Areas Commun., vol. 23, no. 8, pp. 1658–1669, 2005.
[8] N. Akar and E. Karasan, “Exact Calculation of Blocking Probabilities
for Bufferless Optical Burst Switched Links with Partial Wavelength
Tomasz Hołyński received MSc degree in Telecommunications and Computer
Science from the International Faculty of Engineering (IFE) at the Technical
University of Lodz, Poland, in 2009. Since 2007 he has been working at
the Institute of Telecommunications (former the Institute of Broadband Communications)
at the Vienna University of Technology as a project assistant.
His master thesis on queueing theoretical modelling and analysis of data
link protocols was distinguished by the Austrian Electrotechnical Association
(ÖVE) with the GIT-award. His current doctoral research concerns transformbased
methods and related complex variable techniques in selected areas of
queueing theory and performance evaluation.
Muhammad Faisal Hayat received BSc (Hons) and MSc degrees in Computer
Engineering from University of Engineering and Technology, Lahore,
Pakistan in 2000 and 2005, respectively. In 2001 he joined the abovementioned
university where he worked as a lecturer (2001-2005) and as an assistant
professor (2005-2008). Since 2008 he has been pursuing his PhD at the
Institute of Telecommunications at the Vienna University of Technology,
Austria. His research focus is modelling, analysis and simulation of all-optical
networks.

ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011 31
Scheduling and Capacity Estimation in LTE
Olav Østerbø
Abstract—Due to the variation of radio condition in LTE
the obtainable bitrate for active users will vary. The two
most important factors for the radio conditions are fading and
pathloss. By considering analytical analysis of the LTE conditions
including both fast fading and shadowing and attenuation due
to distance we have developed a model to investigate obtainable
bitrates for customers randomly located in a cell. In addition
we estimate the total cell throughput/capacity by taking the
scheduling into account. The cell throughput is investigated for
three types of scheduling algorithms; Max SINR, Round Robin
and Proportional Fair where also fairness among users is part
of the analysis. In addition models for cell throughput/capacity
for a mix of Guaranteed Bit Rate (GBR) and Non-GBR greedy
users are derived.
Numerical examples show that multi-user gain is large for the
Max-SINR algorithm, but also the Proportional Fair algorithm
gives relative large gain relative to plain Round Robin. The Max-
SINR has the weakness that it is highly unfair when it comes to
capacity distribution among users. Further, the model visualize
that use of GBR for high rates will cause problems in LTE due
to the high demand for radio resources for users with low SINR,
at cell edge. Persistent GBR allocation will be a waste of capacity
unless for very thin streams like VoIP. For non-persistent GBR
allocation the allowed guaranteed rate should be limited.
Index Terms—LTE, scheduling, capacity estimation, GBR.
I. INTRODUCTION
THE LTE (Long Term Evolution) standardized by 3GPP is
becoming the most important radio access technique for
providing mobile broadband to the mass marked. The introduction
of LTE will bring significant enhancements compared
to HSPA (High Speed Packet Access) in terms of spectrum
efficiency, peak data rate and latency. Important features of
LTE are MIMO (Multiple Input Multiple Output), higher order
modulation for uplink and downlink, improvements of layer 2
protocols, and continuous packet connectivity [1].
While HSPA mainly is optimized data transport, leaving the
voice services for the legacy CS (Circuit Switched) domain,
LTE is intended to carry both real time services like VoIP in
addition to traditional data services. The mix of both real time
and non real time traffic in a single access network requires
specific attention where the main goal is to maximize cell
throughput while maintaining QoS and fairness both for users
and services. Therefore radio resource management will be a
key part of modern wireless networks. With the introduction
of these mobile technologies, the demand for efficient resource
management schemes has increased.
The first issue in this paper is to consider the bandwidth
efficiency for a single user in cell for the basic unit of radio
resources, i.e. for a RB (Resource Block) in LTE. Since LTE
uses advanced coding like QPSK, 16QAM, and 64QAM, the
O. Østerbø is with Telenor, Corporate Development, Fornebu, Oslo, Norway,
(phone: +4748212596; e-mail: olav-norvald.osterbo@telenor.com)
obtainable data rate for users will vary accordingly depending
on the current radio conditions. The average, higher moments
and distribution of the obtainable data rate for a user either
located at a given distance or randomly located in a cell, will
give valuable information of the expected cell performance.
To find the obtainable bitrate we chose a truncated and
downscaled version on Shannon formula which is in line with
what is expected from real implementations and also comply
with the fact that the maximal bitrate per frequency or symbol
for 64 QAM is at most 6 [2].
For the bandwidth efficiency, where we only consider a
single user, the scheduling is without any significance. This
is not the case when several users are competing for the
available radio resources. The scheduling algorithms studied in
this paper are those only depending on the radio conditions, i.e.
opportunistic scheduling where the scheduled user determined
by a given metrics which depends on the SINR (signalto-interference-plus-noise
ratio). The most commonly known
opportunistic scheduling algorithms are of this type like PF
(Proportional Fair), RR (Round Robin) and Max-SINR. The
methodology developed will, however, will apply for general
scheduling algorithms where the scheduling metrics for a user
is given by a known function of SINR, however, now the SINR
may vary in different scheduling intervals taking rapid fading
into account. The cell capacity distribution is found for cases
where the locations of the users all are known or as an average
where all the users are randomly located in the cell [3].
Also the multi user gain (relative increase in cell throughput)
due to the scheduling is of main interest. The proposed models
demonstrate the magnitude of this gain. As for Max SINR
algorithm this gain is expected to be huge, however, the gain
comes always at a cost of fairness among users. And therefore
fairness has to be taken into account when evaluating the
performance of scheduling algorithms.
It is likely that LTE will carry both real time traffic and
elastic traffic. We also analyze scenarios where a cell is loaded
by two traffic types; high priority CBR (Constant Bit Rate)
traffic that requires a fixed data-rate and low priority (greedy)
data sources that always consume the leftover capacity not
used by the CBR traffic. This is actual a very realistic traffic
scenario for future LTE networks where we will have a mix of
both real time traffic like VoIP and data traffic. We analyse this
case by first estimate the RB usage of the high priority CBR
traffic, and then subtract the corresponding RBs to find the
actual numbers of RBs available for the (greedy) data traffic
sources. Finally we then estimate the cell capacity as the sum
of the bitrates offered to the CBR and (greedy) data sources.
The remainder of this paper is organized as follows. In
section II the basic radio model is given and models for
bandwidth efficiency are discussed. Section III gives an outline
of the multiuser case where resource allocation and scheduling

32 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
is taking into account. Some numerical examples are given in
section IV and in section V some conclusions are given.
II. SPECTRUM EFFICIENCY
A. Obtainable bitrate per symbol rate as function of SINR
For LTE the obtainable bitrate per symbol rate will depend
on the radio signal quality (both for up-and downlink). The
actual radio signal quality is signaled over the radio interface
by the so-called CQI (Channel Quality Indicator) index in
the range 1 to 15. Based on the CQI value the coding rate
is determined on basis of the modulation QPSK, 16QAM,
64QAM and the amount of redundancy included. The corresponding
bitrate per bandwidth is standardized by 3GPP [4]
and is shown in Table 1 below. For analytical modeling the
actual CQI measurement procedures are difficult to incorporate
into the analysis due to the time lag, i.e. the signaled CQI is
based measurements taken in earlier TTIs (Transmission Time
Interval). To simplify the analyses, we assume that this time
lag is set to zero and that the CQI is given as a function of the
momentary SINR, i.e. CQI=CQI(SINR). This approximation
is justified if the time variation in SINR is significantly slower
than the length of a TTI interval. Hence, by applying the CQI
table found in [4] we get the obtainable bitrate per bandwidth
as function of the SINR as the step function:
B = fc j , for SINR ∈ [g j , g j+1 ) ; j = 0, 1, ..., 15, (1)
where f is the bandwidth of the channel, c j is the efficiency
for QCI equal j (as given by Table 1) and [g j , g j+1 ) are the
corresponding intervals of SINR values. (We also take c 0 = 0,
g 0 = 0 and g 16 = ∞.)
To fully describe the bitrate function above we also have to
also specify the intervals [g j , g j+1 ). Several simulation studies
e.g. [5] suggest that there is a linear relation between the CQI
index and the actual SINR limits in [dB]. With this assumption
we have SINR j [dB] = 10 log 10 g j = aj + b or g j = 10 aj+b
10
for some constants a and b. It is also argued that the actual
range of the SINR limits in [dB] is determined by the
following (end point) observations: SINR[dB]=-6 corresponds
to QCI=1, while SINR[dB]=20 corresponds to CQI=15. Hence
we then have −6 = a + b and 20 = 15a + b or a = 13/7 and
b = −55/7.
For extensive analytical modelling the step based bandwidth
function is cumbersome to apply. An absolute upper bound
yields the Shannon formula B = f log 2 (1+SINR), however,
we know that the Shannon upper limit is too optimistic.
First of all the bandwidth function should never exceed the
highest rate c 15 = 5.5547. We therefore suggest downscaling
and truncating the Shannon formula and take an alternative
bandwidth function as:
B = d min[T, ln(1 + γSINR)], (2)
with d = f C
c15 ln 2
ln 2
and T =
C
where C is the downscaling
constant (relative to the Shannon formula) and γ is a constant
less than unity. By choosing C and γ that minimize the square
distances between the CQI based and the truncated Shannon
formula (2) above we find C = 0.9449 and γ = 0.4852.
(Upper and lower estimates of the CQI based zigzagging
N ormalised T hroughpu t @ b i t êsê H z D
TABLE I
TABLE 1 CQI TABLE.
CQI index modulation code rate x 1024 efficiency
0 out of range
1 QPSK 78 0.1523
2 QPSK 120 0.2344
3 QPSK 193 0.3770
4 QPSK 308 0.6016
5 QPSK 449 0.8770
6 QPSK 602 1.1758
7 16QAM 378 1.4766
8 16QAM 490 1.9141
9 16QAM 616 2.4063
10 64QAM 466 2.7305
11 64QAM 567 3.3223
12 64QAM 666 3.9023
13 64QAM 772 4.5234
14 64QAM 873 5.1152
15 64QAM 948 5.5547
6
5
4
3
2
1
---- Shannon
---- Modified Shannon
---- LTE CQI table
0 5 10 15 20 25
SINR @dBD
Fig. 1. Normalized throughput as function of the SINR based on: 1.-QCI
table, 2.-Shannon and 3.-Modified Shannon.
bitrate function is obtained by taking γ u = γ10 a/20 = 0.6008
and γ l = γ10 −a/20 = 0.3918).
We observe that a downscaling of the Shannon limit is very
much in line with the corresponding bitrates obtained by the
CQI table as shown in Figure 1 and hence we believe that (2)
yields a quite accurate approximation. In fact the approximated
CQI values c app
j follow the similar logarithmic behaviour:
c app
j = C log 2 (1 + αβ j ), (3)
where now have α = γ10 a/20+b/10 = 0.0984 and β =
10 a/10 = 1.5336.
B. Radio channel models
Generally, the SINR for a user will be the ratio of the
received signal strength divided by the corresponding noise.
The received signal strength is the product of the power P w
times path loss G and divided by the noise component N,
i.e. SINR = PwG
N
. Now the path loss G will typical be a
stochastic variable depending on physical characteristics such

ØSTERBØ: SCHEDULING AND CAPACITY ESTIMATION IN LTE 33
as rapid and slow fading, but will also have a component
that are dependent on distance (and possible also the sending
frequency). Hence, we first consider variations that are slowly
varying over time intervals that are relative long compared
with the TTIs (Transmission Time Intervals). Then the path
loss is usually given in dB on the form:
G = 10 L/10 with L = C − A log 10 (r) + X t , (4)
where C and A are constants, A typical in the range 20-40, and
X t a normal stochastic process with zero mean representing
the shadowing (slow fading). The other important component
determining the SINR is the noise. It is common to split
the noise power into two terms: N = N int + N ext where
N int is the internal (or own-cell) noise power and N ext is
the external (or other-cell) interference. In a CDMA (Code
Division Multiple Access) network, the lack of orthogonality
induces own-cell interference. In an OFDMA (Orthogonal
Frequency Division Multiple Access) network, however, there
is a perfect orthogonality between users and therefore the
only contribution to N int is the terminal noise at the receiver.
The interference from other cells depends on the location of
surrounding base stations and will typically be largest at cell
edges. In the following we shall assume that the external noise
is constant throughout the cell or negligible, i.e. we assume
the noise N to be constant throughout the cell.
Hence, with the assumptions above, we may write SINR on
the form S t /h(r, λ) where S t represent the stochastic variations
which we assume to be distance independent capturing
the slowly varying fading, and h(r, λ) represent the distance
dependant attenuation (which we also allow to depend on the
sending frequency). Most commonly used channel models as
described above have attenuation that follows a power law, i.e.
we chose to take h(r, λ) on the form
h(r, λ) = h(λ)r α , (5)
where α = A/10 is typical in the range 2-4 and h(λ) =
N
P w
10 −C/10 with Z = 10 log 10 (N) − 10 log 10 (P w ) − C given
dB, where we also indicate that h(λ) may depend of the
(sending) frequency. With the description above the stochastic
variable S t = 10 Xt/10 with S t • ln 10
=
10 X t, and hence S t is
a lognormal process with E[S t • ln 10
] = 0 and σ =
10 σ(X t)
where σ(X t ) is the standard deviation (given in dB) for
the normal process X t . With these assumptions we have
the Probability Density Function (PDF) and Complementary
Distribution Function (PDF) of S t as:
s ln (x) =
1
(ln x)2
−
√ e 2σ 2
2πσx
where erfc(y) = 2 √ π
function.
∞∫
x=y
C. Including fast fading
and ˜S ln (x) = 1 2 erfc ( ln x
σ √ 2
)
,
(6)
e −x2 dx is the complementary error
There are several models for (fast) fading in the literature
like Rician fading and Rayleigh fading [6]. In this paper we
restrict ourselves to the latter mainly because of its simple
negative exponential distribution.
It is possible to include fast fading into the description
above. To do so we assume that the fast fading effects are on
a much more rapid time scales than slow fading. We therefore
assume that the slow fading actual is constant during the
rapid fading variations. Hence, condition on the slow fading
to be y then for a Rayleigh faded channel the SINR will be
exponentially distributed with mean y/g(r, λ) Hence, we may
therefore take SINR as S t /g(r, λ) where S t = X ln X e is the
product of a Log-normal and a negative exponential distributed
variables. The corresponding distribution often called Suzuki
distribution have PDF ad CDF given as the integrals:
s su (x) =
∫ ∞
t=0
1
t e− x t sln (t)dt and ˜S su (x) =
∫ ∞
t=0
e − x t sln (t)dt,
(7)
where s ln (t) is the lognormal PDF above by (6). Since
s ln ( 1 t ) = t2 s ln (t) it is possible to express the integrals above in
terms of the Laplace transform of the Log-normal distribution
and therefore the CDF (and PDF) of the Suzuki distribution
may be written as: ˜Ssu (x) = Ŝln(x) and s su (x) = −Ŝ′ ln (x)
where
Ŝ ln (x) =
∫ ∞
t=0
e −xt s ln (t)dt = 1 √
2πσ
∫∞
t=0
(ln(t/x))2
−t−
e 2σ 2
dt (8)
t
is the Laplace transform of the Log-normal distribution. If we
define the truncated transform:
˜S su (x, M) = 1 x
=
∫ M
t=0
1
√
2πσ
e −t s ln (t/x)dt
∫M
t=0
(ln(t/x))2
−t−
e 2σ 2
dt, (9)
t
then ˜S su (x) = lim ˜S su (x, M) and further the corresponding
M→∞
error is exponentially small. An attempt to expand the integral
(8) in terms of the series of the exponential function e −t =
∑ ∞ (−1) k t k
k=0 k!
yields a divergent series; however, this is not
the case for the truncated transform (9). We find the following
series expansion:
˜S su (x, M) = 1 ∞∑ (−1) k
(
x k e k2 σ 2 kσ
2 erfc √ + ln(x/M) )
2 k!
k=0
2 σ √ 2
(10)
Similar the PDF of the Suzuki random variable may be
found from (8) by differentiation:
s su (x) = − ˜S ′ su(x) =
=
∫ ∞
t=0
e −xt ts ln (t)dt
1
√
2πσx
∫∞
t=0
(ln(t/x))2
−t−
e 2σ 2 dt, (11)
and for the PDF we now we take the corresponding truncated
integral to be:
s su (x, M) =
∫M
1
√
2πσx
t=0
(ln(t/x))2
−t−
e 2σ 2 dt (12)

34 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
L og @ 1 0,SHxLD
0
-1
-2
-3
-4
-5
σ = 0.2
σ = 0.6
σ = 5.0
σ = 2.0
σ = 1.0
5 10 15 20 25 30 35 40
x
Fig. 2. Logarithmic plot of the CDF for the Suzuki distribution as function
of x for some values of σ.
σ2 −M+
In this case we find 0 ≤ s su (x) − s su (x, M) = e 2 as a
bound of the truncation error.
By expanding the integral (12) in terms of the exponential
function as above, we now obtain a similar (convergent) series:
s su (x, M)= 1 ∞∑ (−1) k
(
x k e (k+1)2 σ 2 (k + 1)σ
2 erfc √ + ln(x/M) )
2 k!
k=0
2 σ √ 2
(13)
In Figure 2 we have plotted the CDF of the Suzuki distribution
for σ equals 0.2, 0.6, 1.0, 2.0 and 5.0. (The CDF
Suzuki distribution is calculated by applying the series (10)
with M = 20.0 which secure an accuracy of 2.0x10-9 in
the computation.) Note that the k’th moment of the Suzuki
distribution is k! that of the Log-normal.
D. Distribution of the obtainable bitrate for channel of a
certain bandwidth for a user located at a given distance from
the sender antenna
Below we express the distribution of the possible obtainable
bitrate according to the distribution of the stochastic part of
the SINR; namely S t . From (1) we get the bit-rate B t (r) for
a channel occupying a bandwidth f located at distance r as:
B t (r) = fc j when S t ∈ [h(r, λ)g j , h(r, λ)g j+1 ) ,
for j = 0, 1, ..., 15. (14)
Hence, the DF (Distribution Function) of the bandwidth distribution
for a user located at distance r; B(y, r) = P (B t (r) ≤
y) may be written:
B(y, r) = S(h(r, λ)g j+1 ), for y ∈ (fc j , fc j+1 ]
for j = 0, 1, ..., 15, (15)
where S(x) is the DF of the variable fading component.
Hence, we obtain the k’moment of the obtainable bitrate for
a user located at a distance r from the antenna as the (finite)
sum:
∑15
m k (r) = f k (
c
k
j − c k )
j−1 ˜S(h(r, λ)gj ), (16)
j=1
where ˜S(x) = 1 − S(x) is the CDF of the variable fading
component.
Rather than applying the discrete modeling approach above
we may prefer to apply the smooth (continuous) counterpart
defined by relation (2). The bit-rate B t (r) for a channel
occupying a bandwidth f located at distance r is then given
by
B t (r) = d min[T, ln(1 + S t /g(r, λ))], (17)
with d = f C
c15 ln 2
ln 2
and T =
C
and where C is the
downscaling constant (relative to the Shannon formula) and
where we also define g(r, λ) = γ −1 h(r, λ). For the continuous
bandwidth case the DF of the bandwidth distribution for a user
located at distance r is given by:
{
S(g(r, λ)(e
B(y, r) =
y/d − 1)) for y/d < T
(18)
1 for y/d ≥ T
Based on (18) we may write the k’moment of the obtainable
bitrate for a user located at a distance r from the antenna:
m k (r) = d k
∫
g(r,λ)(e T −1)
y=0
(ln (1 + y/g(r, λ))) k s(y)dy +
+d k T k ˜S(g(r, λ)(e T − 1) (19)
E. Distribution of the obtainable bitrate for channel of a
certain bandwidth for a user that is randomly placed in a
circular cell with power-law attenuation
Since the bitrate/capacity for a user will strongly depend of
the distance from the sender antenna, a better measure of the
capacity will be to find the distribution of bitrate for a user that
is randomly located in the cell. This is done by averaging over
the cell area and therefore the distribution of the ∫ corresponding
averaging bitrate B t is given as B(y) = 1 A
B(y, r)dA(r)
A
where A is the cell area. For circular cell shape and power law
attenuation on the form h(r, λ) = h(λ)r α (where we also take
g(λ) = γ −1 h(λ) i.e. g(r, λ) = g(λ)r α ) the corresponding
integral may be partly evaluated. By defining an α-factor
averaging variable S α with DF S α (x) = P (S α ≤ x) given
by
S α (x) = 2 α x− 2 α
and with PDF
∫ x
t=0
s α (x) = 2 α x− 2 α −1
t 2 α −1 S(t)dt = 2 α
∫x
t=0
t 2 2
α s(t)dt =
α
∫ 1
t=0
∫ 1
t=0
t 2 α −1 S(tx)dt (20)
t 2 α s(tx)dt (21)
the bitrate distribution will have the exact same form as (15)
for the discrete bandwidth case and (18) for the continuous
bandwidth case, and with moments given by (16) and (19) by
changing r → R and S(x) → S α (x) (and s(x) → s α (x)).
1) Distribution of the stochastic variable S α for Lognormal
and Suzuki distribution: Based on the definition we
may derive the CDF and PDF of stochastic variable S α for
the Log-normal and Suzuki distributed fading models. For the
Log-normal distribution we have
˜S lnα (x) = 1
αx 2/α
∫
x
t=0
( ) ln t
t 2/α−1 erfc
σ √ dt.
2

ØSTERBØ: SCHEDULING AND CAPACITY ESTIMATION IN LTE 35
By changing variable according to y = ln t in the integral we
find:
˜S lnα (x) = 1 ( ( ) ln x
erfc
2 σ √ +
2
(
+x −2/α e 2σ2 /α 2 2σ 2 ))
− α ln x
erfc
ασ √ (22)
2
and further the PDF is found by differentiation:
s lnα (x) = 1 (
α x−(2/α+1) e 2σ2 /α 2 2σ 2 )
− α ln x
erfc
ασ √ 2
(23)
For the Suzuki distribution we have the CDF given by the
integral ˜Ssu (x) = x ∫ ∞
t=0 t−2 e −t s ln (x/t)dt and therefore we
have:
˜S suα (x) = 2 α
= x
∫ 1
t=0
∫ ∞
t=0
t 2/α−1 ˜Ssu (xt)dt
t −2 e −t s lnα (x/t)dt (24)
where s lnα (x) is given by (23) above for the Lognormal
distribution. As for the Suzuki distribution approximation to
any accuracy is possible to obtain of ˜S suα (x) by truncating
the integral above:
˜S suα (x, M) = x
∫ M
t=0
t −2 e −t s lnα (x/t)dt (25)
and also for this case we find that the truncation error is
exponentially small. By expanding e −t = ∑ ∞ (−1) k t k
k=0 k!
and
integrating term by term we find:
∞∑ (−1)
˜S k x k (
suα (x, M)=
(2 + kα)k! e k2 σ 2 kσ
2 erfc √ + ln(x/M) )
k=0
2 σ √ +
2
( ) (
/α 2
2 2σ
+ e2σ2 γ
α α , M x −2/α 2 )
−α ln(x/M)
erfc
ασ √ 2
(26)
where γ(a, x) = ∫ x
t=0 ta−1 e −t dt is the incomplete gamma
function. (Observe the similarity with the corresponding expansion
for ˜S su (x) by (10).)
The corresponding integral for the PDF is given by:
s suα (x) =
∫ ∞
t=0
t −1 e −t s lnα (x/t)dt (27)
and we take the truncated approximation of the PDF as the
integral:
s suα (x, M) =
∫ M
t=0
t −1 e −t s lnα (x/t)dt (28)
and we find the following error bound: 0 ≤ s suα (x) −
σ2 −M+
s suα (x, M) ≤ e 2 . By the similar approach as for the
CDF we find the following series expansion of the truncated
PDF:
s suα (x, M) =
∞∑ (−1) k x k
(
=
(2+(k+1)α)k! e (k+1)2 σ 2 (k+1)σ
2 erfc √ + ln( x M ) )
k=0
2 σ √ 2
+ e ( ) ( 2σ2
α 2 2 2σ
α γ α +1,M x −(1+2 α) 2 −α ln( x
erfc
M ) )
ασ √ 2
(29)
III. ESTIMATION OF CELL CAPACITY
In the following we assume that the cell is loaded by two
traffic types:
• High priority CBR traffic sources that each requires to
have a fixed data-rate and
• Low priority (greedy) data sources that always consumes
the leftover capacity not used by the CBR traffic.
This is actually a very realistic traffic scenario for future LTE
networks where we actual will have a mix of both real time
traffic like VoIP and typical elastic data traffic. Below, we
first estimate the RB usage of the high priority CBR traffic,
and then we may subtract the corresponding RBs to find the
actual numbers of RBs available for the (greedy) data traffic
sources. Then finally we estimate the cell throughput/capacity
as the sum of the bitrates offered to the CBR and (greedy)
data sources.
A. Estimation of the capacity usage for GBR sources in LTE
The reservation strategy considered simply allocate recourses
on a per TTI bases and allocate RBs so that the
aggregate rate equals the required GBR (Guaranteed Bit Rate)
rate (Non-Persistent scheduling).
1) Capacity usage for a single GBR source : We first
consider the case where we know the location of the CBR
user in the cell, i.e. at a distance r from the antenna. We take
B as the bitrate obtainable for a single RB and consider a GBR
source that requires a fixed bit-rate of b CBR . We assumes that
this is achieved by offering n RBs for every k-TTI interval.
A way of reserving resources to GBR sources is to allocate
RBs so that n k B will be close to the required rate bCBR over
a given period. We take N CBR = n k
to be the number of
RBs granted to a GBR connection in a TTI as (the stochastic
variable):
N CBR =
{ αb
CBR
B
if CQI > 0
0 if CQI = 0 , (30)
where we have introduced a scaling factor α so that on the
long run we obtain the desired GBR-rate b CBR . By choosing
α = p −1
CQI where p CQI = P (CQI > 0) = ˜S(h(r, λ)g 1 ) then
E [N CBR B] = b CBR and hence we also have:
E [N CBR |CQI > 0] = bCBR
p CQI
E [ B −1 |CQI > 0 ] . (31)
The mean numbers of RBs is therefore:
β = β(r, b CBR ) = b CBR m CQI
−1 (r), (32)

36 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
where the conditional moments m CQI
k
(r) =
E [ B k |CQI > 0 ] is found as
⎛
m CQI
k
(r) =
f k
˜S(h(r, λ)g 1 )
⎝c k 1 ˜S(h(r, λ)g 1 )+
⎞
∑15
(
+ c
k
j − c k )
j−1 ˜S(h(r, λ)gj ) ⎠ , (33)
j=2
for the discrete bandwidth case and by
m CQI
k
(r) =
⎛
d k ⎜
⎝
˜S(h(r, λ)g 1 )
g(r,λ)(e
∫
T −1) (
y=h(r,λ)g 1
⎞
(
ln
1+ y
g(r,λ)
)) k
s(y)dy+
+T k ˜S(g(r, λ)(e T ⎟
− 1) ⎠ (34)
for the continuous bandwidth case. Note that by conditioning
on having CQI > 0 we exclude the users that are unable
to communicate due to bad radio conditions and avoid the
problems due to division of zero in the calculation of the mean
of 1/B.
For circular cells and power law attenuation we obtain the
corresponding result as above by changing r → R and S(x) →
S α (x).
2) Estimation of RBs usage for several CBR sources: We
first estimate the RB usage for a fixed number of M CBR
sources located at distances r j from the antenna and with bitrate
requirements b CBR
j j = 1, ..., M. The total usage of RBs
β CBR will be the sum the individual contribution from each
source as given by (32):
β CBR =
M∑
j=1
β(r j , b CBR
j ). (35)
For the case with random location the expression gets even
simpler:
M∑
β CBR = β(R, b CBR
j ), (36)
j=1
i.e. we may add the CBR rates from all the sources in the cell.
The corresponding throughput for the CBR sources is taken
as the sum of the individual rates i.e.
b CBR =
M∑
j=1
b CBR
j (37)
B. Estimation of the capacity usage for a fixed number of
greedy sources
We shall estimate the capacity usage for a fixed number of
greedy sources under the following assumptions:
• There are totally K active (greedy) users that are placed
random in the cell which always have traffic to send, i.e.
we consider the cell in saturated conditions.
• There is totally N available RBs and the scheduled user
is granted all of them in a TTI interval.
1) Scheduling of based on metrics: In the following we
consider the case with K users that are located in a cell with
distances from the sender antenna given by a distance vector
r = (r 1 , ...., r K ) and we assume that the user scheduled in a
TTI is based on:
i schedul = arg max
i=1,..,K {M i}, (38)
where M i = M i (r) is the scheduling metric which also may
depend on the location of all users (through the location vector
r = (r 1 , ...., r K )). Hence, for the scheduler to choose user i,
the metric M i must be larger than all the other metrics (for
the other users), i.e. we must have M i > U i where
U i =
max
k=1,..,K
k≠i
M k . (39)
Since we assume that a user is granted all the RBs when
scheduled, this gives the cell throughput when user is scheduled
(located at distance r i ) to be NB(r i ), where B(r i ) is the
corresponding obtainable bit-rate per RB. Hence, cell bit-rate
distribution (with K users located in the cell with distance
vector r = (r 1 , ...., r K )) may then be written as:
B g (y, r) =
K∑
B i (y, r), where (40)
i=1
B i (y, r) = P (NB(r i ) ≤ y, M i (r) > U i (r)) (41)
is bitrate distribution when user i is scheduled. Unfortunately,
for the general case exact expression of the probabilities
B i (y, r) is difficult to obtain mainly due to the involvement of
the scheduling metrics. However, for some cases of particular
interest closed form analytical expression is possible to obtain.
For many scheduling algorithms the scheduling metrics is only
function of the SINR for that particular user (and does not
depend of the SINR for the other users) and for this case
extensive simplification is possible to obtain. In the following
we therefore assume that the metrics M i only are functions
of their own SINR i and the location r i for that particular
user, i.e. we have M i = M(S i , r i ), where we (for simplicity)
also assume that M(x, r i ) is an increasing function of x
with an unlikely defined inverse M −1 (x, r i ). The distribution
functions for M i and U i =
max
k=1,..,K
k≠i
M k are then
M i (x, r i ) = P (M i ≤ x) = S(M −1 (x, r i )) and (42)
K∏
U i (x, r) = P (U i ≤ x) = S(M −1 (x, r k )) (43)
k=1,k≠i
If we now condition on the value of S i = x in (41), we find
the distribution of the cell capacity when user i is scheduled
as:
B i (y, r) =
∫ ∞
x=0
(
P B(r i ) ≤ y )
∣ S i = x U i (M(x, r i ), r)s(x)dx.
N
(44)

ØSTERBØ: SCHEDULING AND CAPACITY ESTIMATION IN LTE 37
By using (14) as the obtainable bit-rate per RB for the discrete
case we find:
B i (y, r) =
∫
h(r i,λ)g j+1
x=0
F i (x, r)s(x)dx, if y/N ∈ (fc j , fc j+1 ]
for j = 0, 1, ..., 15, (45)
where we now have defined the multiuser “scheduling” function
F i (x, r) by:
F i (x, r) = U i (M(x, r i ), r) =
K∏
k=1,k≠i
S(M −1 (M(x, r i ), r k ))
(46)
Similar for the continuous case based on (17) as the
obtainable bit-rate per RB gives:
⎧
g(r ⎪⎨ i,λ)(e
∫
y/dN −1)
B i (y, r) =
F i (x, r)s(x)dx for y/dN < T
,
x=0
⎪⎩
p i (r)
for y/dN ≥ T
(47)
where p i (r) = ∫ ∞
x=0 F i(x, r)s(x)dx is the probability that user
is scheduled in a TTI (and therefore ∑ K
i=1 p i(r) = 1).
Finally, by assuming that all users are randomly located
throughout the cell the corresponding bit-rate distribution
is found by performing a K-dimensional averaging
over all possible distance vectors r, over the
cell; B g (y) = 1
A K ∫A . . . ∫ A r 1 . . . r K B cell (y, r)dA 1 · · · dA K ,
where A here is the cell area. Due to the special form
of the function F i (x, r) = ∏ K
k=1,k≠i S(M −1 (M(x, r i ), r k ))
the “cell averaging” over the K − 1 dimension variables
r 1 , . . . , r i−1 , r i+1 , . . . , r K (not including the variable r i )
[ ⌢S(M(x, ] K−1
yields the product ri ) where
∫
⌢ 1 S(y) =
A
A
uS(M −1 (y, u))dA(u) (48)
Hence, for the case when user i is located at distance r i
and all the K − 1 other users located at random, then we find
for the discrete case:
∫
B i (y, r i ) =
h(r i,λ)g j+1
x=0
[ ⌢S(M(x,
ri ))] K−1
s(x)dx, if y/N ∈ (fc j , fc j+1 ]
for j = 0, 1, ..., 15 (49)
and for the continuous case:
⎧
g(r i,λ)(e
∫
y/dN −1)
[
⎪⎨
⌢S(M(x, K−1
ri ))]
s(x)dx
B i (y, r i )=
x=0
for y/dN < T
⎪⎩
p i (r i ) for y/dN ≥ T,
(50)
where p i (r i ) = ∫ [
∞ ⌢S(M(x, K−1
ri ))]
x=0 s(x)dx is the probability
that user i is scheduled. (Observe that the p i (r) = p(r)
and B i (y, r) = B(y, r) only depend on the location r i and
hence are equal for all the users.)
For circular cell size the cell bit-rate distribution integrals
above is reduced to:
B g (y) = 2 ∫R
R 2
r=0
r
∫
h(r,λ)g j+1
x=0
[ ⌢S(M(x, ] K−1s(x)dxdr
K r))
if y/N ∈ (fc j , fc j+1 ] ; for j = 0, 1, ..., 15
(51)
for the discrete case and
⎧
⎨
R∫
2
B g (y) = R
rL(y, r)dr for y/dN < T
2
(52)
⎩
r=0
1 for y/dN ≥ T
where L(y, r) = ∫ [
g(r,λ)(e y/dN −1) ⌢S(M(x, ] K−1s(x)dx.
K
x=0 r))
For the continuous case where we now have
⌢
S(y) =
2
R 2
∫R
r=0
uS(M −1 (y, u))du (53)
The moments of the capacity (when the users are located
according to the vector r = (r 1 , ...., r K ) may be written as:
E[B g (r) k ] = f k N k
∫
∑
K h(r
∑15
i,λ)g j+1
c k j
i=1 j=1
x=h(r i,λ)g j
for the discrete bandwidth case and
E[B g (r) k ] =
⎛
∑
K
= d k N k ⎜
⎝
i=1
∫∞
+T k
g(r i,λ)(e T −1)
F i (x, r)s(x)dx (54)
∫
(ln(1+x/g(r i , λ))) k F i (x, r)s(x)dx
x=0
x=g(r i,λ)(e T −1)
⎞
⎟
F i (x, r)s(x)dx⎠ , (55)
for the continuous case.
The corresponding moments for the case where the users
are randomly located in a circular cell are given by:
E[Bg k ]= 2f k N k ∑15
R 2
∫ R
c k j r
j=1
r=0
⎧
⎪⎨
⎪⎩
⎫
∫ [ ⌢S(M(x, ] K−1
⎪⎬
K r)) s(x)dx
⎪⎭ dr
h(r,λ)g j+1
x=h(r,λ)g j
for the discrete bandwidth case and
E[B k g ] =
= 2dk N k
R 2
⎛
∫R
⎜
r⎝
r=0
∫∞
+T k
x=g(r,λ)(e T −1)
∫
g(r,λ)(e T −1)
x=0
(56)
( (
ln 1 + x )) k
L(x, r)s(x)dx
g(r, λ)
⎞
⎟
L(x, r)s(x)dx⎠ dr (57)
for the continuous case, where L(x, r) =
[ ⌢S(M(x, ] K−1.
K r))

38 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
2) Examples: Below we consider and compare three of the
most commonly known scheduling algorithms, namely Round
Robin (RR), Proportional Fair (PF) and Max SINR by applying
the cell capacity models described above.
a) Round Robin : For the Round Robin algorithm each
user is given the same amount of bandwidth and hence this
case corresponds to taking K = 1 i.e. the results in section II
may be applied by to find the cell capacity with f → Nf and
S(x) → S su (x) and also S α (x) → S suα (x).
b) Proportional Fair (in SINR) : Normally, the shadowing
is varying over a much longer time scale than the TTI
intervals, and hence we may assume that the slow fading is
constant during the updating of the scheduling metric M i and
therefore should only account for the rapid fading component.
This means that the shadowing effect may be taken as constant
that may be included in the non varying part of the SINR
over several TTI intervals. Hence, we take SINR as S t /g(r; λ)
where S t = zX e conditioned that the shadowing X ln = z. By
assuming that X ln = z is constant over the short TTI intervals
zXe/h(ri,λ)
zE[X =
e]/h(r i,λ)
the scheduling metrics will be M i =
In the final result we then “integrate over the Log-normal
slow fading component”. We find that the probability of being
scheduled is p(r) = 1 K
and that the conditional bandwidth
distribution for a user at located at distance r (and the K − 1
users random located) is given by the results in section II-D
with f → Nf and S(x) → S K (x) with:
S K (x) =
s K (x) =
∫ ∞
t=0
∫ ∞
t=0
S e
( x
t
) K
sln (t)dt and
Xe
E[X . e]
K
( x
) K−1 ( x
)
t S e se s ln (t)dt, (58)
t t
where S e (x) = 1 − e −x and s e (x) = e −x .
Further, the distribution of the cell capacity is given by
the results in section II-E with f → Nf and further the α-
averaging is given by the integrals:
˜S Kα (x) =
s Kα (x) =
∫ ∞
t=0
∫ ∞
t=0
KS e (t) K−1 s e (t) ˜S lnα
( x
t
KS e (t) K−1 s e (t)t −1 s lnα
( x
t
)
dt and (59)
)
dt (60)
c) Max SINR algorithm.: For this algorithm the scheduling
metric is M i = S i /h(r i , λ). By assuming circular cell size
and radio signal attenuation on the form h(r, λ) = h(λ)r α
gives:
⌢
S(M(x, r)) =
2
R 2
∫R
uS(x(u/r) α )du = S α (x(R/r) α ). (61)
r=0
We find that the probability of being scheduled
p(r) =
∫ ∞
x=0
[S α (x(R/r) α )] K−1 s(x)dx (62)
and that the conditional bandwidth distribution for a user
located at distance r (and the K − 1 users random located)
is given by the results in section II-D with f → Nf and
S(x) → S c (x; r) with:
S c (x; r) = 1
p(r)
∫ x
y=0
[S α (y(R/r) α )] K−1 s(y)dx (63)
It turns out that extensive simplifications occur for the case
where all the users are randomly located in the cell and we find
that the distribution of the cell capacity is given by the results
in section II-E with f → Nf and further the α-averaging
is given by taking S α (x) → S α (x) K i.e. is simply the K’th
power of the α-averaging of S(x).
C. Combining real-time and non real time traffic over LTE
We are now in the position to combine the analysis in
sections III.A and III.B to obtain complete description of the
resource usage in a LTE cell. The combined modeling is based
on the following assumptions:
• There are M CBR sources applying one of the allocation
options described in section III.A.
• There are totally K active (greedy) data sources which
always have traffic to send, i.e. we consider the cell in
saturated conditions.
• The number of available RBs is taken to be N.
Since the CBR sources have “absolute” priority over the data
sources, they will always get the number of RBs they need
and hence the leftover RBs will be available for the Non-
GBR data sources. By conditioning on the RB usage of the
GBR sources we may apply all the results derived in section
III.B with available RBs taken to be the leftover RBs not used
by the CBR sources. Then we may find the average usage of
RBs for the CBR traffic as done in section III.A.
We consider first the case where the location of the sources
is given:
• CBR sources are located at distances s j from the antenna
with bit-rate requirements b CBR
j ; j = 1, ..., M.
• The greedy data sources are located at distance r i (i =
1, ..., K).
With these assumptions the mean cell throughput is given
as:
B cell =
⎛
⎞
M∑
K∑ ∑15
=f⎝N−
β(s j , b CBR ⎠
+
M∑
j=1
j=1
j )
c j
h(r i,λ)g j+1
i=1 j=1
x=h(r i,λ)g j
∫
F i (x, r)s(x)dx +
b CBR
j , (64)

ØSTERBØ: SCHEDULING AND CAPACITY ESTIMATION IN LTE 39
for the discrete bandwidth case and
B cell =
⎛
⎞ ⎛
M∑
K∑
= d ⎝N − β(s j , b CBR ⎠ ⎜
⎝V i (x, r) +
T
∫ ∞
x=g(r i,λ)(e T −1)
j=1
j )
j=1
i=1
⎞
⎟
M∑
F i (x, r)s(x)dx⎠ + b CBR
j , (65)
for the continuous bandwidth case; where V i (x, r) =
∫ g(ri,λ)(e T −1)
x=0
ln(1 + x/g(r i , λ))F i (x, r)s(x)dx, β(r, b CBR )
is given by by (32) and further F i (x, r) is defined by (46). For
circular cells and power law attenuation on the form h(r, λ) =
h(λ)r α and randomly placed sources the corresponding cell
throughput is found to:
where
B cell =
⎛
M∑
= f ⎝N − β(R,
+
V j (x, r) =
M∑
j=1
∫ R
r=0
b CBR
j )
j=1
⎞
⎠ 2 ∑15
R 2 c j V j (x, r)
j=1
b CBR
j (66)
⎧
⎪⎨
r
⎪⎩
h(r,λ)g
∫ j+1
x=h(r,λ)g j
K
for the discrete bandwidth case and
B cell =
= d(N − β(R,
+T
∫ ∞
x=g(r,λ)(e T −1)
M∑
j=1
[ ⌢S(M(x, r))
] K−1s(x)dx
⎫
⎪⎬
⎪ ⎭
dr
b CBR
j )) 2 ∫R
R 2
r=0
r
⎧
⎪⎨
V (x, r)
⎪⎩
⎫
[ ⌢S(M(x, ] K−1
⎪⎬ M
K r)) s(x)dx
⎪⎭ dr + ∑
j=1
b CBR
j
(67)
for the continuous bandwidth case; where V (x, r) =
∫ [ g(r,λ)(e T −1)
⌢S(M(x, ] K−1
ln(1 + x/g(r, λ))K
x=0 r)) s(x)dx,
β = β(r, b CBR ) is given by (32) and further ⌢ S(M(x, r)) is
defined by (53). Observe that the CBR traffic only will affect
the cell throughput by the sum ∑ M
j=1 bCBR j of the rates and
not the actual number of CBR sources.
IV. DISCUSSION OF NUMERICAL EXAMPLES
In the following we give some numerical example of
downlink performance of LTE. Before describing the results
we first rephrase some of the main assumptions:
• The fading model includes lognormal shadowing (slow
fading) and Rayleigh fast fading.
• The noise interference is assumed to be constant over the
cell area.
Parameters
TABLE II
INPUT PARAMETERS FOR THE NUMERICAL CALCULATIONS
Bandwidth per Resource Block
Total Numbers of Resource Blocks
(RB)
Distance-dependent path loss. (The
actual model is found in [4].)
Lognormal Shadowing with standard
deviation
Rayleigh fast fading
Noise power at the receiver
Total send power
Numerical values
180 kHz=12x 15 kHz
100 RBs for 2Ghz
L = C + 37.6 log 10 (r),
r in kilometers and
C=128.1 dB for 2GHz,
8 dB (in moust of the cases)
-101 dBm
46.0 dBm=(40W)
Radio signaling overhead 3/14
• The cell shape is circular.
Basically, there are three different cases we would like to
investigate. First and foremost is of course the actual efficiency
of the LTE radio interface. We choose the bitrate obtainable for
the smallest unit available for users, namely a Resource Block
(RB). Since different implementation may chose different
bandwidth configurations the performance based on RBs will
give a good indication of the overall capacity/throughput
for the LTE radio interface. Secondly, we know that the
scheduling also will affect the overall throughput for a LTE
cell. Based on the modeling we are able to investigate the
performance of the three basic scheduling algorithms: Round
Robin (RR), Proportional Fair (PF) and Max-SINR. All these
three algorithms have their weaknesses and strengths, like
Max-SINR that try to maximize the throughput but at the cost
of fairness among users. Thirdly, we would also investigate
the effect on overall performance by introducing GBR traffic
in LTE. Normally, GBR traffic will higher priority than Non-
GBR or “best effort” traffic and to guarantee a particular rate
the number of radio resources required may vary depending
on the radio conditions. For users with bad radio conditions
i.e. located at cell edge the resource usage to maintain a
fixed guaranteed rate may be quite high so an investigation
of the cell performance with both GBR and Non-GBR will be
important.
A. LTE spectrum efficiency
First, we consider bitrate that is possible to obtainable for
the basic resource unit in LTE namely a RB. In the examples
we have considered sending frequency of 2 GHz. The aim is
to predict the bandwidth efficiency, i.e. the obtainable bitrate
per RB. The rest of the input parameters are given in Table 2.
The mean obtainable bitrate per RB is depicted in Figure
3. With our assumptions the maximum bitrate is just below
0.8 Mbit/s for excellent radio conditions. The mean bit-rate is
as expected a decreasing function of the cell size both for a
randomly placed user and for a user at the cell edge. The mean
bitrate have decreased to 0.1 Mbit/s per RB for cell sizes of
approximately 2 km for shadowing std. equals 8 dB and when
users are random located. The corresponding bit-rate for users
at the cell edge is proximately 0.04 Mbit/s.

40 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
0.8
80
Mean
throughpu
t pe
r R B @ Mbi
t êsD
0.7
0.6
0.5
0.4
0.3
0.2
Located at cell
edge
Random
location
C ell c apacit y @ M bi t êsD
70
60
50
40
30
20
-- PF
-- Max-SINR
-- RR
0.1
10
1 2 3 4 5
Distance @KmD
1 2 3 4 5
Distance @KmD
Fig. 3. Mean throughput right and std. left per RB for a user random located,
and fixed located as function of cell radius with 2 GHz sending frequency and
Suzuki distributed fading with std. of fading σ=0dB, 2dB, 5dB, 8dB, 12dB
from below.
B. Cell capacity and scheduling
Below we examine the downlink performance in an LTE cell
with the input parameters given by Table 2, however, with the
following additional input parameters:
• Type of scheduling algorithm i.e. RR, PF or Max-SINR,
• number of RB available i.e. 100,
• number of active (greedy) users.
In Figure 4 the mean downlink cell capacity is depicted
as function of the cell radius for RR, PF and the Max
SINR scheduling algorithms. As expected the Round Robin
algorithm gives the lowest cell throughput while the Max
SINR algorithm give the highest throughput. For the latter
the multiuser gain is huge and may be explained from the
fact that when the number of users increases those who by
chance are located near the sender antenna will with high
probability obtain the best radio condition and will therefore be
scheduled with high bit-rate. For users located at the cell edge
the situation is opposite and those users will normally have low
SINR and surely obtain very little of the shared capacity. This
explains why the Max SINR will increase the throughput but
is highly un-fair. For the PF only the relative size of the SINR
is important and in this case each user has equal probability
of sending in each TTI. The multiuser gain for this algorithm
is much lower than for the Max SINR algorithm but is not
negligible. When it comes to actual cell downlink throughput
the expected values lays in the range 26-48 Mbit/s for cells
with radius of 1 km while if the radius is increased to 2 km
the cell throughput is reduced to approximately 10-20 Mbit/s.
As seen from Figure 4 the Max-SINR algorithm will over
perform the PF algorithm when it comes to cell throughput.
But if we consider fairness among users the picture is complete
different. When considering the performance of users located
at cell edge the Max-SINR algorithm actually performs very
badly. While PF give equal probability of transmitting in a
TTI for all active users the Max-SINR strongly discriminate
the user close to cell edge. As seen from Table 3 below; if there
are totally 10 active users in a cell the PF fairly give each user
10% chance of accessing radio resource while the Max-SINR
Fig. 4. Multiuser gain as function of cell radius for Max-SINR (red), PF
(blue) and RR (black) scheduling, 2GMHz frequency with 100 RB and with
Suzuki distributed fading with std. σ = 8 dB. The number of users is 1, 2,
3, 5, 10, 25, 100 from below.
TABLE III
PROBABILITY THAT A USER IS SCHEDULED AS FUNCTION OF NUMBERS OF
USERS AND LOCATION FOR PF AND MAX-SINR SCHEDULING
ALGORITHMS, SUZUKI DISTRIBUTED FADING WITH STD. OF 8DB.
Number of users PF MAX-SINR
r/R=1 r/R=0.5 r/R=0.25 r/R=0.1
2 0.50 0.308708 0.594756 0.82579 0.96119
3 0.33 0.147869 0.414839 0.71126 0.92784
5 0.20 0.055113 0.245871 0.56102 0.87130
10 0.10 0.012690 0.104912 0.36531 0.76418
25 0.04 0.001356 0.025222 0.16326 0.56989
100 0.01 0.000019 0.001293 0.02453 0.24325
only give 1.2% chance of accessing the radio resources if a
user is located at cell edge. As the number of user increases
this unfairness increases even more.
Table 3 demonstrates one of the unfortunate properties of
the MAX-SINR scheduling algorithm. While the PF algorithm
distribute the capacity among the users with equal probability
the MAX-SINR algorithm is far more unfair when it comes to
the distribution of the available radio resources. For instance,
the users located at the cell edge e.g. r/R=1 will suffer from
extremely poor performance if the numbers of users is higher
than 10. The Max-SINR algorithm will also be unfair for
small cell sizes where users actually may have so high signal
quality that most of them may use coding with high data rate
i.e. 64 QAM with high rare and there should be no need for
scheduling according highest SINR to obtain high throughput.
C. Use of GBR in LTE
It is likely the LTE in the future will carry both real time
type traffic like VoIP and elastic data traffic. This is possible
by introducing GBR bearers where users are guaranteed the
possibility to send at their defined GBR rate. The GBR traffic
will have priority over the Non-GBR traffic such that the RBs
scheduled for GBR bearers will normally not be accessible
for other type of traffic. However, the resource usage over
the radio interface in LTE will strongly depends on the radio

ØSTERBØ: SCHEDULING AND CAPACITY ESTIMATION IN LTE 41
conditions. This means that the amount of radio resources a
user occupies (to obtain a certain bit rate) will vary according
to the local radio conditions and a user at the cell edge must
seize a larger number of resource blocks (RBs) to maintain a
constant rate (GBR bearer) than a user located near the antenna
with good radio signals.
An interesting example is to see the effect of multiplexing
traffic with both greedy and GBR users and observe the effect
on the cell throughput. In Figure 5 we consider the cases where
10 greedy users are scheduled by the PF algorithm together
with a GBR user with guaranteed rate of 3, 1, 0.3 or 0.1 Mbit/s.
We consider the cases where either the GBR user is located
at cell edge or have random location throughout the cell.
We observe that thin GBR connections do not have big
impact on the cell throughput. From the figures it seems that
GBR bearers up to 1 Mbit/s should be manageable without
influencing the cell performance very much. But a 3 Mbit/s
GBR connection will lower the total throughput by a quite big
factor especially if the user is located at cell edge. For instance
we observe for both cases that the effective reduction in cell
throughput is approximately 20 Mbit/s for a user requiring a
3 Mbit/s GBR connection when located at cell edge. As a
consequence we recommend limiting GBR connection to less
than 1 Mbit/s.
We therefore recommend using high GBR values with
particular caution. The GBR should be limited to a maximum
rate to avoid that a particular GBR user consumes a too large
part of the radio resources (too many RBs). A good choice of
the actual maximum GBR value seems to be around 1 Mbit/s.
V. CONCLUSIONS
With the introduction of LTE the capacity in the radio
network will increase considerably. This is mainly due to the
efficient and sophisticated coding methods developed during
the last decade. However, the cost of such efficiency is that
the variation due to radio conditions will increase significantly
and hence the possible capacity for users in terms of bitrate
will vary a lot depending on the current radio conditions.
The two most important factors for the radio conditions are
fading and attenuation due to distance. By extensive analytical
modeling where both fading and the attenuation due the
distance are included we obtain performance models for:
• Spectrum efficiency through the bitrate distribution per
RB for customers that are either randomly or located at
a particular distance in a cell.
• Cell throughput/capacity and fairness by taking the
scheduling into account.
• Specific models for the three basic types of scheduling
algorithms; Round Robin, Proportional Fair and Max
SINR.
• Cell throughput/capacity for a mix of GBR and Non-GBR
(greedy) users.
Numerical examples for LTE downlink show results which are
reasonable; in the range 25-50 Mbit/s for 1 km cell radius at
2GHz with 100 RBs. The multiuser gain is large for the Max-
SINR algorithm but also the Proportional Fair algorithm gives
relative large gain relative to plain Round Robin. The Max-
SINR has the weakness that it is highly unfair in its behaviour.
C ell c apacit y @ M bi t êsD
C ell c apacit y @ M bi t êsD
C ell c apacit y @ Mbi
t êsD
C ell c apacit y @ M bi t êsD
80
70
60
50
40
30
20
10
80
70
60
50
40
30
20
10
80
70
60
50
40
30
20
10
80
70
60
50
40
30
20
10
0.5 1 1.5 2 2.5
Distance @KmD
0.5 1 1.5 2 2.5
Distance @KmD
GBR=0.3 Mbit/s
-- Non-Persistent, cell edge
-- Non-Persistent, random
-- mean PF 10 users
GBR=1 Mbit/s
0.5 1 1.5 2 2.5
Distance @KmD
GBR=0.1 Mbit/s
-- Non-Persistent, cell edge
-- Non-Persistent, random
-- mean PF 10 users
GBR=3 Mbit/s
-- Non-Persistent, cell edge
-- Non-Persistent, random
-- mean PF 10 users
-- Non-Persistent, cell edge
-- Non-Persistent, random
-- mean PF 10 users
0.5 1 1.5 2 2.5
Distance @KmD
Fig. 5. Mean cell throughput for PF, 10 users and a GBR user of 3.0,
1.0, 0.3, 0.1 Mbit/s using non-persistent scheduling, for 2 GHz and 100 RB
and Suzuki distributed fading with std. σ = 8dB. Red curves corresponds to
random location and blue for user located at cell edge.

42 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
User at cell edge with poor radio condition will obtain very
little data throughput. It turns out that the grade of unfairness
increases with the numbers of active users. This unfortunate
property is not found for the Proportional Fairs scheduling
algorithm.
The usage of GBR with high rates may cause problems in
LTE due to the high demand for radio resources if users have
low SINR i.e. at cell edge. For non-persistent GBR allocation
the allowed guaranteed rate should be limited. It seems that a
limit close to 1 Mbit/s will be a good choice.
REFERENCES
[1] H. Holma and A. Toskala, LTE for UMTS, OFDMA and SC-FDMA Based
Radio Access. Wiley, 2009.
[2] R.-. 3GPP TSG-RAN1#48, “LTE physical layer framework for performance
verification,” 3GPP, St. Louis, MI, USA, Tech. Rep., Feb. 2007.
[3] H. Kushner and P. Whiting, “Asymptotic Properties of Proportional-
Fair Sharing Algorithms,” in Proc. of 2002 Allerton Conference on
Communication, Control and Computing, Oct. 2002.
[4] 3GPP TS 36.213 V9.2.0, “Physical layer procedures, Table 7.2.3-1: 4-bit
CQI Table,” 3GPP, Tech. Rep., Jun. 2010.
[5] M. C, M. Wrulich, J. C. Ikuno, D. Bosanska, and M. Rupp, “Simulating
the Long Term Evolution Physical Layer,” in Proc. of 17th European
Signal Processing Conference (EUSIPCO 2009), Glasgow, Scotland, Aug.
2009.
[6] B. Sklar, “Rayleigh Fading Channels in Mobile Digital Communication
Systems Part I: Characterization and Part II: Mitigation,” IEEE Commun.
Mag., Jul. 1997.
Olav N. Østerbø received his MSc in Applied Mathematics from the
University of Bergen in 1980 and his PhD from the Norwegian University
of Science and Technology in 2004. He joined Telenor in 1980. His main
interests include teletraffic modeling and performance analysis of various
aspects of telecom networks. Activities in recent years have been related
to dimensioning and performance analysis of IP networks, where the main
focus is on modeling and control of different parts of next generation IPbased
networks.

ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011 43
Multi-service Load Balancing in a Heterogeneous
Network with Vertical Handover
Jie Xu, Yuming Jiang, Andrew Perkis, and Elissar Khloussy
Abstract—In this paper we investigate multi-service load balancing
mechanisms in an overlay heterogeneous WiMAX/WLAN
network through vertical handover. Considering the service characteristics
of the overlay heterogeneous network together with
the service requirements of different applications, all streaming
applications are served in WiMAX while elastic applications
are distributed to WiMAX and WLAN. Two load balancing
mechanisms are compared which switch the elastic application
with maximum (MAX) and minimum (MIN) remaining size
respectively to WLAN. Simulation results indicate that MIN
outperforms MAX at the cost of significantly increased number
of load balancing actions. Furthermore, it is discovered that both
load balancing granularity and proper integration of streaming
and elastic applications in WiMAX determine the whole system
performance.
Index Terms—vertical handover, wireless heterogeneous networks,
load balancing, multi-service
I. INTRODUCTION
AFTER decades of research, it is commonly believed that
future wireless network will employ multiple techniques.
Especially, for the access part, multiple radio access technologies
(RATs) will coexist in terms of both space and time. For
example, nowadays there are already lots of WLAN networks
which are also covered by other 3G mobile networks at the
same time.
The coexistence of heterogeneous networks brings up both
challenges and opportunities for providing better wireless
service [1]. On the one hand, since wireless communications
are intrinsically limited by interference, activities of different
networks could interfere with each other and may result in
severe service degradation. On the other hand, multiple overlay
heterogeneous networks can provide more robust communication
guarantee if they could cooperate instead of competition.
Therefore, how to integrate coexisted multiple networks is
of fundamental importance to the success of future wireless
networks.
To take advantage of multiple heterogeneous wireless networks,
vertical handover [1] has been proposed as a means
for enhancing end users’ service quality. Traditionally, due
to its operation difficulty and introduced time delay, vertical
handover is used as a reactive measure to prevent severe service
degradation. Normally vertical handover is only triggered
Jie Xu, Yuming Jiang and Andrew Perkis are with the Centre for Quantifiable
Quality of Service in Communication Systems, Norwegian University of
Science and Technology in Trondheim.
Elissar Khloussy is with Department of Telematics, Norwegian University
of Science and Technology in Trondheim.
Center for Quantifiable Quality of Service in Communication Systems,
Center of Excellence, is appointed by the Research Council of Norway, and
funded by the Research Council, NTNU and UNINETT.
when the served mobile user are about to move out of the
coverage range of current serving network. To this end, various
vertical handover mechanisms have been proposed to improve
the performance of handover user [2][3].
Recently, proper vertical handover are also used as a proactive
means to improve the system performance. In [4][5],
vertical handover is adopted as a tool for joint resource management
in heterogeneous networks. The objective of vertical
handover has been extended to include the whole system
performance instead of the performance of handover user. In
particular, the main idea is to distribute traffic load among
heterogeneous networks in a balanced manner by designing
vertical handover protocols. However, only streaming users
are considered in these studies although the current wireless
network normally serve multi-service applications. In [6], both
streaming and elastic applications are considered. The authors
preferably distribute streaming applications to cellular network
because of its larger coverage and finer QoS guarantee, and the
remaining capacities in cellular/WLAN networks are utilized
for serving elastic applications. While the scheme in [6]
performs well compared to random dispatch, there are still
chances that streaming applications are distributed to WLAN
and vertical handover is triggered whenever there are enough
free capacities in the cellular network.
In this study, we consider system performance of an overlay
heterogeneous wireless network where elastic applications
share network capacity with prioritized streaming applications.
Specifically, we consider the WiMAX/WLAN heterogeneous
network and assume all the traffic firstly arrives to
the WiMAX network. Streaming applications are given strict
preemptive priority over elastic applications in WiMAX. Then
according to the comparison result of expected finish time
in WiMAX and WLAN, vertical handover of certain elastic
applications on their arrivals or during their service to WLAN
is conducted. We compare the performance of two different
handover mechanisms which selected the file with maximum
and minimum remaining size for handover respectively. The
results indicate that selection of files with minimum remaining
size outperforms the other mechanism at the cost of significant
increased number of handovers. Furthermore, based on
analysis of simulation results, we conclude that both the load
balancing granularity and integration of elastic and streaming
applications in WiMAX determine the performance of the
whole system.
The remaining of this paper is arranged as follows. The
system model is described in the next section. In section II, due
to the complexity of exact analysis, theoretical approximations
are given. In Section IV, we describe the simulation results,

44 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
Fig. 1.
WiMAX
WLAN
(a) typical application scenario.
System model.
Streaming applications
Elastic applications
Scheduling
WiMAX
Load balancing
Scheduling
(b) abstraction.
WLAN
followed by discussions in Section V. Finally, we conclude
the paper in Section VI.
II. SYSTEM MODEL
A. WiMAX/WLAN Heterogeneous Network
The network scenario of this study is shown in Fig. 1(a).
Within the coverage area of the WiMAX network, there are
multiple WLAN networks as well. WiMAX is infrastructurebased
and can provide guaranteed service with centralized
control. In addition, as one option for the future mobile
networks, WiMAX has a large coverage area but limited rate
to each end user. On the other hand, WLAN is contention
based and incapable of providing service guarantee. However,
since WLAN uses free frequency it can provide higher data
rate to end users if the network is not congested. Therefore,
WiMAX and WLAN networks are complementary in terms
of service characteristics. It is beneficial to design the overlay
heterogeneous network in a cooperative way.
One possible way of cooperation is to distribute different
types of applications to specific network by taking account of
both the service requirement of applications and the network
service characteristic. In this study, the cooperation scheme is
shown in Fig. 1(b). Specially, all the streaming applications are
served in WiMAX due to their stringent service requirements.
Then the remaining service capacity of WiMAX and the total
service capacity of WLAN are devoted to elastic applications.
Furthermore, to prevent the disturbance of elastic applications,
streaming applications are served with higher preemptive
priority. Namely the streaming applications arrives and leaves
without any disturbance of elastic applications.
For streaming applications, the system can be modeled as
an G/G/K loss-queue system. Specifically, if we assume the
streaming applications arrive according to Poisson process and
the duration follows minus exponential distribution, then the
system can be seen as M/M/K Erlang system for which lots
results have been obtained. Suppose the capacity of WiMAX is
C wimax , then the number of channels K can be calculated as
⌊C wimax /B s ⌋ where B s is the bandwidth requirement of each
streaming application. In this study, when there are already
K streaming applications in the system, the new streaming
arrivals will be simply rejected and discarded.
For elastic applications, both the remaining capacity of
WiMAX and the total capacity of WLAN can be utilized. Due
to the dynamic state of streaming applications, the remaining
capacity of WiMAX varies. For WLAN, we assume the total
capacity is fixed to simplify the analysis. Therefore, there are
actually two servers for elastic applications. In each server,
residing elastic applications share the capacity in processorsharing
(PS) manner. In particular, no requirements on the
maximum or minimum bandwidth for each elastic application
is specified.
B. Load Balancing Mechanisms
Real-time load balancing is performed on application arrivals
and departures as the network state only changes on
these occasions. Once the network state changes, whether load
balancing action should be conducted is checked in order to
improve the performance of elastic applications. According to
the application arrival assumption, in this study we perform
unidirectional handover check only from WiMAX to WLAN.
Two types of load balancing actions could be triggered
depending on the system states. One kind of action is vertical
handover which switches elastic applications that have
already been served partly by WiMAX to WLAN. To proceed
handover, both criteria for handover check and handover
candidate selection need to be clearly defined. In fact, lots of
efforts have been devoted to propose efficient algorithms since
they actually determine the handover performance [3][2]. We
conduct handover check based on the expected finish time of
elastic applications. Since existing elastic applications share
the service in PS way, the expected finish time can be linearly
represented by service rate. Then these mechanisms actually
belong to the bandwidth-based handover decision mechanisms.
The service rates in two networks under current condition
are compared and a handover decision is made if the service
rate could be increased after handover. Handover candidate is
selected from all the elastic applications in WiMAX including
the newly arrival. Specifically, we select handover application
based on remaining size. Two mechanisms which select the
file with maximum and minimum remaining size respectively
are tested. Later we refer the two mechanisms as MAX
and MIN for convenience. In real applications the remaining
size is difficult to get and may introduce lots of complexity.
However, since we determine remaining size on flow level, the
complexity introduced can be seen as affordable.
The other kind of action is dispatching which switches the
elastic application on its arrival to WLAN. Because we assume
all traffic initially arrives to WiMAX, dispatching can be seen
as one special case of vertical handover. However, it should
be noted that the actual cost for dispatching is much lighter
compared with vertical handover since the application has not
been served yet.
C. Performance Metrics
For the aforementioned system model, we are only interested
in the performance of elastic applications since the performance
of streaming applications does not change with the
adopted load balancing mechanism. Specifically, we consider
three common performance metrics for elastic applications as
follows.
• Average sojourn time: The sojourn time defines the
time interval of elastic application from its arrival to
its departure. As users are very sensitive to duration of

XU et al.: MULTI-SERVICE LOAD BALANCING IN A HETEROGENEOUS NETWORK WITH VERTICAL HANDOVER 45
elastic application, this metric is highly related to the user
experience of service quality.
• Time-average throughput: The time-average throughput
defines the ratio of total service amount to total service
time. This metric can be seen as an indicator of system
performance in terms of service capability.
• Call-average throughput: The call-average throughput defines
the mean of individual ratios of service size to
its service time. This metric integrates the influence
of service size on users’ expectation of service time.
Therefore, it is believed to be the best metric representing
the users’ quality of experience (QoE) [7].
In addition, another important metric for load balancing
mechanisms is the number of load balancing actions. Although
no specific cost is considered in this paper, it is still beneficial
to compare the number of load balancing actions as normally
costs of these actions do not vary with different applications.
In addition, due to different costs of vertical handover and
dispatch, we record both of them in simulations respectively.
III. THEORETICAL APPROXIMATION
It is usually fairly complicated to exactly analyze system
performance when integrated services are involved [8][9][10].
Therefore, in this section, we provide a simple approximation
for theoretical analysis of our system model. The simplified
analysis results provide a reference for further comparisons
with our simulation results.
First, the two servers are approximated as one server with
capacity C = C wimax + C wlan . With this approximation,
the system becomes the traditional integrated service system
where elastic applications share the server capacity with prioritized
streaming applications. However, even for this simplified
system, the calculation of stationary results is still very difficult
since no closed formulation can be derived [7].
However, approximate results can be calculated with either
of the two quasi-stationary assumptions. One quasi-stationary
condition assumes elastic applications evolve much faster than
streaming applications. This assumption is reasonable since
the streaming applications usually last longer than elastic
applications. However, theoretical derivation based on this
assumption can only be obtained for rather light elastic traffic
since it requires uniform stationarity [8].
In our analysis, we take the other quasi-stationary condition
which assumes streaming applications evolve much faster than
elastic applications. While this assumption is not quite reasonable,
it can provide upper performance bounds for elastic
applications [8]. In this case, the service devoted to elastic
application can be approximated as the total capacity minus
the average aggregated service rates of streaming applications.
Based on the former simplification, we could get approximate
results for elastic applications. Specifically, since elastic
applications share the capacity with processor-sharing policy,
insensitivity of PS policy to service distribution can be applied.
The average throughput can be expressed as C e ∗(1−ρ e ), and
the mean sojourn time can be expressed as
E[T ] =
E[x]
C e ∗ (1 − ρ e )
(1)
Average sojourn time (s)
Fig. 2.
1.4
1.2
1
0.8
0.6
0.4
0.2
0
MAX
MIN
Theoretical approximation
0.2 0.4 0.6 0.8 1
ρ e
Average sojourn time with minus exponential distributed file size.
where ρ s and ρ e represent the load of streaming and elastic
applications respectively with respect to the capacity of
WiMAX. In addition, C e = C(1−(1−P b )∗ρ s ), E[x] denotes
the average size of elastic applications and P b is the blocking
probability of streaming applications.
IV. NUMERICAL RESULTS
To evaluate the performance of the two handover mechanisms,
we have conducted extensive simulations with varying
parameters. Each simulation result is obtained based on the
average of 30 runs with different seeds. In each run, we simulate
10 6 files and remove the initial stage of the first 5 × 10 3
files. The results of 30 runs are checked with Skewness and
Kurtosis which ensure these runs follow a normal distribution.
This guarantees the validation of our simulation results.
The values of simulation parameters are listed in Tab. I.
Specifically, we calculate ρ e based on the capacity of WiMAX.
A. Exponential Distribution
First we assume the size of elastic applications follows exponential
distribution, which has been assumed and analyzed
extensively for traffic modeling.
In Fig. 2, the average sojourn time of finished files is shown.
It can be seen that for exponential distributed files, the average
sojourn time with MAX is sightly longer than that with MIN.
TABLE I
SIMULATION PARAMETERS
Parameters Meaning Values
C wimax WiMAX capacity 1000 kbps
C wlan WLAN capacity 600 kbps
B s Bandwidth of streaming applications 50 kbps
ρ s Load of streaming applications 0.3
ρ e Load of elastic applications 0.1-1.1
1/µ s Average length of streaming applications 140 s
1/µ e Average size of elastic applications 64 kbits

46 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
Average throughput (kbps)
1200
1000
800
600
400
MAX, call−average throughput
MIN, call−average throughput
MIN, time−average throughput
MAX, time−average throughput
Theoretical approximation
Times
10
5
MAX, dispatch
MAX, handover
MIN, dispatch
MIN, handover
200
0
0.2 0.4 0.6 0.8 1
ρ e
0
15 x 105 ρ e
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
Fig. 3.
Average throughput with minus exponential distributed file size.
Fig. 4.
size.
Dispatch and handover times with minus exponential distributed file
However, compared with the theoretical approximation, the
performance of MAX and MIN are worse. In particular, when
the traffic load is heavy, the average sojourn time of finished
files with MAX and MIN increases very rapidly.
In Fig. 3, the average throughput performance is shown.
It can be seen that the throughput performance of MIN is
better than MAX as well. The time-average and call-average
throughputs are similar for low-load elastic traffic and the gap
increases as the load of elastic applications becomes heavier.
The main reason for the fast decay of call-average throughput
of heavy-loaded elastic applications is the fast increase of
average sojourn time as shown in Fig. 2. However, the averagetime
throughput is not heavily influenced by sojourn time as
it only depends on the system throughput. In addition, when
the load of elastic applications is low, the simulation results
of both MAX and MIN are fairly worse than the theoretical
approximation. However, with the increase of elastic traffic
load, the performance of MAX and MIN first gets closer to and
then the time-average throughput outperforms the theoretical
approximation. The reason for this performance alternation is
due to the use of the service capacity of WLAN for heavyloaded
elastic applications. When the load of elastic applications
is low, almost all the elastic applications are served in
WiMAX according to the handover criteria. However, with
increasing load of elastic applications, more and more files
are dispatched or handovered to WLAN. Thus all the service
capacities of WiMAX and WLAN are utilized when the load
of elastic applications are heavy enough.
In Fig. 4 the dispatch and handover times are shown to
illustrate the cost of each load balancing mechanism. It can
be seen that MIN introduces much more load balancing actions
(dispatch/handover) than MAX and even two times more when
the load of elastic applications is heavy. Moreover, MIN
adopts much more handovers than MAX while the numbers
of dispatch for two mechanisms are comparable.
In summary, for exponential distributed files, the performance
results of MAX and MIN are similar. However, MIN
introduces much more operation costs with a large number of
Average sojourn time (s)
Fig. 5.
0.4
0.35
0.3
0.25
0.2
0.15
0.1
MAX
MIN
0.05
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
ρ e
Average sojourn time with Pareto distributed file size.
load balancing actions. Therefore, we prefer MAX to MIN
with consideration of overall performance in this context.
B. Pareto Distribution
For realistic applications, it is believed that the size of
elastic applications follows heavy-tailed distribution. Normally
Pareto distribution is chosen as the representative heavy-tailed
distribution especially for file sizes. Therefore, we also present
results with Pareto distributed file sizes. Specifically, we take
the shape parameter as 1.2 which is a typical value for Pareto
distribution.
In Fig. 5, the average sojourn time is shown. Compared
with Fig. 2, there are two major differences. First, the average
sojourn time with Pareto distributed file sizes is shorter than
that with exponential distribution. This phenomenon has been
stated in [11] and the reason is that Pareto distribution has
higher variability than exponential distribution. Second, the
difference between MAX and MIN is more visible with

XU et al.: MULTI-SERVICE LOAD BALANCING IN A HETEROGENEOUS NETWORK WITH VERTICAL HANDOVER 47
Average throughput (kbps)
1200
1000
800
600
400
MAX, call−average throughput
MIN, call−average throughput
MIN, time−average throughput
MAX, time−average throughput
Theoretical approximation
Times
12
10
8
6
4
MAX, dispatch
MAX, handover
MIN, dispatch
MIN, handover
200
2
0
0.2 0.4 0.6 0.8 1
ρ e
0
14 x 105 ρ e
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
Fig. 6.
Average throughput with Pareto distributed file size.
Fig. 7.
Dispatch and handover times with Pareto distributed file size.
Pareto distributed file sizes. Moreover, for heavy-loaded elastic
applications, MIN provides shorter average sojourn time than
the theoretical approximation. In fact, since MAX and MIN
actually take advantage of the size information of files, there
are chances that the average sojourn time is shorter than the
theoretical approximation based on PS.
In Fig. 6, the throughput results are shown. It can be seen
that the difference of call-average throughputs with MAX and
MIN is much larger compared with Fig. 3. The difference
complies with the visible difference of average sojourn time
in Fig. 5. These results indicate that the performance difference
of MAX and MIN is much larger with Pareto distributed
files. In addition, there is a crossover between call-average
throughput with MIN and the theoretical approximation. This
is consistent with the result in Fig. 5.
In addition, by comparing Fig. 2 with Fig. 5 and Fig. 3
with Fig. 6, we obtain following observations. For the lightloaded
area, the performance results with Pareto or exponential
distributions are quite similar. However, for the heavy-loaded
area, namely when the load of elastic applications is larger
than 0.9, the performance results with Pareto distribution are
much better than those with exponential distribution.
Fig. 7 presents the numbers of load balancing actions.
Compared with Fig. 4, the difference between MAX and
MIN is even larger. Specifically, for MIN, the total number
of load balancing actions is comparable for both Pareto and
exponential distribution while more handovers are adopted
with Pareto distribution. For MAX, much less load balancing
actions are taken with Pareto distribution especially in the
heavy-loaded area.
C. Comparison
In this subsection, we compare our size-based load balancing
mechanisms with an intuitive load balancing method
which admits elastic applications to certain networks without
help of size information. We refer this intuitive method as
INT. Specifically, whenever there is an elastic application
arrival, INT admits the application into WiMAX or WLAN
Average sojourn time (s)
Fig. 8.
60
50
40
30
20
10
EXP − MIN
EXP − INT
Pareto − MIN
Pareto − INT
0
0 0.2 0.4 0.6 0.8 1
ρ e
Performance comparison in terms of average sojourn time.
based on the expected average bandwidth received. Suppose
the number of active streaming applications in WiMAX is s,
the numbers of elastic applications in WiMAX and WLAN
are d wimax and d wlan , respectively. The expected bandwidth
b e wimax in WiMAX for the arrival elastic application would
be b e wimax = (C wimax − s ∗ B s )/(d wimax + 1). Similarly,
the expected bandwidth b e wlan in WLAN would be be wlan =
C wlan /(d wlan + 1). Based on the expected bandwidth, INT
makes the routing decision. Specifically, we can express INT
decision as
{ WiMAX, if b
e
Route to
wimax ≥ b e wlan
(2)
WLAN, others.
Accordingly, we simulate INT in the same settings as for
MIN. The comparison results with MIN are shown in Fig.
8 and 9. Generally, it can be seen that for both exponential
and Pareto distributions, MIN outperforms INT in terms
of both average sojourn time and average throughput. This
performance advantage of MIN suggests that with help of
size information and vertical handover, the performance of

48 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
Average throughput (kbps)
Fig. 9.
800
600
400
200
EXP − MIN, call−average throughput
0
EXP − MIN, time−average throughput
EXP − INT, call−average throughput
EXP − INT, time−average throughput
Pareto − MIN, call−average throughput
−200
Pareto − MIN, time−average throughput
Pareto − INT, call−average throughput
Pareto − INT, time−average throughput
−400
0 0.2 0.4 0.6 0.8 1
ρ e
Performance comparison in terms of average throughput.
heterogeneous networks could be greatly improved. In particular,
we notice that the performance of INT with exponential
distributed elastic applications becomes much worse when
the traffic load exceeds certain level. However, with Pareto
distributed elastic applications, INT still performs comparable
to MIN. One possible explanation for this difference is that
with higher size variability, Pareto distribution compensates
some performance loss with INT since higher size variability
leads to better performance in WiMAX [11]. For exponential
distribution, the major problem with INT would be that the
performance in WiMAX becomes much worse when the traffic
load exceeds certain level.
V. DISCUSSION
Based on the simulation results and theoretical approximations,
we present the following discussions on the impact
of size of elastic applications and further thinking on load
balancing.
According to the performance advantage of MIN over INT,
we should utilize the size information if the handover cost
is neglectable. This conclusion complies with the advantage
of size-based scheduling over other non-size-based scheduling
policies. By choosing handover candidate based on the
remaining size, we actually conduct some kind of prioritized
scheduling with help of size information.
The simulation results suggest that MIN outperforms MAX
in terms of all the performance metrics for elastic applications.
However, this performance overwhelm comes with cost of
significantly increased number of load balancing actions. Besides
the increased number of handover times, another possible
reason for the better performance of MIN is that MIN lets
large files stay in WiMAX. This moves the system towards
the quasi-stationary assumption that streaming applications
evolves much faster than elastic applications in WiMAX.
However, MAX drives the system towards another quasistationary
assumption that elastic applications evolve much
faster. As stated in [8], the former quasi-stationary assumption
leads to better average performance. However, this statement
applies with condition of uniform stationarity where the load
of elastic applications needs to be fairly low.
Another possible reason for the better performance of MIN
over MAX is the better load balancing granularity. Much more
files need to be distributed to WLAN with MIN to achieve load
balancing since those files are relatively small. Then both the
frequency and size of load balancing actions ensure better load
balancing granularity with MIN. However, as shown in Figs.
4 and 7, this also introduces a large proportion of handover
which is much costly than dispatching.
The dilemma between MAX and MIN inspires us to think
how to keep the advantage of MIN while in the meanwhile
reducing the number of load balancing actions. To this aim,
we point out that two aspects should be taken into consideration.
First, sufficient load balancing granularity needs to be
provided. Second, the characteristics of integrated services in
WiMAX need to be explored and utilized.
It is worth highlighting that in this study we have made
several assumptions in order to investigate the fundamental
effect of different load balancing mechanisms. Specifically, we
assume the capacity of WLAN is fixed and does not depend
on the number of users in the network. While the assumptions
may not always hold, we believe that the trends discovered in
this study will remain under released assumptions. Moreover,
the results in the paper could also be helpful for designing
load balancing mechanisms for other overlay heterogeneous
networks.
VI. CONCLUSION
In this paper we study load balancing for multi-service
in an overlay heterogeneous network. Based on the analysis
of simulation results of two load balancing mechanisms, we
draw the conclusion that both load balancing granularity and
integration of elastic and streaming applications in WiMAX
affect the whole system performance. This knowledge could
provide guidance for further developing better load balancing
mechanisms.
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Handover Decision Algorithms in Fourth Generation Heterogeneous
Wireless Networks,” Computer Networks, vol. 54, no. 11, pp. 1848–
1863, Aug. 2010.
[4] L. Xiaoshan, V. Li, and Z. Ping, “Joint Radio Resource Management
through Vertical Handoffs in 4G Networks,” in Proc. of Global Telecommunications
Conference, 2006. GLOBECOM, 2006, pp. 1–5.
[5] A.-E. M. Tahaa, H. S. Hassaneina, and H. T. Mouftah, “Vertical Handoffs
as a Radio Resource Management Tool,” Computer Communications,
vol. 31, pp. 950–961, 2008.
[6] W. Song and W. Zhuang, “Multi-Service Load Sharing for Resource
Management in the Cellular/WLAN Integrated Network,” IEEE Trans.
Wireless Commun., vol. 8, pp. 725–735, 2009.
[7] R. Litjens, H. van den Berg, and R. J. Boucherie, “Throughputs in
Processor Sharing Models for Integrated Stream and Elastic Traffic,”
Performance Evaluation, vol. 65, no. 2, pp. 152–180, Feb. 2008.
[8] F. Delcoigne, A. Proutièreb, and G. Régnié, “Modeling Integration of
Streaming and Data Traffic,” Performance Evaluation, vol. 55, pp. 185–
209, 2004.

XU et al.: MULTI-SERVICE LOAD BALANCING IN A HETEROGENEOUS NETWORK WITH VERTICAL HANDOVER 49
[9] R. Malhotra and J. L. v. d. Berg, “Flow Level Performance Approximations
for Elastic Traffic Integrated with Prioritized Stream Traffic,”
in Proc. of 12th Int. Telecommun. Network Strategy and Planning
Symposium, NETWORKS 2006, 2006, pp. 1–9.
[10] S. Borst and N. Hegde, “Integration of Streaming and Elastic Traffic in
Wireless Networks,” in Proc. of IEEE Int. Conf. on Computer Commun.
INFOCOM 2007, 2007, pp. 1884–1892.
[11] R. Litjens and R. J. Boucherie, “Elastic Calls in an Integrated Services
Network: the Greater the Call Size Variability the Better the QoS,”
Performance Evaluation, vol. 52, pp. 193–220, 2003.
He is recipient of a fellowship from the European Research Consortium for
Informatics and Mathematics (ERCIM). He was Co-Chair of IEEE Globecom
2005 General Conference Symposium, TPC Co-Chair of 67th IEEE Vehicular
Technology Conference (VTC) 2008, and General/TPC Co-Chair of International
Symposium on Wireless Communication Systems (ISWCS) 2007-2010.
He is author of the book Stochastic Network Calculus published by Springer
in 2008. His research interests include network measurement and the provision
and analysis of quality of service guarantees in communication networks. In
the area of network calculus, his focus has been on developing fundamental
models and investigating their basic properties for stochastic network calculus
(snetcal), and recently also on applying snetcal to performance analysis of
wireless networks.
Jie Xu received B.E. degree in Electronic Information Engineering from
Beijing University of Aeronautics and Astronautics in 2003, his Ph.D.
in Communication and Information Systems from Graduate University of
Chinese Academy of Sciences, Beijing, China in 2010. During his Ph.D.
study, he had involved in several research projects which covered a wide
range of multimedia communications. He is currently postdoctoral fellow in
Center of Quantifiable Quality of Service at Norwegian University of Science
and Technology (NTNU), Trondheim, Norway, conducting research on the
next generation wireless networks and on multimedia communications. He
is also leading the development of a serious multiplayer game which is to
be used for both scientific research and for university recruitment. He is the
author or co-author of more than 10 research publications; he is a member of
IEEE.
Andrew Perkis is a full professor of Digital Image Processing at the Department
of Electronics and Telecommunications at the Norwegian university
of Science and Technology (NTNU) in Trondheim, Norway. He received
his Siv.Ing and Dr.Techn. degrees in 1985 and 1994, respectively. He is
member of the management team of the National Centre of Excellence -
Q2S - Quantifiable Quality of Service in Communication Systems, where he
is responsible for ”Networked Media Handling”. He is Vice Chair of COST
action IC1003 QUALINET European Network on Quality of Experience in
Multimedia Systems and Services (End date: November 2014). Currently he
is focusing on Multimedia Signal Processing, specifically within methods and
functionality of content representation, quality assessment and its use within
the media value chain in a variety of applications. He is a senior member of
the IEEE. He has more than 150 publications at international conferences and
workshops and more than 50 contributions to International standards bodies.
Dr. Yuming Jiang is presently a Professor in the Department of Telematics
and the Centre for Quantifiable Quality of Service in Communication Systems
(Q2S), at Norwegian University of Science and Technology (NTNU), Norway.
He received his B.S. degree in electronic engineering from Peking University
in 1988, M.E. degree in computer science and engineering from Beijing
Institute of Technology in 1991, and Ph.D. degree in electrical and computer
engineering (ECE) from the National University of Singapore (NUS) in 2001.
From 1996 to 1997, he worked with Motorola. He was a Research Engineer
at the ECE Department, NUS, from 1999 to 2001. From 2001 to 2003, he
was with the Institute for Infocomm Research (I2R), Singapore as a Member
of Technical Staff / Research Scientist. He joined NTNU in 2004. He visited
Northwestern University, USA from 2009 to 2010.
Elissar Khloussy received the B.S degree and M.S degree in computer
engineering from the Conservatoire Nationale Des Arts et Métiers, Paris, in
2001 and 2003 respectively. She is now a PhD candidate at the Telematics
department, Norwegian Univeristy of Science and Technology, Norway. Her
current research interests include the interworking of cellular networks and
wireless local area networks, and cognitive networks.

50 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
Resources Management and Services
Personalization in Future Internet Applications
Paweł Świątek, Piotr Rygielski and Adam Grzech
Abstract—The aim of this paper is to introduce a problem of
e-health services quality management. The process of delivering
e-health services to users consists of two major tasks: service
personalization and resources allocation. In this paper we introduce
a use-cases of e-health system and distinguish services that
can be offered. In order to satisfy user requirements one has
to manage resources properly especially when communication
conditions change i.e. in an ambulance. An exemplary solution
has been presented and conclusions for further work have been
formulated.
Patient
data
aquisition
Supervising
physician
PDA
consultation
access
to data
data
transmision
consultation
consultation
Digital
Health Library
access
to data
Ambulance
Consulting
physician
I. INTRODUCTION
ADVANCES in information and communication technologies
allow health service providers to offer e-services in
virtually every aspect of health care. The collection of e-health
services facilitated by current and future ICT architectures
ranges from remote health monitoring, through computeraided
diagnosis, video-consultation, health education, remote
surgery and many others [1].
Each of possible e-health services is a composition of
atomic services provided by either ICT infrastructure or
medical personnel. In some scenarios medical personnel can
be both service provider and service consumer. Delivery of
complex services as a composition of atomic services is the
key feature of service oriented architecture (SOA) paradigm
[2]. Application of SOA approach in e-health services delivery
allows to personalize and flexibly adjust services to individual
needs of service consumers.
According to the SOA paradigm each e-health service is
composed of a set of atomic services providing required
functionalities, which are delivered in certain predefined order.
Each atomic service, which delivers certain functionality may
be provided in different versions, which vary in non-functional
characteristics such as: response time, security, availability, etc
[2], [3]. Composition of complex services from different versions
of atomic services allows to guarantee required quality
of e-health services, which is very often critical in medical
applications.
In this paper we present a general framework for QoSaware
SOA-based composition of e-health complex services.
The presented approach is explained with use of an illustrative
example — remote monitoring of patients health parameters.
The remote monitoring example includes: definition of the remote
monitoring problem as a business process, identification
of complex services playing major roles in the monitoring
Paweł Świątek, Piotr Rygielski and Adam Grzech are with Institute of Computer
Science, Wroclaw University of Technology, Wybrzeze Wyspianskiego
27, 50-370 Wroclaw, Poland
Fig. 1.
Remote monitoring of patients health - an overview.
process, identification of the set of atomic services necessary
to deliver required functionalities and composition of an
exemplary complex service.
II. REMOTE MONITORING OF PATIENT’S HEALTH
As an example of e-health business process consider the
process of remote monitoring of patient’s health (see Fig. 1).
In this scenario it is assumed, that a patient is equipped with
a mobile communication device (e.g. smartphone or PDA),
which collects monitored data from sensors placed on the
patient’s body. Collected data is preprocessed on the patient’s
mobile device and sent for further processing and storage to
Digital Health Library. Further processing of collected data
may involve among others: modelling and identification of
physiological processes, updating of medical knowledge base,
expansion of medical case study database and decision making
for computer-assisted diagnosis. In the last case decision
making algorithm may recognize any abnormal situations
in patient’s health and notify medical personnel about such
events.
Being alarmed, a physician should have an access to
patients’ health records, their current health state, medical
knowledge bases and additional services such as consultation
with patient or other physician. After gathering necessary
information the physician decides whether detected abnormal
situation poses a threat to patient’s health and takes relevant
action, e.g. sends an ambulance to the patient. In the lifethreatening
situation the physician monitors patient’s status
and instructs ambulance crew on how to proceed with the
patient.
The whole process of remote monitoring of patients’ health
can be divided into three phases presented on Fig. 2: basic
monitoring, supervised monitoring and monitoring in the ambulance.
Each of presented monitoring phases is in fact a separate
business process composed of one or more complex services.

ŚWIATEK ˛ et al.: RESOURCES MANAGEMENT AND SERVICES PERSONALIZATION IN FUTURE INTERNET APPLICATIONS 51
Fig. 2.
U1:
Basic
monitoring
NO
YES
Alarm
U2:
Supervised
monitoring
NO
YES
Threat
U3:
Monitoring in
ambulance
The process of remote monitoring of patients health.
a) U2: Supervised monitoring
b)
U2.1:
Detailed
monitoring
U2.3:
Access to
monitored
data
U2.4:
Access to
patients
record
U2.2:
Physician
notification
U2.5:
Access to
Digital
Library
U3.6:
Monitoring from
ambulance
U3.2:
Detailed
monitoring
U3: Monitoring in ambulance
U3.7:
Access to
monitored
data
U3.1:
Ambulance
dispatch
U3.3:
Access to
monitored data
U3.5:
Admittance to
ambulance
U3.8:
Access to
patients
record
U3.4:
Access to
patients record
U2.6:
Teleconsultation
U2.7:
Videoconsultation
U3.9:
Teleconsultation
U3.10:
Videoconsultation
B. Monitoring in ambulance
The process of monitoring in an ambulance consists of two
stages. The first starts when the supervising physician finds
the patient’s health to be at risk and sends an ambulance to
take the patient to the hospital (U3.1). From now on the crew
of the ambulance has on-line access to monitored parameters
of the patient’s health (U3.3) as well as his/her health record
(U3.4).
After being taken by the ambulance (U3.5) patients monitoring
mode changes again. All required patient’s health parameters
are recorded now. Moreover, audio-video monitoring
of the patient in the ambulance is performed as well (U3.6).
Besides the previously accessible services (U3.7 and U3.8)
the ambulance crew can communicate with the supervising
physician through tele- and video-consultation services (U3.9
and U3.10).
Fig. 3. The process of supervised monitoring (a) and the process of
monitoring in an ambulance (b).
Basic monitoring covers routine day to day monitoring of
patient’s vital parameters (e.g. ECG for post-cardiac patients).
Supervised monitoring refers to a case when abnormal
behaviour of monitored parameters is detected. In such a
case an alarm is activated and other parameters (e.g.: body
temperature, pulse and GPS coordinates) are monitored by
the physician providing him/her with information and services
necessary to make decisions concerning further actions.
Monitoring in ambulance applies to life-threatening situations
in which an ambulance was dispatched to collect (possibly
unconscious) patient. In this case both the ambulance crew and
the physician should be provided with necessary information
and communication services [1].
Processes of supervised monitoring and monitoring in ambulance
can be decomposed into separate complex services.
Such an exemplary decomposition of considered processes is
presented on Fig. 3 a) and b) respectively.
A. Supervised monitoring
The process of supervised monitoring starts at the moment
of generation of an alarm concerning abnormal behaviour of
patient’s health parameters. There are two immediate implications
of such an alarm. The first is the change in patient’s
monitoring mode - more parameters are being recorded, possibly
with denser time resolution. The second consequence
is the notification of the patient’s physician about possible
health risks. From this moment the physician has access to
personalised services allowing him/her to gather information
about current condition of the patient and make decision about
further actions. These services may include (see Fig. 3 a)): online
access to monitored health parameters (U2.3), access to
the patient’s health record (U2.4), access to Digital Health
Library containing knowledge about similar cases (U2.5),
and tele- and video-consultation with patient and/or medical
experts (U2.6 and U2.7).
III. REMOTE MONITORING AS BUSINESS PROCESS
Business process is a series of interrelated activities or tasks
that solve a particular problem or lead to achievement of specific
goal. In the SOA paradigm each of activities constituting
in business process is represented as a complex service which
delivers certain predefined functionality (see Fig. 4). Complex
services, in turn, are composed of atomic services, which
provide basic indivisible functionalities. The functionality of a
complex service is an aggregation of functionalities of atomic
services [4]. Similarly, the goal of a business process (its
functionality) is an aggregation of functionalities of performed
complex services.
The difference between business process and complex service
lies in that the former is defined and composed by service
consumer, while the latter is delivered by service provider
as a whole. Service consumer may influence the choice of
particular complex services by specification of Service Level
Agreement (SLA) containing functional and non-functional
requirements. Service provider, on the other hand, composes
complex services from available atomic services basing on
requirements stated in the SLA [5].
In special cases the whole business process may be specified
by single complex service. Such situations may occur for
example when available processes are managed by single
entity basing on certain regulations (e.g. medical processes in
health care). In general, however, this approach is inefficient
and inelastic, since it does not allow consumers to modify their
requirements.
Fig. 4.
Consumers
layer
Providers
layer
Infrastracture
layer
Business
process
Complex
services
Atomic
services
Transport
services
Composition of business processes.

52 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
TABLE I
THROUGHPUT REQUIREMENTS FOR DIFFERENT SIGNALS AND QUALITY
LEVELS CONSIDERED IN THE EXAMPLE.
Required
throughput
[kbps]
Signal Video Voice ECG EMG Heart
sound
High
quality
Low
quality
5000 256 24 600 120 5
640 25 12 100 24 2
IV. SERVICES PERSONALIZATION AND RESOURCES
MANAGEMENT
Heart
rate
Depending on individual needs of service consumers and
capabilities of execution environment each of available complex
services can be delivered in many versions which differ in
non-functional characteristics [6], [7]. As an example consider
monitoring from ambulance service (U3.6) which allows to
transmit monitored signals, voice and video from ambulance to
supervising physician. Depending on individual case different
health parameters are recorded and transmitted through the
network (e.g.: ECG and pulse for cardiac patients or glucose
for diabetics). Additionally, voice and video transmission may
be required by physician. Moreover, individual requirements
and amount of available system resources may influence the
number and the quality of transmitted signals [8], [3].
Assume, that there are six signals possible to be measured
and transmitted from ambulance to physician: video, voice,
ECG, EMG, heart sound (HS) and heart rate (HR). Each signal
can be measured and transmitted in two modes - high and
low quality. High and low quality of health parameters can be
reflected by higher and lower sampling rates. A transmission
of high and low quality signals has different requirements for
communication resources (see table I).
In general, preferences concerning the quality of requested
complex service can be defined by penalty matrix P l = [p ij ],
where each element p ij (i = 1, ..., I; j = 1, ..., J) represents a
penalty for not delivering j-th signal in higher than i-th quality
levels. The exemplary matrix for six signals considered above
and three quality levels is defined by:
⎡
P l = ⎢
⎣
p HI
V ID
p LO
V ID
p NO
V ID
pHI V OI
pLO V OI
pNO V OI
p HI
ECG
p LO
ECG
p NO
ECG
pHI EMG
pLO EMG
pNO EMG
pHI HS
pLO HS
pNO HS
p HI
HR
p LO
HR
p NO
HR
⎤
⎥
⎦ , (1)
where for example p 21 = p LO
V ID is the penalty for not
delivering video signal in high quality and p 11 = p NO
EMG is
the penalty for not delivering EMG signal at all. If penalty
p ij = 0 then i-th quality level of j-th signal is not required.
Denote by D l a binary matrix of quality level delivery,
where each element d ij (i = 1, ..., I; j = 1, ..., J) is defined
as follows:
{ 1 i-th quality level for j-th signal is delivered
d ij =
0 i-th quality level for j-th signal is not delivered .
(2)
Exemplary matrix D l for a complex service in which video
and voice signals are delivered at low quality, ECG signal
is delivered at high quality, and remaining signals are not
transmitted at all is presented below:
⎡
D l = ⎣ 0 0 1 0 0 0
⎤
1 1 0 0 0 0⎦ . (3)
0 0 0 1 1 1
Given the penalty matrix P l and quality delivery matrix
D l for certain complex service request req l it is possible
to calculate overall penalty p l for not satisfying consumers
preferences as follows:
p l =
J∑
p lj · d T lj, (4)
j=1
where p lj and d lj are j-th columns of matrices P l and D l
respectively.
Let R = [r ij ] (i = 1, ..., I; j = 1, ..., J) denote the matrix
of resources consumption, where each element r ij represents
the amount of resources required to deliver j-th signal at i-
th quality level. In the example considered above resources
requirements are stated in terms of required throughput (see
table I). Therefore, the exemplary matrix R is defined as
follows:
⎡
⎤
5000 256 24 600 120 5
R = ⎣ 640 25 12 100 24 2⎦ . (5)
0 0 0 0 0 0
Note, that elements of the last row of exemplary matrix R are
equal to zero since the lowest quality level represents situation
in which signals are not delivered at all.
The amount of resources r l necessary to deliver complex
service at quality level represented by certain matrix D l can
be calculated as follows:
r l =
J∑
r j · d T lj, (6)
j=1
where r j and d lj are j-th columns of matrices R and D l
respectively.
For the model presented above a number of resource
management tasks can be formulated. The goal of each task
may be different. For example, one may want to minimize
the average or maximal penalty caused by violation of
consumers individual preferences or to maximize consumers
satisfaction for each incoming complex service request. The
aforementioned tasks can be formulated as follows.
Task 1: Average penalty minimization
Given: set L(t) of service requests currently being served,
capacity C of the system and matrices of penalties P l and
resources consumption R.
Find: set of quality delivery matrices {D ∗ l
: l ∈ L(t)}
such that average penalty caused by violation of consumers
individual preferences is minimized:
{D ∗ l : l ∈ L(t)} = arg min
∑
{D l :l∈L(t)}
l∈L(t) j=1
J∑
p lj · d T lj (7)

ŚWIATEK ˛ et al.: RESOURCES MANAGEMENT AND SERVICES PERSONALIZATION IN FUTURE INTERNET APPLICATIONS 53
with respect to system capacity constraints:
∑
l∈L(t) j=1
J∑
r j · d T lj ≤ C. (8)
Task 2: Maximal penalty minimization
This task is similar to Task 1 and can be derived by
substitution of objective function in (7) by following formula:
{D ∗ l : l ∈ L(t)} = arg min max
{D l :l∈L(t)} l∈L(t)
J∑
p lj · d T lj (9)
j=1
Task 3: Maximization of service consumer satisfaction
Given: the amount of resources C(t) currently available in the
system, matrix of preferences P l for incoming service request
req l and resources consumption matrix R.
Find: composition of complex service defined by quality
delivery matrix D ∗ l
such that penalty caused by violation of
consumers preferences is minimized:
D ∗ l = arg min
D l
J∑
p lj · d T lj (10)
j=1
with respect to system capacity constraints:
J∑
r j · d T lj ≤ C(t). (11)
j=1
The goal of Task 3 is to compose complex services according
do consumers preferences. It can be performed each time
when new complex service request arrives to the system. It
can also be used for request admission control and Service
Level Agreement renegotiation. Tasks 1 and 2, on the other
hand, are performed in order to optimize utilization of systems
resources and to guarantee average or minimal service
consumer satisfaction.
A. Numerical example
Consider an example in which two monitoring service
requests req 1 and req 2 arrive to the system. Requests req 1
and req 2 are characterized by following preferences matrices:
⎡
P 1 = ⎣ × 0 × 0 0 ×
⎤
× 100 × ∞ 200 × ⎦
× ∞ × ∞ ∞ ×
⎡
P 2 = ⎣ 0 × × 0 0 ×
⎤ (12)
1000 × × 100 10 × ⎦
∞ × × ∞ 200 ×
which mean that request req 1 requires voice and heart sound
signal to be delivered at least at low quality and EMG signal
to be delivered at high quality. Similarly request req 2 requires
video and EMG signal at least at low quality and additional
heart sound signal would improve consumers satisfaction.
Assume, that systems capacity is equal to C = 2510kbps
and that capacity requirements of available signals are given
by matrix R defined in (5). As a result of minimizing average
penalty for not satisfying consumers preferences (Task 1
defined by (7) and (8)) following quality delivery matrices
are calculated:
⎡
× 1 × 1 1
⎤
×
D 1 = ⎣× 0 × 0 0 × ⎦
× 0 × 0 0 ×
⎡
⎤, (13)
0 × × 1 1 ×
D 2 = ⎣1 × × 0 0 × ⎦
0 × × 0 0 ×
resulting in overall penalty p = 1000 for not delivering high
quality video signal for second service request req 2 . Delivery
of high quality video signal in this example is impossible
because HQ video capacity requirements are higher than
overall capacity C of the system. Services composition and
resources allocation represented by matrices D 1 and D 2 (13)
are illustrated on Fig. 5 (state before moment t 1 ).
Assume, that at certain moment t 1 a third service request
req 3 characterized by matrix P 3 arrives to the system. In
order minimize average penalty for not satisfying consumers
preferences systems resources have to be reallocated. Final service
composition and resources allocation depends on penalty
matrices P 1 , P 2 and P 3 .
In order to show the difference between final resources
allocation assume two alternate matrices P 3 :
⎡
P a 3 = ⎣ 0 0 × 0 0 × ⎤
1000 250 × ∞ ∞ × ⎦
∞ ∞ × ∞ ∞ ×
⎡
P b 3 = ⎣ 0 0 × 0 0 × ⎤, (14)
1000 150 × ∞ ∞ × ⎦
∞ ∞ × ∞ ∞ ×
which differ in the penalty for not delivering voice signal in
the high quality. Two different solutions of are represented by
quality level matrices D a 1, D a 2, D a 3 and D b 1, D b 2, D b 3:
⎡
× 0 × 1 0
⎤
×
D a 1 = ⎣× 1 × 0 1 × ⎦
× 0 × 0 0 ×
⎡
0 × × 0 0
⎤
×
D a 2 = ⎣1 × × 1 1 × ⎦, (15)
0 × × 0 0 ×
⎡
0 1 × 1 1
⎤
×
D a 3 = ⎣1 0 × 0 0 × ⎦
0 0 × 0 0 ×

54 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
Final services composition and resources allocation
represented
by the above matrices are illustrated on figures Fig. 5a)
depending on the penalty for
not delivering HQ voice for
request req
3 , HQ voice in req 3 is traded for HQ heart sound
V. CONCLUSIONS
In this paper a general problem of e-health services management
was introduced. It consists of two major tasks: service
personalization and resources allocation. Service personalization
allows to flexibly adjust delivered services based on
individual needs of service consumers. Resources management
allows to reserve and allocate resources necessary to deliver
requested services and satisfy consumers preferences. In the
presented approach both tasks of personalization and resource
allocation are solved simultaneously as single optimization
problem in which certain parameters concern the personalization
task (penalty matrices), while other parameters regard
allocation tasks (resources consumption matrix). Unfortunately
formulated tasks are in general NP-hard, therefore heuristic
Fig. 5. Services composition and resources reallocation for two versions
of third request preferences differing in the value of penalty p 322 for not
delivering HQ voice for request req 3 : (a) p 322 = 250, (b) p 322 = 150.
and
⎡
× 0 × 1 1
⎤
×
D b 1 = ⎣× 1 × 0 0 × ⎦
× 0 × 0 0 ×
⎡
0 × × 0 1
⎤
×
D b 2 = ⎣1 × × 1 0 × ⎦. (16)
0 × × 0 0 ×
⎡
⎤
0 0 × 1 1 ×
D b 3 = ⎣1 1 × 0 0 × ⎦
0 0 × 0 0 ×
and Fig. 5b) respectively. Note that in the presented example,
in req 1 and req 2 . The threshold value of this penalty is
p 322 = p 125 + p 225 = 210.
algorithms should be applied to effectively control processes
of service composition, personalization and resources management.
ACKNOWLEDGEMENTS
This work was partially supported by the European Union
from the European Regional Development Fund within the
Innovative Economy Operational Programme project number
POIG.01.01.02-00-045/09-00 “Future Internet Engineering”.
REFERENCES
[1] D. Niyato, E. Hossain, and J. Diamond, “IEEE 802.16/WiMax-Based
Broadband Wireless Access and its Application for Telemedicine/e-health
Services,” IEEE Trans. Wireless Commun., vol. 14, no. 1, pp. 72–83, 2007.
[2] P. Rygielski and P. Świątek, SOA Infrastructure Tools: Concepts and
Methods. Springer-Verlang, Berlin, 2010, ch. QoS-aware Complex
Service Composition in SOA-based Systems.
[3] K. Shahadatand, F. L. Kin, and E. G. Manning, “The Utility Model For
Adaptive Multimedia Systems,” in Proc. of Int. Conf. on Multimedia
Modeling, 1997, pp. 111–126.
[4] A. Grzech and P. Świątek, “Modeling and Optimization of Complex
Services in Service-Based Systems,” Cybernetics and Systems, vol. 40,
pp. 706–723, 2009.
[5] A. Grzech, P. R. P., and P. Świątek, “QoS-Aware Infrastructure Resources
Allocation in Systems Based on Service-Oriented Architecture Paradigm,”
in HET-NETs, 2010, pp. 35–48.
[6] M. Alrifai and T. Risse, “Combining Global Optimization with Local
Selection for Efficient QoS-Aware Service Composition,” in Proc. of 18th
Int. Conf. on World Wide Web WWW’09. ACM, 2009, pp. 881–890.
[7] Y. Tao, Z. Yue, and K.-J. Lin, “Efficient Algorithms for Web Services
Selection with End-to-End QoS Sonstraints,” ACM Trans. Web, vol. 1,
no. 1, 2007.
[8] A. Grzech and P. Świątek, “Parallel Processing of Connection Streams in
Nodes of Packet-Switched Computer Communication Systems,” Cybernetics
and Systems, vol. 39, no. 2, pp. 155–170, 2008.
Paweł Światek ˛ received his MSc and PhD degrees in computer science from
Wrocław University of Technology, Poland, in 2005 and 2009, respectively.
From 2009 he is with Institute of Computer Science, Wrocław University of
Technology, where from 2010 he works as an assistant professor. His main
scientific interests are focused on services optimization and personalization,
optimization of service-based systems, resources allocation, QoS delivery in
heterogeneous networks and mobility management in wireless networks.
Piotr Rygielski is a Ph.D. student at the Wrocław University of Technology
(WUT), Poland. He received his MSc degree in computer science
from WUT
in 2009. Since 2009 he works as a young researcher in two
Innovative Economy European Union projects: "Future Internet Engineering"
and "New information technologies for electronic economy and information
society based on service-oriented architecture". His main research interests
include resource allocation issues in distributed computer systems, serviceoriented
architecture, resources virtualization, Quality of Service provisioning
in computer networks, discrete optimization and combinatorial algorithms.
Adam Grzech, Ph.D., D.Sc . He is a professor in the Institute of Computer
Science, Department of Computer Science and Management, Wrocław University
of
Technology (WUT). He obtained M.Sc. degree from Department
of Electronics, WUT in 1977, Ph.D. degree from Institute of Technical
Cybernetics, WUT in 1979, D.Sc. degree form Department of Electronics,
Wrocław University of Technology in 1989 and professor title in 2003.
His research interests include design and analysis of computer systems
and networks, requirement analysis, modeling and identification of computer
networks, design and application of local and wide area computer networks,
flow control and congestion avoidance in computer networks, migration
and integration of heterogeneous computer systems and networks, services
integration in networks, intelligent networks, quality of service âĂŞ aware
networks, SOA-paradigm based systems, engineering of the future internet,
security of computer systems and networks, agent-based systems and its
application in optimization and control and intelligent information systems.
He is an author and co-author of nearly 300 research papers published in
books, journals and conference proceedings, supervisor of 8 completed Ph.D.
thesis and supervisor of more than 200 completed M.Sc. thesis in computer
communication engineering.

ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011 55
Compact node-link formulations for the optimal
single path MPLS Fast Reroute layout
Cezary Żukowski, Artur Tomaszewski, Michał Pióro, David Hock, Matthias Hartmann and Michael Menth
Abstract—This paper discusses compact node-link formulations
for MPLS fast reroute optimal single path layout. We
propose mathematical formulations for MPLS fast reroute local
protection mechanisms. In fact, we compare one-to-one (also
called detour) local protection and many-to-one (also called
facility backup) local protection mechanisms with respect to minimized
maximum link utilization. The optimal results provided by
the node-links are compared with the suboptimal results provided
by algorithms based on non-compact linear programming (path
generation) approach and IP-based approach.
I. INTRODUCTION
MULTIPROTOCOL Label Switching (MPLS) technology
enables configuration of end-to-end virtual connections
in communication networks, especially in networks without
connection-oriented capabilities. Labeled packets can be sent
over the connections and forwarded according to the labels
over so-called LSPs (Label Switched Paths).
MPLS is able to detect network failures (link failures)
locally and thus a failure-detecting router can quickly switch
all packets from failing primary LSP path to a backup LSP
path just after a failure is detected. This is so-called fast reroute
(FRR) capability and the failure-detecting router is the socalled
point of local repair (PLR).
The way the backup LSPs are rerouted (from the PLR) depends
on the FRR mechanism. Two mechanisms are possible:
one-to-one backup (OOB) [1] and many-to-one backup (MOB)
[2]. Many-to-one backup is also called facility backup as in
[3]. In OOB and MOB backup LSP paths are rerouted over
the next hop router (NHR) and terminated in NHR if and only
if the failing link is the last one on the failing primary LSP
path.
For instance, in Figure 1 the primary path originates in
router A, it goes through routers A, B, C, D, and terminates
in router D. Link A-B fails, router A is the PLR, router B is
the NHR, and router C is the next next hop router (NNHR).
In the MOB a backup path is rerouted from the PLR router
to the NNHR. On the other hand, in the OOB a backup path
is rerouted from PLR to router D.
When the OOB is used, backup LSP paths originate in the
PLR and terminate in the destination node of the corresponding
primary LSP path.
When the MOB is used, backup LSP paths originate in
the PLR and terminate in the NNHR. In MOB, all primary
paths that go exactly through the same PLR, NHR, NNHR
are rerouted from the PLR to the NNHR on a single LSP
backup path.
Individual demands can be sent (between any pair of network
nodes) on single primary and single backup LSP paths
(single path layout) or split on multiple primary and multiple
backup LSP paths (multipath layout). The single or multipath
layout we select, impacts on the minimized maximum link
utilization value and network configuration complexity as
explained in our previous paper [1].
In this paper, we focus on compact node-link (NL) formulations
for the single LSP paths layout as they provide the
optimal solutions for this layout, they can be easily implemented
(e.g. with CPLEX package), and they haven’t been
presented before. We show and describe the NL formulation
for the one-to-one backup as well as the NL formulation for
many-to-one backup.
We use applicable size networks to show the efficiency of
OOB and MOB. We provide example results related to running
times, the number of used continuous and binary variables to
show the performance of OOB and MOB formulations according
to the network sizes. We provide results for minimized
maximum link utilization values and networks configuration
complexities to compare OOB and MOB solutions qualities.
Additionally, we use the same networks to generate suboptimal
solutions for the single path layout. To do this, noncompact
linear programming (LP) based approach and IPbased
approach were applied. Detailed explanations of these
methods and related work can be found in [1], [4], [5], [6],
[7] and [8].
Then, we discuss the gap between optimal and suboptimal
solutions. Exactly, we compare the minimized maximum link
Cezary Żukowski,Artur Tomaszewski and MichałPióro are with Institute
of Telecommunications, Warsaw University of Technology, 00-665 Warsaw,
Poland, Emails: czukowsk@mion.elka.pw.edu.pl, artur@tele.pw.edu.pl,
mpp@tele.pw.edu.pl
MichałPióro is also with Department of Electrical and Information Technology,
Lund University, 221-00 Lund, Sweden, Email: mpp@eit.lth.se
David Hock and Matthias Hartmann are with Institute of Computer
Science, University of Würzburg, D-97074 Würzburg, Germany, Email:
hock@informatik.uni-wuerzburg.de, hartmann@informatik.uni-wuerzburg.de
Michael Menth is with Dept. of Computer Science, University of Tübingen,
D-72076 Tübingen, Germany, Email: menth@informatik.uni-tuebingen.de
Fig. 1.
Explanation of one-to-one backup and many-to-one backup

56 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
utilization values to show optimal and suboptimal solutions
qualities. Finally, we present conclusions summarizing the
results.
II. NODE-LINK FORMULATIONS
The section discusses the common part of OOB and MOB
formulations.
A. Used symbols
An MPLS/IP network is modeled as a graph G = (V,E)
comprising a set V of nodes and a set E of directed edges (E ∈
V 2 \{(v,v) : v ∈ V }). The nodes correspond to the MPLS/IP
routers and edges correspond to IP links. Symbols a(e) and
b(e) denote the source and the destination node of link e ∈ E.
Sets δ − (v) and δ + (v) denote the incoming and the outgoing
edges for node v ∈ V . A constant C e is the capacity of link
e ∈ E.
Set D denotes the set of demands. Symbols o(d) and t(d)
denote source and destination node of demand d. A constant
h d is the rate of demand d ∈ D.
Set S denotes the set of failure states. In the paper only the
failures of single links are considered, thus S ≡ E.
In both OOB and MOB formulations, the paths of the LSP
connections (in normal state and in each failure state) are
modeled as unitary non-bifurcated flows between appropriate
pairs of nodes.
Variables x ed indicate whether link e belongs to the primary
path for demand d.
The Z denotes the objective function value. It minimizes
maximum link utilization.
B. Feasible and infeasible solutions provided by node-links
Notice that there is no capacity constraints in the formulations
for OOB and MOB. Instead, we use relative link
utilization by addition of the constant (1/C e ) to the NL
formulations.
In the case when we get an optimal solution with Z > 1 it
means the solution is infeasible in terms of required capacity.
On the other hand, when we get some optimal solution with
Z ≤ 1 it means the solution is feasible in terms of required
capacity.
III. NODE-LINK FORMULATION FOR ONE-TO-ONE BACKUP
In this section, a compact NL formulation for one-to-one
backup is described. For each s ∈ S and each d ∈ D, both
the primary and its backup path that is used in the network
state corresponding to the failure of link s can be viewed as
consisting of two subpaths – the path between the source node
of d and the PLR (which is the originating node a(s) of link s),
and the path between the PLR and t(d) – the destination node
of d. Since, according to the FRR mechanism, the primary
and the backup paths share the subpaths that is upstream from
the PLR and differ in the subpaths that are downstream from
the PLR, the backup path can be described in terms of the
primary path and those two downstream subpaths between the
PLR and the destination node of the demand.
The formulation is as follows:
min Z (1a)
Z ≥ ∑ (h d /C e )x ed ,∀e ∈ E (1b)
d∈D
Z ≥ ∑ (h d /C e )(x ed − y des + z des ),s ≠ e,∀e ∈ E,∀s ∈ E
d∈D
(1c)
∑
e∈δ + (v)
x ed −
∑
e∈δ − (v)
and for each d ∈ D, s ∈ E:
y des ≤ x ds ,∀e ∈ E
∑
e∈δ + (v)
y des −
∑
e∈δ − (v)
y des ≤ x de ,∀e ∈ E
z des ≤ x ds ,∀e ∈ E
∑
e∈δ + (v)
z dss = 0
z des −
∑
e∈δ − (v)
⎧
⎨
x ed =
⎩
1, v = o(d)
−1, v = t(d),
0, otherwise
⎧
⎨ x ds , v = a(s)
y des = −x
⎩ ds , v = t(d)
0, otherwise
⎧
⎨ x ds , v = a(s)
z des = −x
⎩ ds , v = t(d)
0, otherwise
z des = 0,∀e ∈ δ + (b(s)),b(s) ≠ t(d)
∀d ∈ D
(1d)
(2a)
(2b)
(2c)
(2d)
(2e)
(2f)
(2g)
We cannot write conservation constraints for variables y de
with flow equal to 1 (the right-hand side of (2b)) because if
x ds is equal to 0 then from (2c) all y de are equal to 0 and we
would arrive at a contradiction. It only makes sense to look
for the backup path described with y ds (and also with variables
z ds described in the sequel) if the primary path fails in state
s. That we know from x ds : if x ds is equal to 1 the primary
path uses link s and thus fails in state s. Thus, putting x ds in
conservation constraints (2b) allows us to look for the backup
path and write the constraints somewhat ‘conditionally’ upon
the failure of the primary path.
The subpath of the backup path that is downstream from
the PLR can be modeled as a unitary flow between the PLR
and the destination node of the demand that must not use
neither the failing link nor the terminating node of that link.
For each e ∈ E, let z des be a binary variable that equals 1 if,
and only if, link s belongs to the primary path of demand
d, and link e belongs to the segment of the backup path that
this downstream from the PLR. This is satisfied by constraints
(2d), (2e), (2f) and (2g).
Similarly to conditions (2a)-(2c) that describe subpath y,
conditions (2d)-(2e) say that we must find subpath z between
the PLR and the destination node; the form and the role of
(2e) is the same as that of (2b). And the conditions for both
types of subpaths paths – y must be embedded into the primary
path and z must detour the failure – are given by (2c), (2f) and
(2g). Constraints (2f) and (2g) say that we cannot use either
the failed link or the links that originate at the terminating
node of the failed link. Although we therefore cannot transit
the terminating node of the failed link, this does not mean

ŻUKOWASKI et al.: COMPACT NODE-LINK FORMULATIONS FOR THE OPTIMAL SINGLE PATH MPLS FAST REROUTE LAYOUT 57
that we cannot enter such a node. Thus, in particular, the last
hop of the primary path is also protected since the destination
node of the demand need not be used as a transit node for the
backup path.
It should be noted that although only link failures are
assumed explicitly in the formulation, the determined backup
paths provide protection of the primary paths against both link
and node failures. But only in terms of flow routing; network
capacity is not sufficient and the flows in fact are not protected.
The meaning of this can be explained with the following
example. Consider the following links, all with capacity equal
to 1: k and l between nodes A and B; m and n between nodes
B and C; and o between nodes A and C. Consider two primary
paths k-m and l-n between nodes A and C, both with flows
equal to 1. Assume that each of those primary paths has path
o as its backup path. Then, theoretically each primary path
is protected with its backup path against the failure of node
B. But there is not enough capacity on link o to reroute both
primary paths at the same time, so in fact the flows are not
protected. Still, if either link k or l fails the affected path can
be rerouted.
IV. NODE-LINK FORMULATION FOR MANY-TO-ONE
BACKUP
In this section, a compact NL formulation for many-to-one
backup is described. The MOB is a restricted version of OOB.
The restrictions hold for all d ∈ D and consist in:
• backup paths terminate in NNHRs (except the case the
NNHR is the terminating node of demand – then terminate
in NHRs),
• backup paths originating in node a(s) and terminating in
node b(q) are rerouted the same path, on the single path
going from node a(s) to node b(q).
For each s ∈ S the formulation can be shown according to
its two cases. The case when b(s) ≠ t(d) and the case when
b(s) = t(d). In the first case, backup LSP paths terminate in
NNHRs and in the second in NHRs. The common part of the
cases is formulated below:
min Z (3a)
⎧
⎨ 1, v = o(d)
∑ x ed − ∑ x ed = −1, v = t(d), ∀d ∈ D
⎩
e∈δ + (v) e∈δ − (v) 0, otherwise
(3b)
Z ≥ ∑ (h d /C e )x ed ,∀e ∈ E (3c)
d∈D
Z ≥ ∑ (h d /C e )x ed + ∑ ∑ (h d /C e )z desq ,∀e,s ∈ E
d∈D
d∈D q∈δ + (b(s))
(3d)
In the case when b(s) ≠ t(d), the constraints for each s ∈ E,
d ∈ D are formulated as follows:
z sdq ≤ x sd ,∀q ∈ δ + (b(s))
z sdq ≤ x qd ,∀q ∈ δ + (b(s))
z sdq ≥ x sd + x qd − 1,∀q ∈ δ + (b(s))
z sdq ≥ 0,∀q ∈ δ + (b(s))
(4a)
(4b)
(4c)
(4d)
f sq ≥ z sdq ,∀q ∈ δ + (b(s))
⎧
⎨
f esq − f esq =
⎩
∑
e∈δ + (v)
∑
e∈δ + (v)
z desq −
∑
e∈δ − (v)
∑
e∈δ − (v)
⎧
⎨
z desq =
⎩
z desq ≤ f esq ,∀e ∈ E,∀q ∈ δ + (b(s))
z dess = 0,∀e ∈ E
f sq ,v = a(s)
− f sq ,v = b(q),
0,otherwise
z dsq ,v = a(s)
−z dsq ,v = b(q),
0,otherwise
(4e)
∀q ∈ δ + (b(s))
z desq = 0,∀e ∈ δ + (b(s)),∀e ∈ δ − (b(s)),∀q ∈ δ + (b(s))
(4f)
∀q ∈ δ + (b(s))
(4g)
(4h)
(4i)
(4j)
The constraints (3b)-(3d) correspond to constraints (1b)-
(1d). The constraint (3c) concerns links load in nominal state
(without failures) and constraint (3d) concerns link load in
each failure state s, where s ∈ S.
Constraints (4a)-(4e) model in fact logical ‘and’ operator.
For each demand d ∈ D, operator takes as an input x sd and x qd
variables and sets f sq variable as a result. If a primary path
goes through link s and link q (x sd = 1 and x qd = 1), it means
that in state s the f sq ( f sq = 1) backup path is selected for
rerouting, for demand d. All primary paths that goes through
link s and q in state s are rerouted on the same route f sq .
The constraint (4f) forms a route f sq . The constraint is
formulated similarly as (2b) and (2e). The route f sq originates
in a(s) (PLR) and terminates in b(q) (NNHR).
Backup paths, used in a failure state s ∈ E by demand d ∈
D, are formed by z desq variables. In a feasible solution all
variables z desq = 1 indicate edges that belong to the backup
path used in state s by demand d. The constraint (4h) ensures
that all primary paths that go through link s and q use f sq path
for rerouting in the state s.
The constraints (4i) and (4j) block links that should not
be used in the state s. The constraints correspond to the
constraints (2f) and (2g) in MOB formulation.
In the case when b(s) = t(d) (s = q), the constraints for
each s ∈ E, d ∈ D are formulated as follows:
z sds ≥ x sd
f ss ≥ z sds
∑
e∈δ + (v)
∑
e∈δ + (v)
f ess −
z dess −
∑
e∈δ − (v)
∑
e∈δ − (v)
z dess ≤ f ess ,∀e ∈ E
z dsss = 0
⎧
⎨ f ss , v = a(s)
f ess = − f ss , v = b(s),
⎩
0, otherwise
⎧
⎨ z dss , v = a(s)
z dess = −z
⎩ dss , v = b(s),
0, otherwise
z desq = 0,q ≠ s,∀e ∈ E,∀q ∈ δ + (b(s))
(5a)
(5b)
(5c)
(5d)
(5e)
(5f)
(5g)
The ‘and’ operator is reduced to constraints (5a) and (5b)
– when a primary path goes through the s link, then f ss path
is selected for rerouting, for this path.

58 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
The constraints (5c) and (5d) simplify (4f) and (4g) constraints
– there is no need to iterate over every q ∈ δ + (b(s)).
Similarly (5e), (5f) and (5g) correspond to (4h), (4i) and
(4j) respectively.
V. SIMULATIONS
In this section, experiments performed in the paper are
explained in details. Network instances and settings used in
the tests are described.
The tests are performed on standard PC computer (2.8 GHz
Intel, 2.5 GB RAM). CPLEX solver (version 12) is used
with non-default mixed integer programming (MIP) parameters.
MIP probing level and cuts generation level are set to
aggressive and MIP emphasis is set to force optimality over
feasibility.
The network instances used in the tests are subnetworks
of networks presented in [1]. They are randomly chosen to
keep their size applicable for the tests. For example, network
instance CO9 is a subnetwork of network cost-239-100 and is
almost as large as cost-239-100.
Each test for the optimal NL runs no more than 24 hours.
Simulations are stopped after that time. There is no time limit
for path generation as it runs no more than a few seconds for
networks in Table I.
Each subnetwork instance contains a full matrix of demands
– for each pair of nodes (a,b) two demands exist: a directed
demand from node a to b and a directed demand from node b
to a. The number of demands is equal to |V | · (|V | − 1) for
each network instance.
VI. NODE-LINK FORMULATIONS COMPLEXITY
In this section, NL formulations complexity for practical
NL instances is described.
The sizes of the applicable networks confirm that their MIP
representations are hard to solve. Even with aggressive MIP
settings for CPLEX, network instances CO9 and AT9 could
not be solved in 24 hours time limit, as shown for MOB.
Though presented NL formulations are compact in the
number of variables, they prove to be unsolvable in reasonable
time and computer memory. For example, the number of
binary variables in OOB CO9 is equal to about 42000. In
MOB CO9 the number of binary variables is equal to about
13000 and number of continuous variables is equal to about
50000. It shows a large size of tested MIP problems.
Additionally, we solve NL formulations with cost239-100 –
the network instance with the smallest number of nodes from
[1]. The test is unsuccessful as it leads to a CPLEX “out of
memory” error.
VII. NUMERICAL RESULTS
In this section, we present and discuss numerical results
obtained in the tests.
A. Optimal OOB and MOB link utilization
In Table I we get the same value of minimized maximum
link utilization for OOB and for MOB, for all tested networks.
B. Optimal and suboptimal link utilization
The suboptimal results for single path layout can be computed
with a linear programming approach (path generation
approach) and an IP-based approach. Though path generation
has to solve several MIP problems it still provides solutions
for large network instances in reasonable time as shown in
[1]. The multipath suboptimal solutions provided by the path
generation determine the lower bounds for the optimal single
path layout solutions. On the other hand the results provided
by the path generation for single path layout determine the
upper bounds for the optimal single path layout solutions.
In Table II we compare optimal and suboptimal solutions.
The results show that a heuristic path generation provides
significantly different values from the optimal one. The values
of multipath solutions are better 32.05% (EX8) and 27.89%
(EB8) than the optimal solution. For AT8 and CO9 networks,
the suboptimal single path solutions are significantly worse
than the optimal solutions.
Due to the relatively small size of the network instances
the maximum path lengths of the primary paths if an IP-based
layout is used are rather small (in most cases not more than
3 hops per path). For these short path lengths, the destination
basically always equals either the NHR or NNHR. Therefore,
all OOB and MOB layouts are supposed to be identical if IPbased
layouts are used. It is thus an expected behavior that the
IP-based values for OOB and MOB are equal for all network
instances.
C. OOB and MOB network configuration effort
The configuration effort of OOB and MOB is related to the
length of the LSP paths. In Table III the maximum and average
configuration effort is shown for each network. Configuration
effort is calculated for each node in the network as a sum of
incoming and outgoing LSP paths. If LSP path goes through
the node it is treated as incoming and outgoing at the same
time. Maximum configuration relates to the node with the
maximum sum of incoming and outgoing LSP paths.
In Table III we observe that network configuration effort for
backup paths is several times greater than for primary paths.
We observe that there is no significant difference between
average primary paths configuration effort of OOB and MOB.
On the other hand, for EX8 and CO8 networks, there appear
significant differences in OOB and MOB configuration effort
for backup paths. The situation for EX8 can be described by
fact that for OOB longer backup paths are used in the optimal
solution. And similarly, for CO8 shorter paths are used.
VIII. SUMMARY AND CONCLUSIONS
The paper presents compact node-link formulations for
MPLS Fast Reroute optimal single path layout. We test the
formulations on network instances with practical sizes.
We provide optimal solutions for the single path layout for
two distinct MPLS local protection mechanisms: one-to-one
backup and many-to-one backup. We obtain the same value of
the minimized maximum link utilization for one-to-one backup
and many-to-one backup, for all tested networks. This seems
to be an interesting fact, taking into account that many-to-one

ŻUKOWASKI et al.: COMPACT NODE-LINK FORMULATIONS FOR THE OPTIMAL SINGLE PATH MPLS FAST REROUTE LAYOUT 59
TABLE I
MINIMIZED MAXIMUM LINK UTILIZATION
Network Optimal NLs Path generation approach IP-based approach
ID Name | V | | E | | D | MOB OOB OOB (multipath) OOB (single path) OOB MOB
CO8 cost239-100_8 8 32 56 90.90% 90.90% 90.44% 102.27% 110.7% 110.7%
CO9 cost239-100_9 9 38 72 - 70.16% 69.38% 89.37% 87.6% 87.6%
GE8 geant_8 8 22 56 62.79% 62.79% 62.78% 71.68% 71.69% 71.69%
GE9 geant_9 9 26 72 58.60% 58.60% 58.60% 71.27% 66.08% 66.08%
EX8 exodus_8 8 36 56 65.15% 65.15% 33.10% 66.62% 74.84% 74.84%
EB8 ebone_8 8 34 56 63.94% 63.94% 36.05% 65.85% 68.03% 68.03%
AT8 atnt_8 8 34 56 52.40% 52.40% 44.43% 73.36% 91.01% 91.01%
AT9 atnt_9 9 38 72 - 59.47% 59.47% 81.23% 81.74% 81.74%
TABLE II
GAPS BETWEEN OPTIMAL AND SUBOPTIMAL SOLUTIONS
Path generation approach IP-based approach
ID OOB (multipath) OOB (single path) OOB MOB
CO8 0.46% 11.37% 19.8% 19.8%
CO9 0.78% 19.21% 17.44% -
GE8 0.01% 8.89% 8.9% 8.9%
GE9 0.0% 12.67% 7.48% 7.48%
EX8 32.05% 1.47% 9.69% 9.69%
EB8 27.89% 1.91% 4.09% 4.09%
AT8 7.97% 20.96% 38.61% 38.61%
AT9 0.0% 21.76% 22.27% -
TABLE III
NETWORK CONFIGURATION EFFORT
Primary paths Backup paths All paths
avg. max. avg. max. avg. max.
CO8 OOB 26.5 44 56.75 102 83.25 142
CO8 MOB 26.75 38 65.25 94 92 132
-0.25 6 -8.5 8 -8.75 10
GE8 OOB 30 48 87 152 117 198
GE8 MOB 30 44 83.5 166 113.5 208
0 4 3.5 -14 3.5 -10
GE9 OOB 34.67 70 106.22 212 140.89 282
GE9 MOB 35.56 60 106.22 198 141.78 250
-0.89 10 0 14 -0.89 32
EX8 OOB 23.75 36 75.25 94 99 130
EX8 MOB 22 30 53.5 72 75.5 102
1.75 6 21.75 22 23.5 28
EB8 OOB 25.75 32 58.5 86 84.25 118
EB8 MOB 22.75 38 55.75 78 78.5 116
3 -6 2.75 8 5.75 2
AT8 OOB 29.75 48 75 150 104.75 194
AT8 MOB 32 60 73.25 110 105.25 170
-2.25 -12 1.75 40 -0.5 24
ACKNOWLEDGMENT
This work was supported by the Euro-FGI FP6 NoE as
well as the Euro-NF FP7 NoE. The Polish authors were
funded by Polish Ministry of Science and Higher Education
under research grant N517 397334. The German authors
were funded by Deutsche Forschungsgemeinschaft under grant
TR257/23-2.
REFERENCES
[1] M. Pióro, A. Tomaszewski, C. Żukowski, D. Hock, M. Hartmann, and
M. Menth, “Optimized IP-Based vs. Explicit Paths for One-to-One
Backup in MPLS Fast Reroute,” in 14 th International Telecommunications
Network Strategy and Planning Symposium, Warsaw, Poland, Sep. 2010.
[2] R. Martin, M. Menth, and K. Canbolat, “Capacity Requirements for the
Facility Backup Option in MPLS Fast Reroute,” in IEEE Workshop on
High Performance Switching and Routing (HPSR), Poznan, Poland, Jun.
2006, pp. 329 – 338.
[3] A. Raj and O. C. Ibe, “A survey of ip and multiprotocol label switching
fast reroute schemes,” Comput. Netw., vol. 51, pp. 1882–1907, June 2007.
[4] D. Hock, M. Hartmann, M. Menth, and C. Schwartz, “Optimizing
Unique Shortest Paths for Resilient Routing and Fast Reroute in IP-Based
Networks,” Osaka, Japan, Apr. 2010.
[5] R. Martin, M. Menth, and K. Canbolat, “Capacity Requirements for the
One-to-One Backup Option in MPLS Fast Reroute,” in IEEE International
Conference on Broadband Communication, Networks, and Systems
(BROADNETS), San Jose, CA, USA, Oct. 2006.
[6] S. Orlowski and M. Pióro, “On the complexity of column generation in
survivable network design with path-based survivability mechanisms,” in
International Network Optimization Conference (INOC), 2009.
[7] M. Pióro, Á. Szentesi, J. Harmatos, A. Jüttner, P. Gajowniczek, and
S. Kozdrowski, “On Open Shortest Path First Related Network Optimisation
Problems,” Performance Evaluation, vol. 48, pp. 201 – 223, 2002.
[8] M. Pióro and D. Medhi, Routing, Flow, and Capacity Design in Communication
and Computer Networks. Morgan Kaufman, 2004.
backup is a restricted version of one-to-one backup. It would
be interesting if we could extend this observation for larger
network instances.
We compare optimal solutions for the single path layout
with suboptimal solutions provided by algorithms based on
path generation approach and IP-based approach. The values
of the optimal solution are usually significantly better than
suboptimal solutions.
Though we are able to compute optimal solutions for a set of
practical network instances, for larger networks more efficient
methods have to be found.
Cezary Żukowski is a master student in the Institute of Telecommunications
at the Warsaw University of Technology, Poland. He received the B.S. degree
in telecommunications in 2009. His studies concentrate on survivable networks
design and routing problems.
Artur Tomaszewski is an assistant professor at the Faculty of Electronics and
Information Technologies. He received the MSc and the PhD degrees from
the Warsaw University of Technology in 1990 and 1993, respectively, both in
telecommunications. With his research interests focused on the architecture
of telecommunications networks, network management and control systems
and software, network planning methodologies and network design and
optimization methods, he is an author or co-author of almost a hundred of
journal and conference papers.

60 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
Michał Pióro is a full professor and the head of the Computer Networks
and Switching Division in the Institute of Telecommunications at the Warsaw
University of Technology, Poland, and a full professor at Lund University,
Sweden. He received the Ph.D. degree in telecommunications in 1979 and
the D.Sc. degree in 1990, both from the Warsaw University of Technology.
In 2002 he received a Polish State Professorship. His research interests
concentrate on modeling, design and performance evaluation of telecommunication
networks. He is an author of four books and around 150 technical
papers presented in the telecommunication and OR journals and conference
proceedings. He has lead many national and international research projects
for telecom industry and EC in the field.
David Hock studied computer science and mathematics at the University of
Würzburg/Germany and at the BTH in Karlskrona/Sweden. He received his
diploma degree in computer science in spring 2009. Since then he has been
pursuing his PhD as a research assistant at the Chair of Distributed Systems at
the Institute of Computer Science in Würzburg. His current research focuses
on resilient IP networks and Fast Reroute.
Matthias Hartmann studied computer science and mathematics at the
University of Würzburg/Germany, the University of Texas at Austin/USA, and
at the Simula Research Laboratory/Oslo, Norway. He received his diploma
degree in computer science in 2007. Currently, he is a researcher at the
Institute of Computer Science in Würzburg and pursuing his PhD. His
current research focuses on IP Fast Reroute and Future Internet Routing in
combination with performance evaluation and resilience analysis.
Michael Menth is a full professor in Computer Science and the head of the
Communication Networks chair in the Faculty of Science at the University of
Tübingen/Germany. He received a Diploma and PhD degree in 1998 and 2004
from the University of Würzburg/Germany. Prior he was studying computer
science at the University of Texas at Austin and worked at the University of
Ulm/Germany. His special interests are performance analysis and optimization
of communication networks, resource management, resilience issues, and
Future Internet. Prof. Menth holds numerous patents and received various
scientific awards for innovative work.

ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011 61
Enhancing Data Transmission Reliability with
Multipath Multicast Rate Allocation
Matin Bagherpour, Mehrdad Alipour and Øivind Kure
Abstract—In this paper, a multipath routing scheme is proposed
for data transmission in a packet-switched network to
improve the reliability of data delivery to multicast destinations,
and to reduce network congestion. A multi-objective optimization
model is presented that utilizes FEC (Forward Error Correction)
across multiple multicast trees for transmitting packets toward
the destinations. This model assigns the transmission rates over
multicast trees so that the probability of irrecoverable loss for
each destination and also the link congestion are minimized.
We propose a genetic algorithm based on SPEA (Strength
Pareto Evolutionary Algorithm) in order to approximate Pareto
optimal solutions of this rate allocation problem with a nondominated
solution set. Numerical results show that splitting data
packets between multiple trees increases reliability and decreases
network congestion when compared with the results obtained for
transmitting data packets over a single tree.
Index Terms—Forward Error Correction (FEC), load balancing,
multicast communication, multipath routing, Quality of
Service
I. INTRODUCTION
PATH diversity can be achieved by setting up multiple
parallel paths between source and destination nodes. Multipath
routing not only can reduce congestion in the network,
but also can be considered as a tool for error resilience by
providing higher bandwidth for each session. The idea of using
multiple parallel paths for transmitting data was first proposed
in [1]. In this work, a message is divided into a number of submessages
and the sub-messages are transmitted over disjoint
paths in the network.
A comprehensive review of multipath routing for load balancing
and traffic engineering considering Quality of Service
(QoS) is presented in [2]. The authors introduced a general
multi-objective optimization model to balance traffic load
among multiple trees and optimize QoS measures such as
average delay, and average delay jitter.
Since transport protocols such as TCP favor reliability over
timeliness, they are not appropriate for real time streaming
applications. Therefore, many approaches have been proposed
to deal with these kind of applications. Layered and errorresilient
video coding are two approaches of this kind. Layered
video codec adapts the internet bit rate to the available
bandwidth and tries to deal with time-varying nature of the
internet [3]. In error-resilient codec, the bit stream is modified
M. Bagherpour is with the Norwegian University of Science and Technology,
Trondheim, Norway (corresponding author to provide phone: 47-735-
92775; fax: 47-735-92790; e-mail: matin@q2s.ntnu.no).
M. Alipour is with Department of Industrial Engineering, University of
Science and Culture, Tehran, Iran (e-mail: m.alipour@usc.ac.ir).
Ø. Kure is with the Norwegian University of Science and Technology,
Trondheim, Norway (e-mail: okure@q2s.ntnu.no).
in a way that the decoded video degrades more smoothly
in lossy environments [3]–[5]. It is shown that multipath
transmission, when combined with error control schemes, can
improve the quality of multimedia services in terms of packet
loss and delay. There has recently been an increasing interest
in using multipath routing for failure recovery of real-time
multimedia applications. For example, Multiple Description
Coding (MDC) and Forward Error Correction (FEC) are
combined with multipath routing to improve data transmission
in internet. In MDC approach, a video source is split into
multiple descriptions and each of them is sent over a different
channel. MDC has been studied in detail in [6]–[10]. FEC is
a channel coding technique which increases reliability at the
expense of bandwidth expansion [11]–[14].
There are also some approaches based on multicasting to
stream multimedia sessions over the internet [15]. Multicast
reduces bandwidth consumption by not sending duplicate
packets on the same physical link of the network [16].
In this paper, we utilize path diversity over packet switched
networks in transmitting data packets from a source node to
multiple destination nodes of a multicast group. We integrate
multicast routing and multipath transmission with failure recovery
to improve reliability in data transmission and reduce
congestion in a packet switched network. We suppose that
multicast trees have the ability to send data packets from
the source to destinations at different rates. In this work,
each network link is modeled as a continuous Gilbert-Elliot
channel as in [17]. A Gilbert-Elliot channel can have two
states, namely “good” and “bad” states. During transmission
of a packet, if the channel is in the good state, the packet
will be delivered to the destination successfully; otherwise, it
will be lost. We use FEC scheme to split data packets between
multicast trees, i.e. the data is encoded into a block of N equal
packets so that each destination is able to recover the video
session by receiving at least K packets (K ≤ N); otherwise,
an irrecoverable loss happens. A multi-objective optimization
model is presented for the aforementioned problem which tries
to minimize the probability of irrecoverable loss (reliability
maximization) and network congestion (by minimizing maximum
utilization of network links).
By this model, we try to exploit both load balancing and
failure recovery advantages of path diversity in transmitting
data packets to receivers. We use simulation to estimate
probability distribution of bad burst times of each path in the
network in order to calculate the probability of irrecoverable
loss for each destination. Since the multi-objective model is
highly nonlinear and cannot be solved by common solvers,
a genetic algorithm based on Strength Pareto Evolutionary

62 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
Algorithm (SPEA) is presented to solve the multi-objective
model for a sample network topology.
The rest of this paper is organized as follows. Related works
are surveyed in this section and motivation of this work is
discussed. In Section II, the network model is introduced.
Our mathematical programming model of the problem is given
in Section III. In Section IV, the proposed genetic algorithm
based on SPEA is presented. In Section V, numerical results
of implementation of the algorithm for a sample network are
presented and the advantages of using multiple trees over
single tree are illustrated. In Section VI, conclusions and
suggestions for future research are given.
A. Related Works
In previous works, multipath routing is combined with MDC
in order to enhance resilience to loss in video streaming [18],
or to reduce rate distortion of video streams [19]. Multipath
routing of TCP packets is used to control the congestion
in networks with minimum signaling overhead [20]. Path
diversity is also used over IP voice streams to increase speech
quality [21]. In addition, the problem of rate allocation over
multiple paths is presented in [22] and [23]. In [22], the authors
consider a leaky bucket model for network paths and try to
minimize the end-to-end delay. The rate allocation problem
with multiple senders to a single receiver is presented in [23].
The authors suppose that the connection between each pair
of source and receiver is a Gilbert-Elliot channel and propose
an algorithm to solve packet partitioning and rate allocation
problems. A rate allocation algorithm is used to minimize
probability of irrecoverable loss in FEC approach.
FEC is a system of error control for data transmission,
where the sender adds redundant data to the messages to increase
the chance of successful data recovering at the receiver.
An irrecoverable loss occurs if the number of successfully
delivered packets is smaller than the number of initial packets
before adding redundant packets. Since complexity of the
proposed model in [23] depends on the number of packets and
increases exponentially by the number of paths, the authors
proposed a brute-force search algorithm to solve the rate allocation
problem for the special case of two disjoint paths. They
considered disjoint paths to facilitate modeling of irrecoverable
loss, but it should be noted that finding completely disjoint
paths may only be possible in highly connected networks.
The advantages of their approach in reducing probability of
irrecoverable loss are investigated by implementing it for the
actual internet in [24].
A rate allocation problem is also presented in [17] where the
authors take advantage of path diversity to send data packets
from the source to destinations over general packet switched
networks, like internet, in order to minimize the probability of
irrecoverable loss. They assume that the paths are disjoint, and
each path is modeled as a continuous Gilbert-Elliot channel.
The authors calculate probability of irrecoverable loss by
using a continuous approximation for probability distribution
of the time each path spends in the bad state during a block
time. However, in order to simplify calculation of probability
distribution of bad state time, they assume that each path
cannot have more than one bad burst time during a block
time.
A. Link Model
II. NETWORK MODEL
We model the network links with a two-state continuous
time Markov process: Gillbert-Elliot. According to the Gilbert-
Elliot model, a channel spends an exponentially distributed
amount of time with mean 1/µ g in the good state. Then, it
alternates to the bad state and stays in the bad state for another
exponentially distributed amount of time with mean 1/µ b .
Although this model is used for network paths in [17], we
make use of it for each link in the network. This assumption is
justified by the fact that the Gilbert-Elliot model has the ability
to model a single transmission channel whereas network paths
usually consist of several links and cannot be considered as
single transmission channels. On the other hand, independent
Gilbert-Elliot channel model is only applicable for disjoint
paths. In this paper, each path consists of several links that
each is modeled as an independent Gilbert-Elliot channel. It
is also assumed that the good time mean 1/µ g of a link is
much greater than its bad time mean 1/µ b , and the channel
state does not change during transmission of a packet [17]. If
a packet is transmitted during the bad state of a link, it will
be lost before reaching the downlink node; otherwise, it will
be delivered to the downlink node successfully. This model
is widely used for transmission channels for the applications
where delay is not a critical factor [17].
B. Error Correction Model
In this work, FEC is applied across multiple multi-rate
trees to reduce probability of irrecoverable loss occurrence
for each destination. In this scheme, data is encoded into
a block of N equal packets so that each destination can
recover the whole data by receiving at least K packets.
K represents the number of initial packets before adding
redundant data packets. In other words, an irrecoverable loss
occurs for a destination if at least N − K packets are lost out
of N packets that are transmitted toward that destination. By
modeling network links as Gilbert-Elliot channels, we are able
to formulate the irrecoverable loss for non-disjoint multicast
trees for transmitting data packets to multicast destinations.
Mathematical optimization formulation of the aforementioned
problem is presented in section III.
III. MATHEMATICAL FORMULATION
In this model, MT represents the set of multicast trees, M
the set of destinations, and L the set of network links. It is
assumed that each multicast tree has the ability to transmit
packets from the source to all the destinations in M at
different rates. The problem is formulated as a multi-objective
mathematical programming model as follows:
⎛
⎞
|MT |
min P j E = P ∑
⎝ B ij X ij ≥ N−K ⎠∀j = 1, . . . , |M| (1)
i=1

BAGHERPOUR et al.: ENHANCING DATA TRANSMISSION RELIABILITY WITH MULTIPATH MULTICAST RATE ALLOCATION 63
Parameter
TABLE I
NOTATIONS: PARAMETERS AND DECISION VARIABLES
Description
N Total number of packets to be sent to each destination;
K Minimum number of data packets needed in each destination
to recover the whole data (number of information
packets);
T Total block time;
path ij Path associated with the jth destination in the ith multicast
tree;
B ij Random variable representing the portion of time at least
one of the links of path ij spends in the bad state during
the total block;
P j E Probability of irrecoverable loss for the jth destination;
λ uv
ij 1 if the link (u, v) exists in path ij , otherwise 0;
Cuv
max Maximum allowable capacity of the link (u, v) for data
transmission;
K ′ Maximum number of paths to transmit packets for each
destination;.
Decision variables
X ij
|MT |
∑
i=1
Number of packets sent over path ij toward jth destination.
|MT |
∑
i=1
min max
|MT |
∑
i=1
|M|
max
j=1
(u,v)∈L
⌈
Xij
N
⎛
⎜
⎝
|MT
∑
|
i=1
|M|
max
j=1
C max uv
(
Xijλ uv
ij
T
)
⎞
⎟
⎠
(2)
X ij = N ∀j = 1, . . . , |M| (3)
(
Xij λ uv )
ij
≤ Cuv max ∀(u, v) ∈ L (4)
T
⌉
≤ K ′ ∀j = 1, . . . , |M| (5)
0 ≤ X ij ≤ N, X ij Integer
The model parameters and decision variables are defined in
Table I.
In this model, P j E
, the probability of irrecoverable loss for
the j th destination, is calculated by continuous approximation
as in [17] i.e. the number of lost data packets in each path
equals to the portion of time that the path spends in the
bad state multiplied by the number of data packets that are
transmitted over this path. This approximation is rational if
we suppose that the packet inter-arrival time is much shorter
than each typical bad burst of each link in the network,
T
N

64 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
Means of these random variables are generated according to
a uniform distribution. Simulation results will be presented in
Section V.
B. Multi-Objective Evolutionary Algorithm Approach
We propose a multi-objective evolutionary algorithm to
solve the traffic splitting problem modeled in Section III. A
survey of the works successfully used multi-objective evolutionary
algorithms for traffic engineering problems is available
in [2].
Genetic algorithm is one of the widely used successful
evolutionary algorithms. In the genetic algorithm, an initial
population of feasible solutions is generated as the starting
point of the search. Individuals are evaluated based on the
value of a fitness function. The fittest individuals are selected
as parents according to a selection method to generate the next
generation by using genetic operators such as crossover and
mutation. This procedure continues repeatedly by replacing
the old generation with the new one and keeping the best
individuals of each generation until a terminating condition is
satisfied.
In this paper, a genetic algorithm based on SPEA [25] is
proposed. In SPEA, in each generation an external set with the
best Pareto solutions are held in addition to the evolutionary
population. In the multi-objective optimization context, a solution
x from the solution space dominates another solution y
from that space if and only if x is as good as y regarding every
objective, and is strictly better than y in at least one objective
function. In the case that neither x nor y dominates the other,
it is said that they are Pareto solutions or non-dominating
solutions in contrast to each other. In SPEA, solutions in
the external set are pruned and updated in each generation
whenever a solution from the population dominates at least
one solution in the external Pareto set.
Our proposed multi-objective genetic algorithm is structured
like SPEA with some modifications in generating the initial
population and fitness assignment strategy. These changes
are necessary because SPEA is constructed to solve nonconstrained
multi-objective problems, whereas our problem is
constrained. Since generating a feasible initial population in
a way that satisfies all the constraints is not trivial, and also
the population will not necessarily remain feasible after using
crossover and mutation operators over the individuals, we use
a penalty based approach to penalize the individuals that are
not feasible based on their degree of infeasibility according
to [26]. In this approach, an adaptive penalty function and a
distance function are used to penalize infeasible individuals to
reduce their chance of being selected as parents. Penalty based
approaches have a good reputation in solving constrained optimization
problems with evolutionary algorithms. This method
is easy to implement and does not need any parameter tuning
when compared with the other available approaches.
The proposed multi-objective genetic algorithm has the
following steps:
Step 1: The initial population P is generated randomly in a
way that each individual is feasible according to the constraints
(3) and (5), but it can be infeasible regarding the capacity
constraints represented by (4). Also, an empty set P ′ of nondominated
solutions is created.
Step 2: The non-dominated individuals of P are copied into
P ′ and the solutions within P ′ which are covered by the other
members of P ′ are removed. The solution x is said to cover
the solution y, if and only if, x dominates y or x and y have
the same fitness considering all the objective functions.
Step 3: If the number of non-dominated solutions exceeds
a given maximum number N ′ , thenP ′ is pruned by using
a clustering method to limit the size of Pareto solutions
to the specified size N ′ . Clustering is used to reduce the
size of non-dominated solution set to its predefined size by
keeping representative solutions that have specifications of all
the solutions. We use average linkage method because it has
proven to perform well with SPEA algorithm [25].
Step 4: For each individual x, the values of |M| objective
functions as formulated in (1), and link utilization as in (2)
are calculated and preserved in the vector Obj x (Obj x is a
vector of |M| + 1 scalar values). Then, the values of objective
functions are modified for each solution according to the
penalty based approach. The degree of violation of capacity
constraints is calculated for each individual x as follows:
v(x) = 1
|L|
∑
2
|L| 2
C j (x)
, (6)
j=1
Cmax
j
where C j (x) represents the degree of violation of the j th
capacity constraint for individual x, and:
C j max = max
x
C j (x) (7)
C j (x) takes positive value if j th capacity constraint in equations
(4) is violated by solution x; otherwise, it is 0.
The distance value of the individual x in each dimension i
of objective function (i th element of vector Obj x ) is calculated
as follows:
{ v(x) if rf = 0
d i (x) = √
Objx (i) 2 + v(x) 2
(8)
Otherwise
where Obj x (i) represents the i th element of vector Obj x , and
r f indicates the portion of feasible individuals in the current
population. r f takes value from [0,1]. If there is no feasible
individual in the current population, the individuals with
smaller capacity constraint violation values will have smaller
distance function in the i th dimension and will dominate the
other individuals in this dimension. If there is at least one
feasible individual in the population, those feasible individuals
with smaller objective function value will dominate the other
individuals in the i th dimension. In this case, among the
infeasible individuals, the ones that are closer to the origin
in Obj x (i) − v(x) space will have smaller distance function
regarding the i th dimension [26].
The penalty function for the i th objective function of
individual x is calculated according to (9):
where
p i (x) = (1 − r f )X i (x) + r f Y i (x), (9)
{ 0 if rf = 0
X i (x) =
v(x) Otherwise
(10)

BAGHERPOUR et al.: ENHANCING DATA TRANSMISSION RELIABILITY WITH MULTIPATH MULTICAST RATE ALLOCATION 65
{
0 if x is a feasible individual
Y i (x) =
Obj x (i) Otherwise
(11)
This penalty function penalizes the infeasible individuals even
more. The first part of this penalty function,(1 − r f )X i (x),
has larger values for the individuals with large amount of
constraint violation and will have more effect when r f tends
to zero. In the second part of the penalty function, r f Y i (x),
the infeasible individuals with larger objective function value
will be penalized more. This penalty function has more impact
when r f tends to one [26].
Finally each dimension i of the modified objective function
for the individual x is obtained by using (8) and (9) as follows:
Modified Obj x (i) = d i (x) + p i (x) (12)
Fig. 1.
V-NSF network topology
Step 5: Fitness function of individuals in P and P ′ is
calculated as follows:
Each individual i ∈ P ′ is assigned a strength value s i =
n/N +1) ∈ [0, 1], where n represents the number of individuals
in P which are dominated by i, and N represents the size
of P . Fitness of each individual j is defined is follows:
{
sj j ∈ P ′
f j = 1 + ∑ s i j ∈ P (13)
i,i≥j
Step 6: The individuals are selected from P +P ′ as parents to
form the mating pool according to their fitness. In this study,
the Roulette wheel selection is used to choose the parents.
Step 7: Crossover and mutation operators are applied to
the parents. In this work, we use flat and random operators
which are proposed in [27] and [28] respectively. As a result,
population of the next generation is generated.
Step 8: The procedure terminates if the domination rate
of the current generation is zero, otherwise it is continued
from Step 2. Domination rate in a generation is defined as
the portion of the individuals in the non-dominated set of
the previous generation which are dominated by the nondominated
individuals in the current generation.
In the next section, numerical results of implementation of
the multi-objective genetic algorithm for a sample network are
presented.
A. Simulation Results
V. NUMERICAL RESULTS
The 14-node NSF (National Science Foundation) network
topology is chosen to study the performance of proposed
algorithm. This network topology is shown in Fig. 1. We
consider node N 0 as the source of the multicast transmission
and nodes N 4 , N 5 , N 9 , and N 12 as the destination nodes.
We also consider that three multicast trees are available to
transmit data packets from the source to destinations. Let
MT = {T 1 , T 2 , T 3 } be the set of multicast trees. The multicast
trees T 1 , T 2 and T 3 are illustrated in Fig. 2 by using red, blue,
and green colors respectively.
As mentioned before, discrete event simulation is used to
estimate probability distribution of the portion of time that
each path of multicast trees spends in the bad state out of
the total block time T . For this purpose, we assume that
Fig. 2.
V-NSF network multicast trees
the total block time T for transmitting data packets is 1 s.
We consider network links with uniformly distributed random
good time and bad time means, and simulate the system to
observe and record the behavior of network paths in order
to derive distribution of the bad time portions. The good
time mean for each network link is generated according to a
uniform distribution with parameters 0.9 s. and 1 s. and the bad
time mean of each network link is uniformly distributed with
parameters 0.01 s. and 0.02 s. The range of these parameters
is chosen based on the previous works [17] and [23].
We replicate the simulation 1000 times for each path in
order to have adequate number of observations to be able
to find the shape of probability distribution functions, and
estimate the parameters of the distribution. Three well-known
statistical hypothesis tests are applied to data samples, namely
Kolmogorov-Smirnov test, Anderson-Darling test, and Chisquared
test. The results show that the distribution that fits
best with the data samples of the bad time portion of each
path and successfully passes all statistical tests is the shifted
Log-Normal. Data samples for each path pass the hypothesis of
following shifted Log-Normal distribution. The parameters of
the shifted Log-Normal distribution for each path are obtained
by using maximum likelihood estimation. Values of parameters
obtained for the Log-Normal distribution associated of each
path are given in Table II. In this table, P ath T i,Nj represents
the path associated with destination N j in tree T i
When a random variable X has shifted Log-Normal distribution
with parameters (µ, σ, γ), variable (X − γ) has
Log-Normal distribution with parameters (µ, σ), i.e. Y =

66 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
Fig. 3. Data histogram of path T1,N4 and fitted Log-Normal (µ, σ, γ) =
(−1.74, 0.124, −0.07)
Fig. 5. Data histogram of path T1, N9 and fitted Log-Normal (µ, σ, γ) =
(−2.037, 0.141, −0.054)
Fig. 4. Data histogram of path T1, N5 and fitted Log-Normal (µ, σ, γ) =
(−1.701, 0.114, −0.095)
Fig. 6. Data histogram of path T1, N12 and fitted Log-Normal (µ, σ, γ) =
(−1.098, 0.071, −0.206)
log(X − γ) has normal distribution with parameters (µ,σ 2 ).
Histograms of the observed bad time portions of the paths
associated with destinations N 4 , N 5 , N 9 , and N 12 in T 1 are
illustrated in Fig. 3 to Fig. 6 respectively. These figures also
demonstrate Log-Normal distribution curve that is fitted on
data samples.
B. Genetic Algorithm Implementation Results
After obtaining probability distribution of the bad time
portion of paths, we use our proposed algorithm to find
solutions for the optimization problem presented in Section
III. In each generation of the proposed genetic algorithm, we
need to calculate the irrecoverable loss probabilities according
to (1) for each individual. To be able to calculate these
probabilities, we need to have the cumulative probability
distribution of the weighted sum of Log-Normal variables.
P j E
is calculated supposing that B ijs in (1) have shifted
Log-Normal distribution. Since distribution of sum of Log-
Normal variables cannot be found in the closed form, we
use the well-known approximation of Fenton and Wilkinson
[29]. They approximated summation of Log-Normal variables
with another Log-Normal variable. If we assume that X j
j = 1, ..., n has Log-Normal distribution with parameters
(µ j , σ j ), then sum of X j s is approximated by a Log-Normal
variable with parameters (µ, σ) as follows:
⎛ n∑
⎞
e 2µj+σ2 j (e
σ 2 j − 1)
σ 2 j=1
= log ⎜
⎟
⎝ ∑
( n ⎠ (14)
e µj+σ2 j /2 ) 2
j=1
⎛
⎞
n∑
µ = log ⎝ e µj+σ2 j /2 ⎠ − σ2 j
(15)
2
j=1
By this approximation, fitness value of each individual in
the genetic algorithm can be easily calculated from (1). We
implemented the proposed genetic algorithm for the network
and paths illustrated in Fig. 2 with random good and bad time
for network links.
The values of genetic algorithm parameters are presented
in Table. III. We run the algorithm with two values for the
maximum number of paths for each destination. Also, the
proposed genetic algorithm is run for 12 different capacity
sets for network links.
Figs. 7-10 illustrate the average of irrecoverable loss probability
versus K obtained by single-tree transmission and
multi-tree transmission. In multi tree case, we are allowed
to use all the aforementioned trees to send the data packets
toward the destinations, whereas in single tree case, we can
use only one specific tree to deliver the data packets to the

BAGHERPOUR et al.: ENHANCING DATA TRANSMISSION RELIABILITY WITH MULTIPATH MULTICAST RATE ALLOCATION 67
TABLE II
LOG-NORMAL DISTRIBUTION PARAMETERS
Path Parameter µ Parameter σ Parameter γ
Path T1,N4 -1.823 0.132 -0.065
Path T2,N4 -1.917 0.147 -0.079
Path T3,N4 -1.563 0.129 -0.106
Path T1,N5 -2.322 0.146 -0.040
Path T2,N5 -1.865 0.172 -0.049
Path T3,N5 -1.412 0.103 -0.027
Path T1,N9 -1.990 0.130 -0.063
Path T2,N9 -0.658 0.046 -0.401
Path T3,N9 -1.642 0.129 -0.078
Path T1,N12 -1.530 0.108 -0.094
Path T2,N12 -1.919 0.138 -0.082
Path T3,N12 -2.284 0.174 -0.037
Fig. 7. Average value of irrecoverable loss vs. K for single tree and multi-ree
for the first destination
TABLE III
GENETIC ALGORITHM PARAMETERS
Parameter
Value
Total packet number (N) 1000
Initial packet number (K) 875, 880, 885, 890, 895, 900
Maximum number of paths (K ′ ) 2, 3
Network links capacity (C) 12 different capacity sets
Population size 100
Non-dominated set size 300
Crossover rate 0.85
Mutation rate 0.05
destinations. Since we have multiple non-dominated solutions
in each implementation of genetic algorithm, we calculate
the average value of each objective function over different
solutions in order to obtain one representative in each µσγ
implementation of the algorithm.
We can see from Fig. 7 that for NSF network topology, the
average probability of irrecoverable loss for destination N 4 by
using multiple trees is smaller than that by using only trees
T 1 and T 3 . However, it is greater than the value obtained by
using only T 2 . The similar observation can be seen for the
other destinations in other figures.
To compare multi-tree transmission and single-tree transmission,
we can see from Fig. 7 to Fig. 10 that if we use
only the tree T 1 to send data packets toward the destinations,
probability of irrecoverable loss for the destinations N 9 are
smaller as compared to the multi-tree case. However, probabilities
of occurrence of irrecoverable loss for N 4 , N 5 , and
N 12 in single-tree case are respectively more than 0.5, approximately
0.3 and more than 0.8 that are much greater than the
probability under multi-tree transmission. These probabilities
of irrecoverable loss for these destinations can be considered
very unacceptable. We can observe similar behavior for other
destinations. In the presented results, we observe that sending
all the data packets over only one tree results to enhance the
probability of irrecoverable loss for some destinations, but
can not necessarily keep the probability low enough for all
destinations and make them much worse as compared to multi
tree case.
Fig. 8. Average value of irrecoverable loss vs. K for single tree and multi-ree
for the second destination
Fig. 9. Average value of irrecoverable loss vs. K for single tree and multi-ree
for the third destination
Fig. 10. Average value of irrecoverable loss vs. K for single tree and multiree
for the fourth destination

68 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
TABLE IV
NUMERICAL RESULTS
Multicast
trees
Decision variables
Objective
functions
T 1
X 12 = 1000, PE 2 = 0.1172,
X 11 = 1000, PE 1 = 0.4925,
X 13 = 1000, PE 3 = 0.1072,
X ij =0 for i=2, 3, j=1, 2, 3, 4. P 4 E = 0.8641.
T 2
X 22 = 1000, PE 2 = 0.1255,
X 21 = 1000, PE 1 = 0.0041,
X 23 = 1000, PE 3 = 0.4711,
X ij =0 for i=2, 3, j=1, 2, 3, 4. P 4 E = 0.4980.
T 3
X 32 = 1000, PE 2 = 0.5024,
X 31 = 1000, PE 1 = 0.1183,
X 33 = 1000, PE 3 = 0.4905,
X ij =0 for i=2, 3, j=1, 2, 3, 4. P 4 E = 0.1180.
T 1 , T 1 , T 3
X 14 = 2, X 21 = 692, X 22 = 488, PE 2 = 0.0547,
X 11 = 61, X 12 = 508, X 13 = 977, PE 1 = 0.0019,
X 23 = 19, X 24 = 4, X 31 = 247, PE 3 = 0.1071,
X 32 = 4, X 33 = 4, X 34 = 994, P 3 E = 0.1190.
Fig. 11. Domination rate, K = 950
To show that sending data packets over multiple trees can
improve reliability of transmission to multicast destinations in
comparison with single-tree, we implemented the model with
a different parameter setting. In this test, the means of good
and bad times for all network links are equal to 0.1 s and
0.01 s respectively. We relaxed the capacity constraint of links.
This allows the decision variables associated with a destination
take values independent from values of decision variables
associated with other destinations. We used the first objective
functions in (1) as the fitness function in the proposed
genetic algorithm. By this setting, values of decision variables
associated with each destination are independent from those
of other destinations according to the mathematical model in
Section III. The results of implementing the genetic algorithm
for single-tree and multi-tree transmission and for K ′ = 950
are illustrated in Table. IV. It can be observed that when we
are allowed to use all the multicast trees to send data packets,
probabilities of irrecoverable loss are significantly less thansingle
tree transmission. Number of data packets transmitted
over trees T 1 , T 2 , and T 3 are equal to the maximum number of
packets that are being transmitted to different destinations over
these trees and can be calculated having values of decision
variables.
As mentioned before, a domination rate is calculated at each
iteration of the genetic algorithm that represents the portion
of Pareto solutions in that iteration that dominate the Pareto
solutions of the previous iteration. Fig. 11 to Fig. 13 show the
domination rate at iterations of the proposed genetic algorithm
for K = 950, 955, and 960. The genetic algorithm stops when
there is only one non-dominated solution remained in the nondominated
set in several subsequent iterations of the algorithm.
We can see from these figures that the domination rate in the
Pareto solutions at initial iterations is higher and it gradually
Fig. 12. Domination rate, K = 955
Fig. 13. Domination rate, K = 960
converges to zero after around 100 generations. This rate can
be pegged as a convergence sign of the genetic algorithm.
Multi-tree transmission can also reduce network congestion
in comparison to single-tree transmission. Fig. 14 represents
the average value of maximum link utilization function versus
link capacity for multi-tree and single-tree. The single-tree
curve represents the average of results obtained from sending
data packets over the first, the second and the third tree. We
can see from Fig. 14 that the average of network congestion
in multi-tree transmission is much smaller than this value for
single-tree cases. It can also be inferred from this figure that
when the links have lower capacity, the single tree solutions

BAGHERPOUR et al.: ENHANCING DATA TRANSMISSION RELIABILITY WITH MULTIPATH MULTICAST RATE ALLOCATION 69
Fig. 14.
Average value of maximum link utilization versus link capacity
are not feasible considering capacity constraints, because the
value of maximum link utilization is greater than 1. However,
the average congestion for multi-tree solution is always below
1. These results indicate that multi-tree transmission can be
the better choice when we have strict capacity constraints.
VI. CONCLUSION
In this work, we proposed a multi-objective mathematical
formulation for multipath multicast rate allocation problem in
order to minimize the probability of irrecoverable loss and
also minimize network congestion. For calculating probabilities
of irrecoverable loss for each destination, we estimated
distribution of the time that each path spends in the bad state
out of the total block time. Discrete event simulation was
used to derive this probability distribution for NSF network
topology. We observed that the bad time portion of network
paths follows shifted Log-Normal distribution. We proposed
a multi-objective genetic algorithm based on SPEA to solve
the model and to find the Pareto solutions. Numerical results
show that multipath routing significantly decreases probability
of irrecoverable loss in comparison to single-tree transmission.
Deriving the relationship between parameters of Log-
Normal distribution found for bad state time and number of
links in each path and the parameters of Gilbert-Elliot model
can be considered as a future research to the work presented in
this paper. This work can further be expanded by considering
other QoS measures such as end-to-end delay and delay jitter.
ACKNOWLEDGEMENTS
This work was supported by Centre for Quantifiable Quality
of Service in Communication Systems, Centre of Excellence,
appointed by the Research Council of Norway,
and funded by the Research Council, NTNU and UNINETT
(http://www.q2s.ntnu.no).
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Mehrdad Alipour is graduated from the Graduate School in Industrial
Engineering, University of Science and Culture (USC), Tehran, Iran. He
received his B.Sc. degree in Industrial Engineering from the Isfahan University
of Technology (IUT), Iran in 2008. His research interests include optimization
in telecommunication networks, meta-heuristic optimization approaches, and
stochastic programming.
Matin Bagherpour is a postdoctoral researcher in centre for Quantifiable
Quality of Service in Communication Systems (Q2S) in the Norwegian
University of Science and Technology (NTNU). She received her PhD
in Industrial Engineering from Tarbiat Modares University (Iran) in May
2008. She has worked as an assistant professor in University of Science
and Culture (Iran) since then. Her research interests include optimization
(mathematical programming, integer programming, meta-heuristic algorithms,
combinatorial optimization), especially optimization of telecommunication
networks (routing, scheduling, resource allocation, pricing, QoS, etc.), and
ICT economics.
Øivind Kure is a Professor at centre for Quantifiable Quality of Service in
Communication Systems (Q2S) in the Norwegian University of Science and
Technology (NTNU). He received his PhD from the University of California,
Berkeley, USA. His current research interests include quality of service in
wired and wireless network, sensor networks, and routing.

ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011 71
Analytical Model for Virtual Link Provisioning in
Service Overlay Networks
Piotr Krawiec, Andrzej Bęben and Jarosław Śliwiński
Abstract—In this paper, we propose analytical model of Virtual
Link used in the Service Overlay Networks. The Virtual Link
exploits Selective Repeat ARQ scheme with time constrained
number of retransmission and the playout buffer mechanism.
Our model allows deriving equations that express trade-off
between loss and delay characteristics experienced by packets
transferred through VL. The main innovation of our model is
the ability to cope with variable delay experienced by packets
transferred by underlying network. Following the analytical
model, we propose a method for Virtual Link dimensioning. The
accuracy of the proposed model and dimensioning method is
illustrated by simulation results.
I. INTRODUCTION
THE Service Overlay Networks (SON) [1] operate at the
application layer to offer new services in the Internet,
such as QoS [2], reliability [3], multicast [4], privacy [5], etc.
The nodes in SON, so called overlay nodes that are connected
using underlying network, perform service specific functions
related to both packet forwarding and service control. Since
transfer characteristics of underlying network are usually not
adequate for SON requirements, the overlay nodes engage
additional mechanisms to adjust packet transfer characteristics
to specific SON needs. This concept, called Virtual Link (VL),
was introduced in [2] and then it was extended by several
authors, e.g., [6], [7]. These studies show how the ARQ (Automatic
Repeat reQuest) and/or FEC (Forward Error Correction)
mechanisms applied at VL recover lost packets and finally
improve the quality of transferred VoIP or video streams. The
VL concept was enhanced in [8], where authors applied hybrid
ARQ scheme jointly with the playout buffer mechanism to not
only recover lost packets, but also to mitigate packet delay
variation. Such improvement was achieved at the expense of
reduced capacity and increased packet transfer delay.
In this paper, we introduce analytical model for VL with
the Selective Repeat ARQ scheme and the playout buffer
mechanism. Although the anaysis of delay characteristics of
ARQ schemes have been already presented in literature, e.g.,
in [9], [10], [11], [12], [13], [14], they are based on the
assumtion of constant round trip time. The main novelty of
our model are: (1) the ability to cope with variable transfer
delays between sender and receiver (2) time limited number
of retransmissions. These features originate from characteristics
of underlying network, where packet transfer delays
are usually described by parameters of a random variable.
As a consequence, VL behaves similar to a queueing system
Piotr Krawiec, Andrzej Bęben and Jarosław Śliwiński are with Institute of
Telecommunications, Warsaw University of Technology Nowowiejska 15/19,
00-665 Warsaw, Poland Email: {pkrawiec, abeben, jsliwinski}@tele.pw.edu.pl
Fig. 1.
The Virtual Link concept.
with randomly delayed feedback. Such model has not been
solved yet, therefore different approximations are considered,
e.g., [15]. Our model allows to approximate the distribution
of packet transfer time starting from the moment when a
packet arrives to VL at the sender side until the moment
when the packet leaves the receiver side or until it is lost due
to exceeding the threshold of packet transfer delay. On that
basis, we are able to express VL characteristics as a function
of packet transfer characteristics of underlying network and
the assumed transfer time threshold. Using this analysis we
propose a method for dimensioning of the VL.
The paper organisation is the following. In Section II, we
introduce the VL concept. Then in Section III, we present
proposed analytical model of the VL jointly with simulation
results showing its effectiveness. In Section IV, we propose
VL dimensioning method, which takes advantages of proposed
analytical model. Finally, Section V summarises the paper and
gives outline of further works.
II. VIRTUAL LINK
The SON concept assumes that overlay nodes connect each
other by Virtual Connections (VC), which are offered by
underlying network, as presented on Fig. 1. Since usually,
there is no direct relation between SON and underlying network,
the overlay nodes engage additional mechanisms, called
Virtual Link (VL), to adjust packet transfer characteristics
offered by VC to SON needs. As proposed in [2], [8], the
VL engages the selective repeat ARQ mechanism supported
by the playout buffer mechanism. The selective repeat ARQ
mechanism recovers lost packets at the expense of increased
packet transfer delay and reduced link capacity. On the other
hand, the playout buffer mechanism enforces the same delay
for each packet transferred through VL, which emulates the
behaviour of an ordinary synchronous link.

72 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
packets
arriving from
ON1 input ports
output port of ON1
packets are
served with
CVL rate
delay control
mechanism
time
stamp
VL sender side
ARQ RTX
buffer
VC shaper
VC in underlying
network of CVC capacity
(CVL < CVC )
ARQ feedback
input port of ON2
VL receiver side
playout buffer packets going
to ON2 output
ports with
CVL rate
packet transfer
delay control
ARQ decision
point
delay experienced on VC and D max denotes the time limit
for successful packet delivery through VL. This time limit
determines number of packet retransmissions. Equation (2)
defines worst case limit of IP LR V L as a function of packet
loss ratio on VC, defined by IP LR V C and the minimum
number of packet retransmissions
Fig. 2.
The mechanisms of Virtual Link.
Fig. 2 presents exemplary VL, which is established between
neighbouring overlay nodes ON 1 and ON 2 . The packet arriving
to the output buffer in ON 1 enters the queue, which
is served with the rate of VL, named C V L . The VL begins
packet service by the ARQ mechanism, where the copies of
particular packets are stored in ARQ retransmission buffer
(ARQ RTX). To each packet, we add time stamp with its
arrival time to VL. We used this time stamp at the receiver side
to recover traffic profile in the playout buffer. The receiving
side controls the sequence of the incoming packets and it sends
acknowledgements for received packets as well as requests
for retransmissions for lost packets. If a packet is lost, then
the sending side retransmits it upon receiving retransmission
request or expiration of the time-out. The number of retransmissions
is limited by value D max , which defines the
time limit for successful packet delivery. At the receiver side,
we put received packets into the playout buffer. The playout
buffer delays the packet departure to allow for retransmissions
of previously lost packets and mitigate the variable packet
transfer time in VL. Moreover, playout buffer recovers the
sequence and the inter-packet gaps of transferred packets,
based on their timestamps. When a packet arrives too late,
the playout buffer simply drops it. More detailed description
of VL mechanisms is presented in [8].
The starting point in the VL analysis are characteristics
of VC. They correspond to available capacity, denoted as
C V C , and the packet transfer characteristics expressed in
terms of QoS metrics [16] such as: 1) minimum IP Packet
Transfer Delay, minIP T D V C , 2) IP Packet Delay Variation,
IP DV V C , jointly with random variable describing random
part of IP Packet Transfer Delay, as well as, 3) IP Packet Loss
Ratio, IP LR V C . These data may come from contracts agreed
with Internet Service Provider or from the measurements
performed by overlay nodes. Anyway, in our analysis, we left
the problem of gathering VC characteristics for further studies,
assuming that VC characteristics are known a priori.
Summarising, the VL mechanisms give a trade-off between
packet transfer delay and packet transfer loss characteristics
provided by VL. In principle, greater value of IP T D V L
allows VL mechanisms for more retransmissions what improve
packet loss characteristics but on the other hand might not
be acceptable for delay sensitive traffic. This trade-off may
be expressed by generic equations (1), (2) and (3). Equation
(1) defines the value of IP T D V L experienced by packets
transferred through VL
IP T D V L = minIP T D V C + D max = const, (1)
where minIP T D V C is the minimum value of packet transfer
IP LR V L = IP LR V C
1+⌊ Dmax
RT Tmax ⌋ , (2)
where RT T max is the maximum value of round trip time
experienced by packets transferred through VC and turned
around to the source by reverse VC.
Note that every retransmission reduces the effective value
of C V L . Therefore, we can approximate the allowed capacity
of VL by the value corresponding to the infinite number of
retransmissions
C V L ≤ C V C ∗ (1 − IP LR V C ). (3)
Taking into account that implementation of the VL requires
introducing some overhead in the form of a VL header, we
obtain the final value of allowed capacity for the VL by
multiplying C V L from equation (3) by expression L d/(L d +L V L )
, where L d denotes size of packet arriving to the VL, and L V L
is the VL header length.
Remark that presented above equations are valid for the VL,
which uses selective repeat ARQ scheme and playout buffer
mechanism.
III. PROPOSED MODEL
The Virtual Link features a retransmission scheme combined
with delay based decision process. Consequently, the
model for performance analysis has to take into account the
correlation between retransmissions and the packet transfer
characteristics between sender and receiver (in both directions).
Our analysis aims to derive the packet transfer characteristics
of the Virtual Link expressed by packet transfer
delay IP T D V L and packet loss ratio IP LR V L with regard
to its assumed capacity C V L and retransmission delay limit
D max .
A. Definition of model
We assume that Virtual Connection has the capacity C V C
and has different propagation delays for data and acknowledgement
packets, which are t pd and t pa , respectively. Furthermore,
we assume that data (acknowledgement) packets are of
constant size L d (L a ) with transmission delay t Xd = L d/C V C
(t Xa = La /C V C ). Sum of propagation delay t p and transmission
delay t X equals minIP T D V C metric. Moreover, the
random variable X i (Z i ) defines the variable part of packet
transfer delay in the data (acknowledgement) direction. We
presume that capacities of VCs are significantly lower than
capacities avaiable in underlying network, and hence there is
no correlation between handling, in underlying nodes, of two
consecutive packets transferred through given VC. It allowes
us to neglect correlation between losses and delays of consequtive
packets transferred through VC. Therefore, the packet
losses may follow independent model with loss probability

KRAWIEC et al.: ANALYTICAL MODEL FOR VIRTUAL LINK PROVISIONING IN SERVICE OVERLAY NETWORKS 73
VL
input
Fig. 3.
time
stamp
Dq
Input
buffer
RTO
start
RTX
buffer
CVC
RTX
start
Drtx
The Virtual Link model.
Dt
tXd + tpd + Xi ; pd
tXa + tpa + Zi ; pa
p d (p a ) in data (acknowledgement) direction. Additionally,
the above assumptions implies that random variables defining
packet transfer delay (X i and Z i ) and packet losses are all
independent of each other.
The packets arriving to the Virtual Link have constant bit
rate profile with bit rate C V L (constant packet inter-arrivals).
We assume, that the sequence number space ARQ mechanism
utilises, is large enough to not stop the packet sending process.
The overview of the Virtual Link model is presented in
Fig. 3. The variables used in the model are the following:
• Dq – random variable which describes the waiting time
in the input buffer for “fresh” packets. Dq duration is
defined by the time instant when a packet enters the input
buffer and by the time instant when its service begins, i.e.,
the first transmission in Virtual Connection.
• Dt – random variable which describes the packet transfer
delay from the sender to the receiver (in Virtual Connection).
It is defined as time interval from the start of first
transmission of the “fresh” packet in Virtual Connection,
until the moment of arrival of the first packet copy to the
receiver. Virtual Link drops packets having no chance
for reception before the deadline D max ; therefore, we
assume that for dropped (i.e., lost) packets Dt takes
infinite value.
• Dp – random variable which describes the duration of
packet’s stay in the playout buffer.
• Drtx – random variable which describes a queueing
delay of retransmitted packets. We assume that retransmitted
packets access the Virtual Connection with higher
priority than “fresh” packets.
According to the Virtual Link concept, assuming the packet
is not lost, its total transfer delay in VL is constant and it is
given by (see eq. 1)
IP T D V L = t Xd + t pd + Dmax = Dq + Dt + Dp (4)
Random variables Dq and Dt are constrained by IP T D V L
pd
Yi
1-pd
Dp
Playout
buffer
CVL
VL
output
Dq + Dt ≤ IP T D V L . (5)
Duration Dp, which complements the sum of Dq and Dt to
constant time IP T D V L , varies from 0 to Dmax
Dp = IP T D V L − Dq − Dt, (6)
Dp ∈ [0; Dmax] .
Let P s defines the probability of the event that packet is
successfully transferred by Virtual Link in time t i.e., the
packet’s copy arrives to the receiver before t
P s = P r{Dq + Dt ≤ t}. (7)
In the Virtual Link, the rate of incoming packets is limited by
capacity C V L . Next, the packets are taken for service from
input queue with rate C V C > C V L or they wait in the input
queue until service of retransmitted packets from RTX buffer
is finished. Because packet losses higher than a few percent
are rather rare in normal operation of network ([17]), for
further analysis we assume that queueing time Dq is negligible
compared to Dt. Consequently, we can state that
P s = P r{Dt ≤ t}. (8)
Thanks to the assumed independence between packet delay
and packet losses characteristics, we can write the following
formula which defines the conditional probability of packet’s
successful delivery in time not longer than t, assuming that
there were i th transmission attempts
P r{Dt ≤ t} =
=
∞∑
P r{Dt ≤ t ∧ T r = i} (9)
i=1
∞∑
P r{Dt ≤ t | T r = i}P r{T r = i},
i=1
where T r is the random variable describing number of
packet transmissions (including retransmissions) until successful
packet delivery to the receiver. Assuming independent
packet loss model, T r has a geometric distribution
P r{T r = i} = (1 − p d )p (i−1)
d
. (10)
Next, we analyse duration between time instant when the
first transmission of a packet starts, until the successful reception
after i th transmission. Probability that packet transfer
time is not greater than t, assuming success on the first attempt
(T r = 1), is given by
P r{Dt ≤ t | T r = 1} = (11)
= P r{t Xd + t pd + X i ≤ t ∧ T r = 1}
P r{T r = 1}
= P r{t Xd + t pd + X i ≤ t}P r{T r = 1}
P r{T r = 1}
= P r{t Xd + t pd + X i ≤ t}
In this case the time Dt has two components: 1) data packet
transmission time on VC link (t Xd ), and 2) variable propagation
time through VC link (t pd + X i ).
Probability that packet transfer time is not greater than t,
assuming success on the second attempt (T r = 2), equals
P r{Dt ≤ t | T r = 2} = (12)
= P r{min[RT O; Y i + t Xd + t pd + X i
+t Xa + t pa + Z i ] + Drtx +
+t Xd + t pd + X i ≤ t}

74 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
Ld/CVL
S
P1
R
S
P1
R
Yi
Tf = 4
RTO
P1
NACK1
NACK1
RTX
P1
Fig. 4.
An Y i random variable.
RTX
P1
In this case time Dt consists of the four components: 1)
time required to detect lost packet (ARQ decision delay; it is
defined as a minimum of a retransmission timeout RTO and
time, after which NACK for lost packet arrives to a sender),
2) waiting time in the retransmission buffer (Drtx), 3) data
packet transmission time on VC link (t Xd ), and 4) variable
propagation time of retransmitted data packet through VC link
(t pd + X i ).
Time, after which NACK arrives to a sender, is a sum of
following values (see Fig. 4): 1) time Y i , 2) data packet transfer
time (t Xd + t pd + X i ), and 3) transfer time (t Xa + t pa + Z i )
of acknowledgement for data packet, which carries NACK for
lost packet.
Random variable Y i denotes time required for the sender
to transmit consecutive data packets, which are essential in
order to receive an acknowledgement indicating the packet
loss. Because packets arrive to VL with rate C V L/L d , r.v. Y i
can take the following discrete values (see Fig. 4):
Y i = j · L d
C V L
, j ∈ {1, 2, . . .} (13)
Let T f be a random variable which describes number of
consecutive packets, which must be sent by the sender to
receive information about packet loss. Fig. 4 illustrates the
case for T f = 4. The T f depends on the data and the ACK
packets loss probabilities (p d and p a , respectively) and has
geometric distribution (see Appendix A):none
P r{T f = j} = (1 − p d )(1 − p a )[p d + (1 − p d )p a ] (j−1) (14)
Using the law of total probability, we can rewrite the
formula (12) as:
P r{Dt ≤ t | T r = 2} = (15)
∞∑
{ [
= P r min RT O; j · L d
+
C V L
j=1
]
+t Xd + t pd + X i + t Xa + t pa + Z i +
}
+Drtx + t Xd + t pd + X i ≤ t ·
·P r {T f = j}
The SR ARQ scheme used in Virtual Link assumes, that
only the first packet retransmission is controlled by NACK,
Fig. 5.
RTX
ACK1
The Virtual Link retransmission schema.
while the second, third, etc., occurs after retransmission interval
RTX, as it is shown on Fig. 5. Such approach allows
us to maintain high responsiveness for the first retransmission
and, at the same time, to impose the limit on the additional
traffic generated due to retransmissions. Taking this feature
into account, we can express the probability that packet
transfer time is not greater than t, assuming that i − 1 packet
transmission attempts fail and there is a success in the i th
attempt (i ≥ 2,) by
P r{Dt ≤ t | T r = i} = (16)
∞∑
{ [
= P r min RT O; j · L d
+
C V L
j=1
+t Xd + t pd + X i + t Xa + t pa + Z i
]
+
+(i − 2)RT X + Drtx + t Xd + t pd +
}
+X i ≤ t · P r {T f = j}
Finally, according to the formula (none9) the probability,
that Dt (successful packet transfer from the sender to the
receiver) is not greater than t, assuming unlimited number of
retransmission, has the following form
P r{Dt ≤ t} = (17)
= P r {t Xd + t pd + X i ≤ t} (1 − p d )p 0 d +
[
∞∑ ∑ ∞ { [
+ P r min RT O; j · L d
+
C V L
i=2
j=1
+t Xd + t pd + X i + t Xa + t pa + Z i
]
+
+(i − 2)RT X + Drtx + t Xd + t pd +
}
]
+X i ≤ t · P r {T f = j} (1 − p d )p (i−1)
d
where P r {T f = j} is given by formula (14).
B. Model evaluation
We evaluate the analytical results, which are obtained using
the proposed model, with results of simulations. The following

KRAWIEC et al.: ANALYTICAL MODEL FOR VIRTUAL LINK PROVISIONING IN SERVICE OVERLAY NETWORKS 75
assumptions are taken:
• since RTO timer is usually set to relatively high value,
we consider RTO timeout expiration as exceptional, rare
event, therefore the sender obtains information about
packet loss mainly thanks to receiving negative acknowledgements;
• taking into account, that retransmitted packets have
higher priority and packet losses at VC are usually a few
percent at most, we consider queueing delay Drtx of
retransmitted packets as a negligible part of total packet
transfer time Dt.
Therefore, we can write formula (17) as:
P r{Dt ≤ t} = (18)
= P r {t Xd + t pd + X i ≤ t} (1 − p d )p 0 d +
[
∞∑ ∑ ∞ { j · Ld
+ P r + t Xd + t pd + X i +
C V L
i=2
j=1
+t Xa + t pa + Z i + (i − 2)RT X + t Xd + t pd +
}
]
+X i ≤ t · P r {T f = j} (1 − p d )p (i−1)
d
Let consider the expression under the summation:
j · L d
C V L
+ t Xd + t pd + X i + t Xa + t pa + (19)
+Z i + (i − 2)RT X + t Xd + t pd + X i
For fixed i and j we can write it as a sum of independent
random variables and constants:
X i + Z i + X i + a + j · L d
C V L
+ (i − 2)RT X (20)
where a is a constant value, which equals to 2(t Xd + t pd ) +
t Xa + t pa .
Probability density function of Dt can be obtained as a
convolution of pdf s for X i and Z i random variables and
the constants, by exploitation of the Laplace transform (δ()
denotes the Dirac delta function):
f Dt (t) = L −1{ L { } { ( )} }· X i · L δ t − tXd − t pd (21)
⎡
∞∑ ∞∑
·P r{T r = 1} + ⎣ L
{L −1 { X i
}·
i=2
j=1
L { } { } { ( j · L d
Z i · L Xi · L δ t − a − −
C V
⎤ L
−(i − 2)RT X )}} · P r{T f = j} ⎦ · P r{T r = i}
We calculate distribution of Dt using (21) for the case,
when random variables which describe variable part of packet
transfer delay through VC link are exponentially distributed
with mean equals none 1 /m X for direction sender-to-receiver
and 1 /m Z for direction receiver-to-sender, respectively: X i ∼
Exp(m X ), Z i ∼ Exp(m Z ). We assume that VC links for
CCDF
10 0
10 -1
10 -2
10 -3
10 -4
10 -5
pd=pa=5% - analysis
pd=pa=5% - simulation
10 -6
pd=pa=0.5% - analysis
pd=pa=0.5% - simulation
10 -7
0 20 40 60 80 100 120 140 160 180
Dt [ms]
Fig. 6. Complementary CDF of time Dt for case#1: VC with low packet
transfer delay variation.
CCDF
10 0
10 -1
10 -2
10 -3
10 -4
10 -5
10 -6
10 -7
pd=pa=5% - analysis
10 -8
pd=pa=5% - simulation
10 -9 pd=pa=0.5% - analysis
pd=pa=0.5% - simulation
10 -10
0 20 40 60 80 100 120 140 160 180
Dt [ms]
Fig. 7. Complementary CDF of time Dt for case#2: VC with high packet
transfer delay variation.
both directions are the same: m x = m z , t pd = t pa , p d = p a ,
with C V C = 1 Mbps and two values of packet loss ratio: 5%
and 0.5%. The VL bit rate C V L = 650 Kbps and packet size
L d = 200 B. We consider two cases:
• case#1: VC is characterised by low packet delay variation
(t pd = t pa = 25 ms, m x = m z = 1 ms, IP DV V C =
7 ms);
• case#2: VC is characterised by relatively high packet
delay variation (t pd = t pa = 5 ms, m x = m z = 5 ms,
IP DV V C = 34.5 ms).
During simulation experiments we generate at least 4·10 8
packets for each considered case.
Fig. 6 and Fig. 7 depicts complementary cumulative distribution
function of time Dt, calculated on the basis of
formula (21), as well as obtained experimentally (solid line
and dashed line, respectively), for both cases. We observe
that the proposed model closely approximates the simulation
results. The reason of small shift between the appropriate

76 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
CCDF
10 0
10 -1
10 -2
10 -3
10 -4
10 -5
10 -6
10 -7
10 -8
pd=pa=5% - analysis
10 -9 pd=pa=5% - simulation
pd=pa=0.5% - analysis
10 -10
pd=pa=0.5% - simulation
10 -11
0 20 40 60 80 100 120 140 160 180
Dt [ms]
Fig. 8. Complementary CDF of time Dt, in case when X i and Z i random
variables have uniform distribution.
curves, is that the approximation takes the worst case from
the point of view of packet transmission time. We assume,
that each packet is transmitted with rate limited by the VC
shaper to C V C (see Fig. 2). During simulations, such limitation
occurred rarely, and transmission time for most packets was
much shorter, because they were sent with physical link bit
rate, a hundred times greater than VC bit rate. Consequently,
the proposed model can be treated as an upper bound for Dt
time distribution.
Notice, that in some intervals the simulated curves are above
the calculated ones for greater values of Dt in case#2 (see
Fig. 7). This is due to packet stream integrity condition, which
we assumed during simulations. To avoid packet reordering,
which is possible in high packet delay variation case, we allow
only such values of single packet delay, generated according to
exponential distribution, which keep packet order. In this way,
distribution of X i and Z i random variables used in simulations
differ slightly comparing to calculation.
In Fig. 8 we present complementary cumulative distribution
function of time Dt for case#2, i.e. when VC is characterized
by high packet delay variation, but when the random variables
X i and Z i have a uniform distribution over interval [0 ms,
35 ms]. In this case, a distribution of packet transfer delay
through VC link used for calculation was identical with the
distribution applied in simulation experiments. Consequently,
the analytical curve is above the simulated one, and can be
treated as an upper bound for numerical results, as in case#1
(see Fig. 6).
IV. APPLICATION FOR VIRTUAL LINK DIMENSIONIG
The Virtual Link concept assumes, that packet transfer is
successful, if its copy arrives to the receiver in time not greater
than IP T D V L :
P s = P r{Dt ≤ IP T D V L } (22)
Therefore, the packet loss probability on VL link can be
defined as:
TABLE I
IP LR V L FOR VC WITH LOW PACKET TRANSFER DELAY VARIATION
(CASE#1).
pd (= pa) IP T D V L IP LR V L
analytical model simulation
40 ms 5·10 −2 5·10 −2 ± 4·10 −5
5% 70 ms 5·10 −2 5·10 −2 ± 3 · 10 −5
110 ms 2.5·10 −3 2.5·10 −3 ± 5 · 10 −6
40 ms 5·10 −3 5·10 −3 ± 6·10 −6
0.5% 70 ms 5·10 −3 5·10 −3 ± 9·10 −6
110 ms 2.5·10 −5 2.5·10 −5 ± 3·10 −7
IP LR V L = 1 − P s = 1 − P r{Dt ≤ IP T D V L } (23)
However, exact computation of P r {Dt ≤ IP T D V L } is
not trival, since in the VL number of possible transmission
attempts for each packet is limited by time. Sender transmit
packet only if it has chance to be received by receiver in the
assumed time interval limit IP T D V L . Othervise, packet is
droped. Therefore, we propose to approximate an IP LR V L
metric by calculating distribution P r {Dt ≤ t} with assumption
of unlimited number of retransmissions, as defined by
equation (17). Next, we determine packet loss probability on
the VL as a fraction of packets, for which transfer time Dt
was greater than IP T D V L :
IP LR V L ≈ P r{Dt > IP T D V L } (24)
In tables I and II we present values of IP LR V L metric
obtained from simulations and calculated analytically according
to rule presented above. Simulations were performed for
the same scenarios and the values of parameters as in section
III-B. Table I refers to case#1, with low delay variation,
whereas table II refers to case#2, with greater delay variation.
Parameter Dmax had appropriate values to obtain packet
transfer delay in the VL equals to 40, 70 and 110 ms. The
results were obtained by repeating the simulation tests 10 times
and calculating the mean values with the corresponding 95%
confidence intervals. For each iteration, we simulated at least
50·10 6 packets.
Results presented in table I show, that proposed method
allows to determine packet loss ratio in the Virtual Link
with high accuracy in the case, when variation of delay is
relatively low comparing to constant part of packet transfer
delay through underlying VC. In the case#2, for tests with
higher values of IP T D V L and packet losses in VC equal
to 0.5%, the IP LR V L measured in simulations is above the
calculated values (see table II). This mismatch is similar to the
values observed for analytical and simulated curves depicted
in Fig. ??. However, analytical results still constitute a good
approximation for the IP LR V L obtained by simulations.
Summarizing, presented analytical method helps us to approximate
packet loss ratio provided by the Virtual Link,
taking as input data the packet transfer characteristics of
VC, such as: bit rate C V C , packet loss ratio p d and p a ,
constant (t pd , t pa ) and variable (X i , Z i ) transfer delay, as

KRAWIEC et al.: ANALYTICAL MODEL FOR VIRTUAL LINK PROVISIONING IN SERVICE OVERLAY NETWORKS 77
TABLE II
IP LR V L FOR VC WITH HIGH PACKET TRANSFER DELAY VARIATION
(CASE#2).
pd (= pa) IP T D V L IP LR V L
analytical model simulation
40 ms 1.9·10 −2 1.4·10 −2 ± 3 · 10 −5
5% 70 ms 9.1·10 −4 1.1·10 −3 ± 4·10 −6
110 ms 1.3·10 −5 1.7·10 −5 ± 1 · 10 −7
40 ms 2.8·10 −3 1.7·10 −3 ± 4 · 10 −7
0.5% 70 ms 2.8·10 −5 5.4·10 −5 ± 7 · 10 −7
110 ms 4.0·10 −8 6.6·10 −8 ± 1.5 · 10 −8
well as assumed parameters of the VL: bit rate C V L and delay
IP T D V L . Jointly with formula (3), which defines maximum
allowed capacity of VL, it can be used for dimensioning of
the Virtual Link. A procedure of the VL dimensioning we
present below. Notice, that the VL admits a controlled tradeoff
between packet loss level, offered capacity and constant
delay introduced by the VL.
A. Virtual Link dimensioning algorithm
Using the formula (24) to determine upper bound of packet
loss ratio in the VL, together with the formula (3) for approximation
of the allowed VL capacity, we can dimension the
Virtual Link according to the following algorithm:
• Step 1: determine values of parameters for Virtual Connection,
which is used for establishing the VL (bit rate
of VC, packet loss ratio, minimum packet transfer delay
on VC, distribution of the variable part of packet transfer
delay on VC).
• Step 2: for given value of the VL capacity C V L , which
satisfies the condition described by formula (3), calculate
distribution of packet transfer time between sending and
receiving overlay node P r = {Dt ≤ t} (according to
formula (18) ).
• Step 3: according to formula (24), find such value T V L
in obtained Dt time distribution, for which probability
P r = {Dt > T V L } equals required value of
IP LR V L . In case when the input parameter is value of
IP T D V L , from obtained Dt time distribution find value
of IP LR V L as probability P r = {Dt > IP T D V L }.
• Step 4: calculate value of D max parameter for the VL as
the difference between time T V L and minimum packet
transfer delay on VC: D max = T V L – minIP T D V C .
In case when the input parameter is value of IP T D V L ,
then D max = IP T D V L – minIP T D V C .
Using the following steps, at the top of given VC we can
establish the VL with bit rate C V L , constant packet transfer
time IP T D V L (= T V L ) and packet loss ratio not greater than
IP LR V L .
V. SUMMARY
In this paper we considered the performance analysis of
Virtual Link. The Virtual Link is established between nodes of
the Service Overlay Network in order to improve packet transfer
characteristics of the underlying network. The presented
analysis focuses in the packet transfer delay distribution as
observed during handling in the VL when the retransmission
delay limit is infinite. Comparing to other analytical methods
for ARQ systems, our model features variable transfer delays
between sender and receiver, and moreover, it uses delaybound
scheme for number of retransmissions. The accuracy
of the proposed model was verified by means of simulation
in exemplary scenario with exponentially distributed delay
characteristics of the underlying network. The analytical and
numerical results differ slightly due to worst case assumptions
and due to the method of packet transfer delay emulation
that maintains the order of packets in the underlying network
(for the case with greater value of delay variation). Finally,
we proposed a method for dimensioning of VL with finite
retransmission delay limit that allows for controlled use of
trade-off between packet transfer delay and packet losses.
One of the remaining problems, which is not directly
related to the VL analysis, is the reliable characterisation of
packet transfer characteristics in the Virtual Connection. In the
situation when operator of underlying network do not provide
required parameters of the VC, for example, in the form of
an SLA (Service Level Agreement) contract, the SON owner
can obtain them using measurements. Those measurements
can be performed by external tools, such as OWAMP (One-
Way Active Measurement Protocol) tool [18], or by internal
measurement module integrated with the VL. In the latter case,
the packet transfer characteristics of the VC can be measured
by means of a passive measurement method. For this purpose,
we can use timestamps and sequence numbers, which are
carried in each VL packet header, to determine packet transfer
delay and loss characteristics.
In the further work we will extend the proposed model to
include the FEC mechanism.
REFERENCES
[1] Z. Duan, Z.-L. Zhang, and Y. T. Hou, “Service overlay networks: SLAs,
QoS, and bandwidth provisioning,” IEEE/ACM Trans. Netw., vol. 11,
no. 6, pp. 870–883, 2003.
[2] L. Subramanian, I. Stoica, H. Balakrishnan, and R. H. Katz, “OverQoS:
an overlay based architecture for enhancing internet QoS,” in NSDI’04:
Proceedings of the 1st conference on Symposium on Networked Systems
Design and Implementation. Berkeley, CA, USA: USENIX Association,
2004, pp. 6–6.
[3] D. Andersen, H. Balakrishnan, F. Kaashoek, and R. Morris, “Resilient
overlay networks,” SIGOPS Oper. Syst. Rev., vol. 35, no. 5, pp. 131–145,
2001.
[4] M. Castro, P. Druschel, A.-M. Kermarrec, and A. Rowstron, “Scribe: A
large-scale and decentralized application-level multicast infrastructure,”
IEEE Journal on Selected Areas in Communicastions, vol. 20, no. 8, pp.
1489–1499, October 2002.
[5] R. Dingledine, N. Mathewson, and P. Syverson, “Tor: The secondgeneration
onion router,” in Proceedings of the 13th USENIX Security
Symposium. USENIX Association, August 2004.
[6] Y. Amir, C. Danilov, S. Goose, D. Hedqvist, and A. Terzis, “An
overlay architecture for high-quality voip streams,” IEEE Transactions
on Multimedia, vol. 8, no. 6, 2006.
[7] Z. Cen, M. W. Mutka, D. Zhu, and N. Xi, “Supermedia Transport for
Teleoperations over Overlay Networks,” in Proceedings of NETWORK-
ING 2005: 4th International IFIP-TC6 Networking Conference, ser.
LNCS, vol. 3462. Springer, May 2005, pp. 1409–1412.
[8] W. Burakowski, J. Śliwiński, A. Bęben, and P. Krawiec, “Constant Bit
Rate Virtual Links in IP Networks,” in Proceedings of the 16th Polish
Teletraffic Symposium. Łódź, Poland: Technical University of Łódź,
2009, pp. 23–30.

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[9] L. Badia, M. Rossi, and M. Zorzi, “Queueing and delivery analysis
of SR ARQ on Markov channels with non-instantaneous feedback,”
in Proceedings of the IEEE Global Telecommunications Conference
GLOBECOM’05. IEEE Communications Society, 2005, pp. 3717–
3721.
[10] J. G. Kim and M. Krunz, “Delay analysis of selective repeat ARQ for
a Markovian source over a wireless channel,” IEEE Transactions on
Vehicular Technology, vol. 49, no. 5, pp. 1968–1981, September 2000.
[11] M. Rossi, L. Badia, and M. Zorzi, “SR ARQ delay statistics on N-state
Markov channels with non-instantaneous feedback,” IEEE Transactions
on Wireless Communications, vol. 5, no. 6, pp. 1526–1536, June 2006.
[12] W. Luo, K. Balachandran, S. Nanda, and K. Chang, “Delay analysis
of selective-repeat ARQ with applications to link adaptation in wireless
packet data systems,” IEEE Transactions on Wireless Communications,
vol. 4, no. 3, pp. 1017–1028, May 2005.
[13] N. Cardwell, S. Savage, and T. Anderson, “Modeling TCP latency,” in
Proceedings of the Nineteenth Annual Joint Conference of the IEEE
Computer and Communications Societies INFOCOM 2000. IEEE
Communications Society, March 2000, pp. 1742–1751.
[14] B. Sikdar, S. Kalyanaraman, and K. S. Vastola, “Analytic models for the
latency and steady-state throughput of TCP Tahoe, Reno, and SACK,”
IEEE/ACM Transactions on Networking, vol. 14, no. 6, pp. 959–971,
December 2003.
[15] E. A. Pekoz and N. Joglekar, “Poisson Traffic Flow in a General
Feedback Queue,” Journal of Applied Probability, vol. 39, no. 3, pp.
630–636, September 2002.
[16] ITU-T Recommendation Y.1541, “Network performance objectives for
IP-based services,” May 2002.
[17] V. Paxson, “End-to-End Internet Packet Dynamics,” IEEE/ACM Transactions
on Networking, vol. 7, no. 3, pp. 277–292, June 1999.
[18] S. Shalunov, B. Teitelbaum, A. Karp, J. Boote, and M. Zekauskas,
“A One-way Active Measurement Protocol (OWAMP),” RFC 4656,
September 2006.
Tf = 1
S
R
P1
NACK1
a) Example, when r.v. Tf is equal 1
S
R
P1
Tf = 2
Tf = 2
NACK1
b) Example, when r.v. Tf is equal 2
S
R
P1
Tf = 3
Tf = 3
NACK1
S
R
P1
S
S
S
P1
P1
P1
NACK1
NACK1
R
R
R
APPENDIX A: TF R.V. DISTRIBUTION
Random variable T f describes number of consecutive packets,
which must be sent by the sender to receive information
about lost packet.
R.v. T f takes value 1, if the first packet sent after lost
packet, reachs a receiver, and sender receives acknowledgement
for that packet (which contains NACK for lost packet) -
see Fig. 9.
Probability, that T f is equal 1, is:
Fig. 9.
Tf = 3
Tf = 3
NACK1
c) Example, when r.v. Tf is equal 3
A T f random variable.
NACK1
P r{T f = 1} = (1 − p d )(1 − p a ) (25)
Probability, that T f is equal 2, is (see Fig. 9):
P r{T f = 2} = p d (1 − p d )(1 − p a ) + (26)
+ (1 − p a )p a (1 − p d )(1 − p a )
= (1 − p d )(1 − p a )[p d + (1 − p d )p a ]
Probability, that T f is equal 3, is (see Fig. 9):
P r{T f = 3} = p 2 d(1 − p d )(1 − p a ) + (27)
+ p d (1 − p a )p a (1 − p d )(1 − p a )
+ (1 − p d )p a p d (1 − p d )(1 − p a )
+ (1 − p d )p a (1 − p d )p a (1 − p d )(1 − p a )
= (1 − p d )(1 − p a )[p d + (1 − p d )p a ] 2
Finally, random variable T f has the geometric distribution:
P r{T f = j} = (1 − p d )(1 − p a )[p d + (1 − p d )p a ] (j−1) (28)
where p d and p a denotes packet loss probability for direction
sender-to-receiver and receiver-to-sender, respectively.
Piotr Krawiec received M.Sc. and Ph.D. degrees in telecommunications from
the Warsaw University of Technology, P oland, in 2005 and 2011, respectively.
Now he works as assistant at the Institute of Telecommunications, Warsaw
University of Technology. His research interests focus on quality of service
in IP networks, NGN architecture and new networks techniques.
Andrzej Bęben received M.Sc. and Ph.D. degrees in telecommunications
from Warsaw University of Technology (WUT), Poland, in 1998 and 2001,
respectively. Since 2001 he has been assistant professor with the Institute
of Telecommunications at Warsaw University of Technology, where he is
a member of the Telecommunication Network Technologies research group.
His research areas include IP networks (fixed and wireless), content aware
networks, traffic engineering, simulation techniques, measurement methods,
and testbeds.
Jarosław Śliwiński was born in Toruń, Poland, in 1979. He received M.Sc.
and Ph.D. degrees from Warsaw University of Technology in 2003 and 2008,
respectively. His research interests cover traffic control, systems’ design and
implementation methodology.

ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011 79
Decisive Factors for Quality of Experience of
OpenID Authentication Using EAP
Charlott Lorentzen, Markus Fiedler, and Peter Lorentzen
Abstract—When using the web, long response times are bones
of contention for users, i.e. they damp the Quality of Experience
(QoE). Though, if one knows the cause of the long response
time one may examine what could be done to eliminate the
obstacle. In this paper, we determine the weak point of the
Extensible Authentication Protocol Method for GSM Subscriber
Identity Modules (EAP-SIM) with the OpenID service with
regards to excessive authentication times, which determine the
response times. In order to provoke controlled increases of the
latter, we emulate bad network performance by introducing
bi-directional delay between the supplicant (client) and the
authentication server. The same procedure is also applied to
several other EAP methods. Based on a recent, exponential
relationship between QoE and response time, we then identify,
quantify and compare the decisive factors for QoE reduction
as functions of the components of the authentication times. The
results we obtain clearly show that one task of the EAP-SIM
authentication contributes significantly more to the total response
times than the other tasks, which points out the direction for
future optimisation of user perception of authentication times.
I. INTRODUCTION
OPENID [1] is a system that allows for automatic
confirmation of a user’s identity when visiting
other authentication-enabled sites or communities supporting
OpenID. In other words, a user is always authenticated, but
only the first authentication will have to be initiated by the
user. OpenID is promising for uses in a seamless environment,
where the goal is to remain seamlessly authenticated while
switching network, device or even application.
An authentication procedure typically produces a chain of
messages before completing. And the more messages the chain
consists of, the greater the risk of unacceptable response times
(RT) becomes. These kinds of chains of messages, and/or
chains of requests to different servers and databases form
service chains (SC) [2] that can be quite large and complex.
We previously discovered significant RTs for the authentication
to the OpenID server when using networks with
low bandwidth, such as mobile networks. Such waiting times
challenge user patience [3] and increase the risk of users trying
to bypass or turn off security features. Once the Quality of
Experience (QoE) [4] is really bad, users might even abandon
the service [5]. The concept of QoE refers to the totality of end
user experience of the delivered service [6], and in this case
of the RT of the service. Typically different parts, or steps,
of a service contribute to a certain RT and there might be a
specific part that contributes more than others to the total RT.
Charlott Lorentzen, Markus Fiedler, and Peter Lorentzen are with School
of Computing, Blekinge Institute of Technology, Karlskrona, Sweden, Email:
@bth.se
Given the background above, this paper will identify and
quantify the decisive factors for QoE of Extensible Authentication
Protocol Method for GSM Subscriber Identity Modules
(EAP-SIM) with the OpenID authentication service as functions
of network impairments in form of additional delay. The
study will show what parts of the EAP-SIM authentication
make the greatest contribution to RT, when authenticating via
OpenID. Furthermore, the study will find the decisive factors
of the following authentication methods: EAP Message-Digest
algorithm 5 Challenge (EAP-MD5), EAP Tunneled Transport
Layer Security (EAP-TTLS) with MD5, EAP-TTLS with
Password Authentication Protocol (PAP), EAP-TTLS with
Challenge Handshake Authentication Protocol (CHAP), EAP-
TTLS with Microsoft CHAP version 2 (MSCHAPv2), and
Protected EAP (PEAP) with MSCHAPv2. The decisive factors
for each authentication method will then be compared.
There are several studies dealing with the evaluation and
optimisation of different EAP authentication methods in different
network environments and scenarios, such as studies
on performance evaluation of EAP for roaming [7] and handover
[8] in WLAN environments. However, to the best of
our knowledge, the combination of EAP-SIM authentication
method with OpenID for web authentication has not been yet
investigated, nor have there been studies done on decisive
factors of different EAP methods.
The organization of this paper is as follows: Section II
gives an overview of the authentication method and services
used for the OpenID EAP-SIM authentication. Section III
discusses the impact of different network parameters and
describes the methodology of the study, and Section IV
describes the OpenID EAP-SIM authentication experiments
with corresponding setup, procedure and RT measurements.
The results of the latter study and the following analysis
of the results are presented in Section V, followed by a
discussion of the results in aspects of QoE in Section VI.
Section VII describes an additional study of decisive factors
for several authentication protocols, and presents and discusses
the results. Finally, Section VIII provides a conclusion of the
paper and points out future work.
A. OpenID
II. TECHNICAL BACKGROUND
OpenID is a service that handles one’s authentications. If
users are logged in to their OpenID server, they are automatically
logged in at visited web pages that have previously been
enabled with OpenID for their particular user account.
An OpenID identity is a unique URL which contains the
trusted provider and the username. The provider is the host

80 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
User
PC
Internet
Service provider
AAA/
MAP GW
SIM
Supplicant
Authenticator
Fig. 1.
Setup of the Ubisafe OpenID authentication, with BTH client side.
of the URL, in our case Ubisafe AS, in Norway, and the
username/URL will be openid.ubisafe.no/, but
the provider can also be for example Yahoo, or any other
site that provides OpenID as authentication service. With
OpenID users need one password or authentication credential
and username to be able to authenticate oneself to all enabled
sites, and the password or authentication credential only needs
to be used when logging in at the OpenID server.
When a user account have OpenID enabled, for example on
a community, the user logs in at the OpenID server and then
it is possible to visit the community and provide the OpenID
username/URL, and the authentication to the community will
be completed without an additional password. This applies to
all OpenID-enabled pages during one web browsing session.
OpenID was chosen according to the requirements for
seamless network and service access, to be provided by the
IMS platform of the Mobicome project [9], [10].
B. EAP-SIM Authentication
In the EAP-SIM authentication method the actors are the
SIM, the supplicant, the authenticator and the authentication
server. The authenticator and the authentication server can be
the same actor or situated in the same physical device (see
Fig. 1). The supplicant is the user client, and the SIM-card is
connected to the supplicant. The user just plugs in the SIMcard
or makes sure the supplicant has access to it, and the
supplicant is then the entity that communicates with the SIMcard.
The authentication procedure is as follows.
• A connection (physical and virtual) is established between
the supplicant and authenticator.
• The authenticator requests the identity (ID) from the
supplicant (EAP-Request/Identity).
• The supplicant produces a response and sends its ID to
the authenticator (EAP-Response/Identity).
• The authenticator challenges the supplicant in one or
several steps to verify the ID of the supplicant (EAP-
Request/SIM/Start and EAP-Request/SIM/Challenge).
• The supplicant handles and responds to the challenge(s)
from the authenticator (EAP-Response/SIM/Start and
EAP-Response/SIM/Challenge).
• If everything is correct with the challenge response the
supplicant is authenticated and a success notification is
sent from the authenticator (EAP-Success).
C. Authentication service chain
When a user requests to login to the Ubisafe OpenID server
on the web page [11], a chain of messages to supply the
Fig. 2.
SC for EAP-SIM authentication with OpenID.
service, i.e. a SC, is started. The SC for this authentication
method is visualised in Fig. 2. In the sequel, let T Ik denote
internal durations within the supplicant, while T Nk refer to
durations involving network communications. The user request
enters the supplicant which starts the setup of a connection to
the authenticator, after making sure the SIM-card authentication
is a valid method for both supplicant and server (duration
T I1 ). Once the connection is established, the authenticator
sends back a request (end of time T N1 ) for the ID of the
supplicant, as described in the list in the previous section
(Sect. II-B). Please, note that T N1 includes the time for setting
up a connection between the authenticator and the supplicant,
before sending the ID response to the supplicant. The setup
of a connection is made visible with the dotted line in Fig. 2
and the vertical dots below it, since these messages are not
EAP-SIM messages.
When the supplicant receives requests from the authenticator,
the SIM-card is needed to produce a response to the
requests (time T I2 ) since the SIM-card has the ID, and the
keys, before sending the response to the authenticator. The
SIM-card is also needed to produce a response (time T I3 ) for
the SIM-challenge.
Two further durations shown in Fig. 2, namely ɛ (between
user click and initiation of the authentication) and δ (between
completion of the authentication and displaying the results to

LORENTZEN et al.: DECISIVE FACTORS FOR QUALITY OF EXPERIENCE OF OPENID AUTHENTICATION USING EAP 81
the user) have shown to be of minor importance in the context
of this study. We will therefore assume that the RT is well
approximated by the authentication time, i.e. the sum of its
internal and network components.
III. NETWORK IMPACT
In the course of our work, we seek to determine the RTs
for the different part of the authentication method in question.
The user perception is of course based on a whole RT, but if
the greatest contribution to the RT was found, then it might
also be minimised or made more scalable for large network
delays with the goal to preserve a good QoE.
Timestamps were recorded for each task within the authentication,
and RTs were calculated from the start timestamp and
end timestamp for each task.
The objective of calculating RTs is to see whether there
are any parts of the authentication that contribute most to
the total RT or whether some parts are particularly sensitive
to degradations in network performance. For this reason, we
measure and compare the parts of the RT, in particular to see
differences between RT for different parts of the authentication
process, as well as their impact.
On network level, in most cases, adding delay or imposing
bandwidth constraints gives a similar effect, namely higher RT
values. In this study, bad network performance is emulated
with a traffic shaper situated in the supplicant that shapes bidirectionally
on the network interface of the latter.
Bandwidth can in some shapers be difficult to use for
provoking the results we are looking for. For a single packet
message the bandwidth constraint might never give any effect
as the shaper might use a previous packet arrival to determine
the next one. The latter was visible in the trials with bandwidth
that were done early on in this study, where the RT for
some parts did not change when decreasing the bandwidth
and finally a timeout was received without any change in the
RT for those parts.
Loss will result in higher RTs because of necessary retransmissions,
but if one packet is lost in each part of the
authentication, it will have the same impact on the RT for each
part. To compare the effect of loss for each part would be quite
difficult because of the encrypted traffic for the authentication.
Therefore, loss has not yet been used as network performance
degradation parameter in this study.
Delay is added to every packet that passes the traffic shaper,
and the delay can be constant or variable. Variable delay has
been tested in a previous project for map services [2]. Even
though a constant delay might not be the most realistic case
for emulating delay, it has shown a crucial enabler for the
quantitative results presented in this study.
IV. EXPERIMENTS
The experiment setup consisted of a client computer with a
SIM dongle, a traffic shaper for adding delay on the network
interface of the client, and a server situated in Oslo, Norway, as
shown in Fig. 1. All trials on the client computer were carried
out on campus, during the same period of the day to withhold
consistency, namely during evenings when most personnel
were not at work. The delays that were added by the shaper
were 0 ms, 250 ms, 500 ms, 750 ms, and 1 s in both directions.
The timestamps were recorded via a JavaScript. Even though
JavaScript logging of timestamps have proven to be only fairly
accurate [12], the accuracy is sufficient for this experiment.
Although the shaper adds constant delays on network level,
the corresponding RT values are varying slightly, as there are
many random impacts affecting the way between user and
authentication service. Nevertheless, the chosen delays allowed
to change the order of magnitudes of the RT such that trends
regarding QoE could be clearly seen [3].
The experiment considered the login procedure on the
Ubisafe OpenID server web page. On the web page “USB-
SIM Dongle” was chosen in the Java applet handling the login.
After clicking “Login”, the Java applet logged timestamps for
starting and ending all parts of the EAP-SIM authentication
(see Fig. 2). When the login was completed and the new page
was loaded, a logout was done and then the procedure was
repeated.
For each delay the experiment was done 45 times, and the
log file was saved for later analysis. Although caching was
disabled and cookies were not saved, the first five trials for
each delay were discarded in order to avoid any potential bias
of the measurements. The results were averaged, and 95 %
confidence intervals were calculated; the latter have however
shown to be too small to be visible in the plots of Figure 3.
V. RESULTS AND ANALYSIS
The authentication procedure consists of 16 steps, from initiation
to success, including both internal processing time (T I )
and communication time spent in the network (T N ). Though, it
can be abstracted down to seven steps, of which three (indexed
by I1 to I3) are internal durations and four (indexed by N1 to
N4) are external communication, i.e. network communication
outside the supplicant (cf. Fig. 2). These steps are formalised
as
T R − δ − ɛ =
4∑
T Nk +
k=1
3∑
T Ik = T N + T I , (1)
k=1
where T R is the total RT, T N is the total time for the
network communication steps, and T I is the total time for the
internal processing steps, including communication between
the supplicant and the SIM-card. As indicated before, we
assume δ → 0 and ɛ → 0.
When comparing T N and T I , the main contributions to
the RT change with the increase of the RT. In case of no
or low delays, RT is dominated by the processing time, T I .
For high delays, the RT is instead dominated by the network
communication time, T N . For a delay of 1 s the RT of about
24 s consist of more than 90 % of network communication
time, while for a transparent shaper, the relation is almost the
opposite, as the processing time takes up about 70 % of the
total RT.
The steps including network communication are affected by
the delay, whilst the internal communication, e.g. communication
between supplicant and SIM-dongle, is not affected. The
parts of the RT that are interesting in the results are therefore

16505
16509
16513
16517
16521
16525
16529
16533
16537
16541
16545
16549
16553
16557
16561
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More
Response time [s]
Frequency
82 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
25
20
8
7
6
15
10
5
0
0 200 400 600 800 1000
Delay added in shaper [ms]
TN1
TN2
TN3
TN4
TR
5
4
3
2
1
0
Response time [ms]
Fig. 3.
RT components versus bi-directional delay added in the shaper.
Fig. 4.
Frequency of T N1 , for a bi-directional delay d =1 s, bin width 2 ms.
T N1 , T N2 , T N3 and T N4 , whereas the rest of the tasks or steps
include only internal processing times that will not change
with regard to increasing delay.
T N1 provides the largest contribution to the total RT when
there is no delay added, as can be seen in Fig. 3. It can
also be seen that T N1 is most sensitive to additional delay of
the four network communication steps. When the additional
delay is 1 s, both ways, T N1 is already about 16 s long.
For the remaining three tasks the RT grows equally fast, but
substantially slower than for task N1, and they do start at a
lower RT values in the case of no additional delay introduced
by the shaper. Comparing the four tasks behind T N , it is also
for T N1 that the most roundtrips in communication can be
seen, due to the setup of a connection.
For T N1 the linear growth in T R , with respect to changes
of the network delay added in the shaper d, is eight times as
large as compared to T N2 , T N3 and T N4 :
while
T N1 ≈ 16d = 8 × 2d (2)
T N2,N3,N4 ≈ 2d (3)
Thus, for the total network time, we get the approximation
T N ≈ 16d + (3 × 2d) = 22d. (4)
The fact that the tasks with one round trip get a RT of
double the delay (cf. Equation 3), as the delay is added in
both directions, might indicate a relation between the number
of packets sent back and forth and the factor of growth. If
two messages, counting both ways, get two times the delay,
then 16 times the delay should indicate 16 messages when
counting both ways, and thus eight round trips. Eight is also
the factor between T N1 (Equation 2) and the other components
(Equation 3).
When looking at the distribution of the RT values, they are
a bit different from trial to trial, and from delay to delay.
Most of the distributions are similar to a normal distribution,
but in some cases with a (rather short) tail on the right-hand
side. In some cases there are a few values that are bigger than
the average, the median and the 90 % percentile. Such values
belong to the so-called tail and can be quite bad when it comes
to (perceived) network performance. However, for a RT in the
order of magnitude of around 16 s, a parts of a second is not
that large of a difference. In Fig. 4 the tail value is about 70 ms
from the center of the distribution and the RTs are all larger
than 16 s. Short tails, in this order of magnitude, do not have
to be considered.
VI. QOE ASPECTS FOR EAP-SIM
Considering the user perception of the RT of the authentication,
or QoE, and the changes of the latter with regard to the
changes in RT, a previously researched user model [3] is used.
Equation 5 was developed in the previous study for the same
system and in the same environment and represents basically
a Mean Opinion Score (MOS) [13], which enables us to use
the equation in this study in a straightforward manner:
QoE ≈ 4.7e −0.1TR/s . (5)
Obviously, each additional second factor of the network part
of the RT yields a relative damping of the QoE by factor 0.9.
From the measurements, it has been observed that processing
time is approximately constant, which can be formulated as
3∑
T Ik ≈ 1.8 s, (6)
k=1
Thus, equation 5 can be rewritten as
which yields
QoE ≈ 4.7e −0.18 e −0.1TN/s
≈ 3.9e −0.1TN/s (7)
QoE ≈ 3.9e −2.2d/s . (8)
Obviously, for the fixed line connection used in this experiment,
it can be seen in Equation 8 that the QoE cannot exceed
3.9.
In Figure 5 one may see that, because of the exponential
slope, already at 150∼200 ms of delay, the MOS has gone
below the rating “Fair”, and at 250 ms of delay the MOS is
closing in on the rating “Poor”. The QoE reaches the MOS
value 1, or “Bad”, at about 650 ms of added delay. Since the

Response Time [s]
MOS
LORENTZEN et al.: DECISIVE FACTORS FOR QUALITY OF EXPERIENCE OF OPENID AUTHENTICATION USING EAP 83
5
4
3
User
PC
Supplicant
Switch
Authentication
Server
Server
Authentication
Server
2
1
0
0 250 500 750 1000
Delay added in shaper [ms]
Fig. 6. Setup of the EAP authentication experiments.
1,2
Tn2
Tn4
1
Tn1
0,8
Fig. 5. QoE in terms of MOS versus added delays, using Equation 8.
MOS scale goes from 1 to 5 when users are rating, values
below 1 can be transformed to 1 as shown in Equation 2 in
[14].
Dividing Equation 8 into the parts that grow equally gives
QoE ≈ 3.9e −1.6d/s (e −0.2d/s ) 3 , (9)
where the first e-term shows the impact of T N1 and the second
e-term shows the joint impact of the remaining times, namely
T N2 , T N3 and T N4 on QoE. One may see that the first part
has a significantly higher impact:
γ = e−1.6d/s
e −0.6d/s = e−d/s < 1. (10)
Equation 10 describes the QoE damping factor γ between
the impact of the connection setup time, T N1 , and the impact of
the remaining network times, T N2 , T N3 and T N4 , as function
of the one-way delay d introduced by the shaper. It can be
seen that, as d is growing, the damping impact of the connection
setup supersedes the one of all the remaining network
communication times. Even for low delays d, the connection
setup time has a greater impact than all the remaining times,
though in a lower order of magnitude.
Assume that one could reduce the number of messages
during the connection setup by 50 %, and thereby also reduce
the connection setup time T N1 , one would observe a much
less critical impact of the delay on the QoE, namely a factor
of e −0.2d/s .
As far as we can tell from this study, it is the setup of a
connection and secure tunnel between the supplicant and the
authenticator in OpenID with EAP-SIM that does not scale
nicely with an increasing delay.
VII. PERFORMANCE OF OTHER EAP METHODS
In this study the authentication methods EAP-MD5, PEAP-
MSCHAPv2, EAP-TTLS-PAP, EAP-TTLS-MD5, EAP-TTLS-
CHAP, and EAP-TTLS-MSCHAPv2 were studied in a laboratory
environment.
The experiments were done in a similar, but laboratory,
environment, which excluded the Internet but included all
other parties as in the previous study (see Fig 6). Though, the
0,6
0,4
0,2
0
0 20 40 60 80 100
Delay added in shaper [ms]
Fig. 7. RT components for EAP-MD5 versus bi-directional delay added in
the shaper.
authenticator and the authentication server are two separate
devices in this setup. The traffic shaper is placed between
the authenticator and server, in this experiment setup. The
new setup has the network traffic shaper on the server side
of the authenticator, since the delay is introduced on the
network layer (IP layer), and the traffic between supplicant
and authenticator is not sent using IP addresses. This setup
gives the same result in addition of network delay as in the
previous study for all tasks, except for the first task including
the two initial messages, which are only sent to and from the
authenticator.
Time stamps were logged during all experiments; both at the
supplicant side and the server side, and RTs were calculated
for each run in each experiment. The experiments were run 40
times for each delay setting. The network delays added in the
network shaper in this experiment were 0 ms, 20 ms, 40 ms,
60 ms, 80 ms, and 100 ms, in both directions.
The EAP methods were analyzed to find the decisive factors.
The RTs in these additional experiments are considerably
lower, but the linear behavior in RT increase with increased
delay shows the same “per packet” proportionality as in the
above study.
A. Authentication method overview
EAP is the underlying protocol for authentication procedure
and TTLS is used to setup a tunnel for the authentication.
The tunnel is established between the supplicant and the
authenticator for secure data, and between supplicant and
authentication server for secure password authentication.
PAP, MD5, CHAP, and MSCHAPv2 are the authentication
algorithms used in the authentication procedure. The security

Response Time [s]
Response Time [s]
Response Time [s]
84 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
1,2
1
0,8
Tn3
Tn2
Tn4
Tn1
1,2
1
0,8
Tn4
Tn3
Tn2
Tn1
0,6
0,6
0,4
0,4
0,2
0,2
0
0 20 40 60 80 100
Delay added in shaper [ms]
0
0 20 40 60 80 100
Delay added in shaper [ms]
Fig. 8. RT components for EAP-TTLS-PAP/EAP-TTLS-CHAP versus bidirectional
delay added in the shaper.
Fig. 10. RT components for PEAP-MSCHAPv2 versus bi-directional delay
added in the shaper.
1,2
1
0,8
0,6
0,4
0,2
0
Tn3
Tn4
Tn2
Tn1
0 20 40 60 80 100
Delay added in shaper [ms]
Fig. 9. RT components for EAP-TTLS-MD5/EAP-TTLS-MSCHAPv2 versus
bi-directional delay added in the shaper
level is a bit different for these algorithms. In PAP the user
name and password are sent unencrypted. Without a tunnel
PAP would, in other words, be insecure and therefore it is
not supported by EAP itself, but by TTLS. In TTLS the
tunnel hides the password, so sending it unencrypted is not
a security issue. Though, the password is stored as a hash at
the authentication server side and can therefore not be stolen.
CHAP was standardised for PPP from the beginning and
is only supported by TTLS, since it is not an EAP method.
The authentication server challenges the supplicant, which
responds to the challenge by proving the possession of a shared
secret, i.e. a password. The password is sent as a hash over
the network, but must be available in plain text at both the
supplicant side (by typing it) and the authentication server
side (in a stored file, e.g. /etc/passwd) in order to confirm that
the hash in the challenge response is valid.
EAP-MD5 was standardized with EAP from the beginning.
MD5 is supported by EAP and can be used with EAP, PEAP
or TTLS. Though, the password needs to be available on
both supplicant side and authentication server side, as in
CHAP. When MD5 is used as EAP-MD5, the ID is sent from
the beginning, but when it is used in EAP-TTLS-MD5, the
supplicant is anonymous in the beginning and the ID is instead
sent in the authentication phase, which is reflected in the
response times for those phases, as there is one more roundtrip
from supplicant to server for this task.
MSCHAPv2, like MD5 and CHAP, sends a hash of the
password, but in this case it does not have to be stored in
plain text on both sides. A particular one-way hash of the
password, which will then serve as the password, is stored at
the authentication server side. The supplicant, who knows the
hash algorithm, will be able to produce a matching “password”
from the original password, which can be used in the response
of a challenge from the authentication server. MSCHAPv2 also
provides mutual authentication. MSCHAPv2 can be used with
EAP, PEAP and TTLS.
B. Results and Analysis
For each method the messages have been separated into
four tasks, and what is included in the RT for each task is are
presented in a list below. The RTs are all have the supplicant as
base. All methods include all the four tasks, except for EAP-
MD5 which does not setup a tunnel for the communication,
and thus lacks the response time increase from T n3 .
• T n1 : Initiation of the connection with the authenticator.
• T n2 : Negotiation of authentication protocol with the authentication
server.
• T n3 : Setup of a secure tunnel to the authenticator and
authentication server.
• T n4 : Authentication with challenge(s) and response(s).
One of the authentication methods, namely EAP-MD5, does
not have a setup of a tunnel. In this method the authentication
challenge has the longest RT, T n4 (see Fig. 7). The increase in
RT of the decisive task, T n4 , is four times the added delay, and
since the delay is added in both directions four times means
two round trips between the supplicant and the authentication
server.
For EAP-TTLS-PAP and EAP-TTLS-CHAP the task with
the RT of largest impact is the setup of the TTLS tunnel (see
Fig. 8). The RT of this task, T n3 , increases with six times the
added delay. The increase in RT for T n3 is just two times the

Complexity: Response time [s]
Response Time [s]
LORENTZEN et al.: DECISIVE FACTORS FOR QUALITY OF EXPERIENCE OF OPENID AUTHENTICATION USING EAP 85
1,2
1
0,8
0,6
0,4
0,2
PEAP-MSCHAPv2 : Tn4
EAP-TTLS-PAP/CHAP : Tn3
EAP-TTLS-MD5/MSCHAPv2 : Tn3
EAP-MD5 : Tn2
TABLE I
DECISIVE FACTORS AND SECURITY LEVEL FOR EACH METHOD.
EAP-MD5 e −0.4d/s 1
EAP-TTLS-CHAP e −0.6d/s 2
EAP-TTLS-PAP e −0.6d/s 3
EAP-TTLS-MD5 e −0.6d/s 4
EAP-TTLS-MSCHAPv2 e −0.6d/s 5
PEAP-MSCHAPv2 e −1.0d/s 6
EAP-TTLS-CHAP e −1.6d/s -
Fig. 11.
0
0 20 40 60 80 100
Delay added in shaper [ms]
The decisive factors for each authentication method.
The decisive factors for each of these methods are derived
from the RT of the task with the largest impact on the total
RT. The T n for each method is translated into a dependence
on delay based in Equation 5. The decisive factors for each
method are presented in Table I.
2,5
2
1,5
1
0,5
0
1 2 3 4 5 6
Security level
Fig. 12. Security vs. Complexity for several authentication methods, with
100 ms added delay.
added delay larger than for the task with the next largest RT,
T n2 , which is the time for the negotiation of authentication
protocol. The increase in response time for the authentication
challenge is only two times the added delay.
EAP-TTLS-MD5 and EAP-TTLS-MSCHAPv2 also have
the largest impact on the total RT from the setup of the TTLS
tunnel, with the same increase in RT. The RT of this task, T n3 ,
increases with six times the added delay (see Fig. 9), whereas
the tasks that has the RTs with the next largest impact on the
total RT, namely T n2 and T n4 , are four times the added delay.
The EAP method that has the task which distinguishes itself
the most, in terms of largest impact on the total RT, is PEAP-
MSCHAPv2. Though the next largest RT, T n3 , increases with
six times the added delay, the RT of T n4 increases with ten
times the added delay (see Fig. 10).
Fig. 11 shows the RTs with the largest impact for each
of the EAP methods in this additional study. As seen in the
figure, PEAP-MSCHAPv2 is the method that has the highest
RT with T n4 . EAP-MD5 has the lowest RT with T n2 , which in
fact is lower than the next largest RT for PEAP-MSCHAPv2,
and equal to the next largest RT for EAP-TTLS-MD5, and
EAP-TTLS-MSCHAPv2.
C. Simplicity versus Security
In the previous study [15] the compromising relationship
between simplicity and security is discussed. If one party
is increased the other party will sooner or later suffer from
degradation. In this section we look at the relationship between
security and simplicity with regard to the six EAP methods,
described and analysed above.
The EAP methods have been arranged from highest security
level (6) to lowest security level (1) in a simple manner (see
Table I). For example, a plain text password is, within this
comparison example, considered to provide a lower security
level than a hashed password, and a tunnel is considered to
add security. Response time will, in this example, be compliant
with complexity, which is the inverse of simplicity. The higher
the RT, the lower the simplicity. The RT order of magnitude
is due to the number of messages sent back and forth for each
task.
In Fig. 12 it can be seen that the simplicity is increasing with
the decrease in security. The EAP method that is considered to
have the lowest security level, EAP-MD5, is in fact the simplest
method, and the PEAP-MSCHAPv2, which is considered
to have the highest security together with EAP-TTLS-MD5
and EAP-TTLS-MSCHAPv2 has the least simplicity. This is of
course a generalisation and the model is not exactly compliant
with every existing authentication method. Though, it gives
a rough picture of the options that exist when choosing an
authentication method. If the situation or solution requires a
high level of security, then it can be justified to add complexity
to the system, even though it might give higher RTs.
VIII. CONCLUSION AND FUTURE WORK
This paper has described the study of finding the most
vulnerable part of EAP-SIM authentication method using
the OpenID authentication service. After initial tests of the
methods and the network connection, the experiments were
performed with constant delay added in a shaper on the
network interface of the supplicant, or client machine. A
constant delay, which was increased for each trial, was added
to provoke a change in RT for the different parts of the
authentication.

86 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMBER 2011
When analysing the results for OpenID authentication with
EAP-SIM, it could be clearly seen that one of the network
times is growing faster than the others, namely the one that
refers to the initiation and setup of a secure connection
between the supplicant and the authenticator, followed by an
ID request from the authenticator. The fact that this initial
task has the largest contribution to the total RT and therefore
also had the greatest impact on QoE was shown from several
angles. The initial is also the task with most packets sent back
and forth.
The results for OpenID using EAP-SIM were then connected
to the QoE user model that was developed in the
previous study of the same system. From this mapping it
was shown that the increase in RT for the initial secure
connection setup task would result in a degradation of QoE to
the extent that it reaches a rating of 1 (lowest grade, meaning
“bad”) at about 650 ms of added delay in both directions. To
achieve a factor of the impact on the RT that is more tolerable
and scalable with large delays, one would need to reduce
the number of messages during the connection setup. The
reduction of the latter by factor two would entail a significant
gain in scalability, seen from a smaller damping factor.
The other EAP based authentication methods were found to
have the lower decisive factors than the OpenID solution with
EAP-SIM. The largest contribution to the total RT for PEAP-
MSCHAPv2 is given by T n4 , which is the authentication phase
including the challenge. The method that had the decisive
factor with the lowest impact was EAP-MD5. In EAP-MD5
the initiation of a connection between the supplicant and the
server gave the largest impact on RT, with T n2 . The rest of
the authentication methods had almost equal decisive factors,
with the largest impact in RT from T n3 , i.e. the setup of the
secure tunnel.
After comparing the simplicity and security levels of the
EAP based authentication methods, the compromise between
security and simplicity was shown in a quantitative manner.
Adding a security level will compromise the simplicity in
most cases, depending on how the increase in security level is
defined.
The accurate impact of variable delay, and also loss, could
be evaluated in the future. Since bandwidth has already been
tried without giving a realistic result, a suitable traffic shaper
has to be found before it can be further evaluated. Variable
delay will perhaps result in a bit lower RT than constant
delay, but that needs to be proved, or counter-proved. Also,
loss would be interesting to evaluate as network performance
parameter.
The setup of a connection between the supplicant and
the authenticator for OpenID using EAP-SIM needs to be
examined closer, to see if there is a possibility to optimize it.
Since the supplicant and the authenticator shares information
from the SIM-card, there might be other possibilities to setup a
connection. Then it might also be a good option if the OpenID
authentication service is provided by the operator issuing the
SIM-card. These possibilities will be closer examined with
regards to trustworthiness and functionality in future work.
ACKNOWLEDGEMENTS
The authors would like to thank Dr. Ivar Jørstad at Ubisafe
AS in Olso, Norway, for providing and supporting the authentication
server setup, and Johan Lindh for his assistance in
gathering parts of the underlying data.
REFERENCES
[1] “The OpenID Foundation website,” http://openid.net, [online], cited
2011-01-15.
[2] M. Fiedler, C. Eliasson, S. Chevul, and S. Eriksén, “Quality of Experience
and Quality of Service in a Service Supply Chain,” in EuroFGI
IA.7.6 Workshop on Socio-Economic Issues of Future Generation Internet,
Santander, Spain, Jun. 2007.
[3] C. Lorentzen, M. Fiedler, H. Johnson, J. Shaikh, and I. J. rstad, “On User
Perception of Web Login - A Study on QoE in the Context of Security,”
in Proc. of Australasian Telecommunication Networks and Applications
Conference (ATNAC 2010), Auckland, New Zealand, Nov. 2010.
[4] Vocabulary for performance and quality of service. Amendment 2:
New definitions for inclusion in Recommendation P.10/G.100, ITU-T
Recommendation P.10/G.100 (2006)/Amendment 2 (07/2008).
[5] M. Fiedler, T. H. feld, and P. Tran-Gia, “A Generic Quantitative
Relationship between Quality of Experience and Quality of Service,”
IEEE NETWORK, Special Issue on Improving QoE for Network Service,
vol. 24, no. 2, pp. 36–41, Mar. 2010.
[6] P. Reichl, “From Quality-of-Service and Quality-of-Design to Qualityof-Experience:
A Holistic View on Future Interactive Telecommunication
Services,” in Proc. of Software Telecommunications and Computer
Networks, Split, Croatia, Sep. 2007.
[7] J. Cordasco, S. Wetzel, and U. Meyer, “Implementation and Performance
Evaluation of EAP-TLS-KS,” in Proc. of Security and Privacy
in Communication Networks (SecureComm’06), Baltimore, MD, USA,
Aug. 2006.
[8] S. F. Hasan, N. H. Siddique, and S. Chakraborty, “On Evaluating the
Latency in Handing Over to EAP-enabled WLAN APs from Outdoors,”
in Prof. of IEEE, IET International Symposium on Communication Systems,
Networks and Digital Signal Processing (CSNDSP’10), Newcastle,
UK, Jul. 2010, pp. 278–282.
[9] “The Mobicome website,” http://www.mobicome.org [online], [Cited
2011-01-15.].
[10] I. J. rstad, D. V. Thuan, T. J. nvik, and D. V. Thanh, “Utilising Emerging
Identity Management Frameworks in IMS,” in Proc. of the 12th International
Conference on Intelligence in service delivery Networks (ICIN),
Bourdeaux, France, Oct. 2008.
[11] “The Ubisafe AS OpenID server website,” https://openid.ubisafe.no/
[online], [Cited 2011-01-15.].
[12] K. Wac, M. Fiedler, R. Bults, and H. Hermens, “Estimations of Additional
Delays for Mobile Application Data from Comparative Output-
Input Throughput Analysis,” in Proc. of NOMS 2010, Osaka, Japan, Apr.
2010.
[13] Methods for subjective determination of transmission quality, ITU-T
Recommendation P.800, 1996.
[14] M. Fiedler and T. Hossfeld, “Quality of Experience-related differential
equations and provisioning-delivery hysteresis,” in Proc. of 21st Specialist
Seminar on Multimedia Applications & Traffic, Performance and
QoE, Miyazaki, Japan, Mar. 2010.
[15] C. Eliasson, M. Fiedler, and I. J. rstad, “A Criteria-Based Evaluation
Framework for Authentication Schemes in IMS,” in Proc. of the 4th International
Conference on Availability, Reliability and Security (AReS),
Fukuoka, Japan, Mar. 2009, pp. 865–869.
Charlott Lorentzen received her master degree in electrical engineering from
Blekinge Institute of Technology, Karlskrona, Sweden, in 2006. After working
in some research projects she proceeded with doctoral studies in telecommunication,
with emphasis on network security and network performance, at
Blekinge Institute of Technology. She just received her licentiate degree, in
May 2011, with the licentiate dissertation “User Perception and Performance
of Authentication Procedures”.

LORENTZEN et al.: DECISIVE FACTORS FOR QUALITY OF EXPERIENCE OF OPENID AUTHENTICATION USING EAP 87
Markus Fiedler received his doctoral degree in electrical engineering/ICT
from Universitt des Saarlandes, Saarbrücken, Germany, in 1998. Since then,
he has been with Blekinge Institute of Technology, Karlskrona, Sweden. He
has been holding the Docent degree in telecommunication systems since 2006.
Being an Associate Professor within the School of Computing (COM) at
BTH, he performs and supervises research on Quality of Experience; seamless
communications; network virtualization; service chains; and networks of the
future (NF). He is leading and participating in several national and European
projects. He is serving on the Steering Board of the European Network of
Excellence Euro-NF, and is coordinating Euro-NF’s research activities.
Peter Lorentzen has recently finished his master thesis work, “Evaluation
of EAP-methods”. He will get his master degree in software engineering,
with emphasis on telecommunication, from Blekinge Institute of Technology,
Karlskrona, Sweden, in the second half of 2011.

88 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMPBER 2011
Agent based VoIP Application with Reputation
Mechanisms
Grzegorz Oryńczak and Zbigniew Kotulski
Abstract—In this paper we introduce our new VoIP model the
aim of which is to meet the challenges of modern telephony.
We present project concepts, details of implementation and our
testing environment which was designed for testing many aspects
of VoIP based systems. Our system combines mechanisms for
ensuring best possible connection quality (QoS), load balance
of servers in infrastructure, providing security mechanisms and
giving control over the packet routing decisions. The system is
based on Peer-to-Peer (P2P) model and data between users are
routed over an overlay network, consisting of all participating
peers as network nodes. In the logging process, each user is
assigned to a specific node (based on his/her geographic location
and nodes load). Every node also has a built-in mechanism
allowing to mediate between the user and the main server (e.g.
in logging process). Besides that, because nodes are participating
in data transmission, we have control over the data flow route.
It is possible to specify the desired route, so, regardless of the
external routing protocol, we can avoid paths that are susceptible
to eavesdropping. Another feature of presented system is usage
of agents. Each agent acts with a single node. Its main task
is to constantly control the quality of transmission. It analyzes
such parameters like link bandwidth use, number of lost packets,
time interval between each packets etc. The information collected
by the agents from all nodes allows to built a dynamic routing
table. Every node uses Dijkstra’s algorithm to find the best at
the moment route to all other nodes. The routes are constantly
modified as a consequence of changes found by agents or
updates sent by other nodes. To ensure greater security and
high reliability of the system, we have provided a reputation
mechanism. It is used during updating of the information about
possible routes and their quality, given by other nodes. Owing to
this solution nodes and routes which are more reliable get higher
priority.
Index Terms—voice over IP, IP telephony security, speech
quality control, software agents
I. INTRODUCTION
VOICE sending is an incredibly useful and worth developing
feature among many possibilities given by the
Internet. One of the first attempts of creating a protocol for
transferring human speech over computer network was the
Network Voice Protocol [1] (NVP) made by Danny Cohen of
the InformationSciences Institute fromUniversityof Southern
California in 1973. NVP was used to send speech between
distributed sites on the ARPANET. Since that time telephony
based on Internet Protocols has become more and more popular.
Nowadays, it becomes a serious competitor to standard
Grzegorz Oryńczak is a PhD student at Jagellonian University, Department
of Physics, Astronomy and Applied Computer Science, Cracow, Poland
(corresponding author, email grzegorz.orynczak@uj.edu.pl)
Zbigniew Kotulski a professor at Institute of Fundamental Technological
Research of the Polish Academy of Sciences and professor at Department of
Electronics and Information Technology of Warsaw University of Technology,
Poland (email: zkotulsk@ippt.gov.p)
telephony. Many advantages of this form of communication
like cheap (or free) calls, wide range of additional features
(video calls, conference calls, etc.) made it popular among
companies and ordinary homes. Taking into account the continuous
increase of Voice over IP (VoIP) users, it is safe to
say that internet telephony will be one of the main forms of
communication. However, there are still some challenges that
it has to face, like providing a mechanism to ensure proper
quality of service (QoS) and good security for data transfer
and signaling.
Because VoIP is a real-time application it has specific
requirements from the lower layers. The most important of
them are related to delay, jitter and packet loss. In telephony,
the callers usually notice roundtrip voice delays of 250 ms
or more, sensitive people are able to detect about 200 ms
latencies. If that threshold is passed, communication starts
to be annoying. ITU-T G.114 [2] recommends maximum of
150 ms one-way latency. And because it includes the entire
voicepath,thenetworktransmitlatencyshouldbesignificantly
smaller than 150 ms. Unfortunately, for real-time applications
we cannot use standard internet transport protocols such as
TCP and UDP because they are not designed for this specific
use, so they do not give us control over delay and jitter.
BecauseTCPisaconnectionorientedprotocolitisslowerthen
UDP and built-in retransmission mechanism is often useless
forreal-timetransmission–retransmittedpacketsareoutdated.
For multimedia data, reliability is not as important as timely
delivery,so UDP is a preferable choice to base on for building
real-time protocols. Although UDP has its benefits when it
comes to speed, protocols based on it have to deal with lack
of some important mechanisms. First of them is a congestion
control mechanism which is not present in UDP and if the
sender exceeds transmission rate that can be handled by the
networkit leadsto congestionproblemsandnetworkoverload.
The protocol should also implement mechanisms for timestamping
packets to allow synchronization and minimize jitter
problems. RTP/RTCP defined in RFC 1889 [3] is currently
most widely used transport protocol for real-time services. It
can estimate and control actual data transmission rate but QoS
is still not guaranteed.
In this paper we introduce our new VoIP model the aim
of which is to meet the challenges of modern telephony. As
opposedtostandardclient/serverarchitectureusedforexample
in SIP [4] or H.323 [5], we chose to base our system on
Peer-to-Peer (P2P) model. During last years P2P systems have
become popular not only in domains like file sharing but also
proven to be successful for voice and video communication
(e.g. Skype). There are many benefits of using this network

ORYŃCZAK AND KOTULSKI: AGENT BASED VOIP APPLICATION WITH REPUTATION MECHANISMS 89
Fig. 1. Overlay network model.
Fig. 2. Infrastructure components.
model; they are described in the next section. Another choice
that we made was using agents for analyzing infrastructure.
In many tasks agent-based solutions appeared to be more
efficient [6], this paper shows that they are also useful in
VoIP applications. Our goal was to design a secure system,
which will ensure the best possible connectionquality(QoS) –
which we achieved by path switching technique based on our
own routing protocols assisted with reputation mechanisms.
Security mechanismsthat we providedand biggercontrolover
the packet routing decisions (owing to P2P model) make this
system a good choice even in the environment where a high
security level is required. To make the system more efficient
and reliable, mechanisms for node load balance were also
provided.
The paper is organized as follows. In the Section 2 the
system architecture is described with node model and general
communication flow. The Section 3 is devoted to security and
QoS mechanisms. Finally, the Section 4 concludes our work.
II. SYSTEM ARCHITECTURE
VoIP application presented in this paper is based on a P2P
network. As opposed to traditional client/server architecture
nodes of the P2P system (peers) act both as a client and a
server and sometimes as relay for other peers in the network.
When using a P2P model it is possible to implement an
abstract overlay network that is build at Application Layer
and consists of all participating peers as network nodes. This
abstract network allows to build system independent from the
physical network topology, because data transport service is
provided by Transport Layer considered as part of underlying
network.
We chose the P2P model for our application because of
several important reasons. First of all, owing to overlay
network it is possible to make our own routing decisions
and be more independent from external routing protocols.
It is important because widely used routing protocols are
often not real-time traffic friendly [7], but now, by monitoring
path quality between peers, it is possible to choose the best
route for packets transmission and quickly respond to any
quality changes. Another P2P feature, that has proven to
be useful in described VoIP application, is self-organization,
which implies that any peer can enter or leave network at any
time without a risk of overall system stability degradation.
Owing to self-organization,system can be easily extendedand
is more reliable and less vulnerable to failures and attacks.
Additionally, nodes load-balancing mechanisms implemented
in this application increase overall performance and stability.
Another benefit of this system is an automatic elimination
of problems with clients that are behind NATs. In normal
circumstances, when both clients are behind NATs they are
unable to establish direct connection. Although there are
techniques like Session Traversal Utilities for NAT (STUN)
[8] that can detect the presence of a network address translator
and obtain the port number that the NAT has allocated for
the applications UDP connection, they are often ineffective
[9]. In this case additional server for traversal transmission
between clients is required. In most cases that additional relay
server is not on optimal path between those two clients, so it
imposes additional delay in real-time communication. On the
other hand, in P2P network peers are used for data routing, so
no additional server is required, and because we chose peers
that form the optimal path between clients transmission delay
is minimized. Finally, owing to overlay network architecture
and own routing protocol, we were also able to implement
additional security mechanisms; they are described in Section
III.B.
A. Application components
Our VoIP applications consists of three main elements:
Login Server
As the name suggests, the main task of the server is to
provide services for authentication and authorization. Each
user who wants to connect to the VoIP system must be
previously logged into this server. Registration of new users
and account management is also supported by the server. It
can be used for charge calculation as well. Also every node
must previously bypass the authorization check before it can
be attached to the infrastructure. In the user logging process
each user is assigned to a specific node, selection is based
on a geographic location and load information. The server
contains up-to-date information about every user state, its

90 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMPBER 2011
current IP address, port number and assigned node ID, so it is
used to determine current user location by other VoIP users.
Because the server has full knowledge about current state of
nodes and path qualities it plays the most important function
in informing other nodes about any changes, so nodes can
quickly recalculate their routing tables. As one may notice,
the presence of the server is critical for this VoIP application,
so it is important to provide appropriated hardware resources
for its operation. For big systems, it is also possible to split
these services between several servers.
Nodes
Nodes are essential part of our application and every P2P
network. Their main task is to handle end-user support. As
it was written before, during the logging process each user is
assigned to a specific node and that node is used to route VoIP
signaling and real-time data between other users and nodes.
Theyalso haveabuilt-inmechanismallowing themto mediate
between the user and the Logging Server (e.g. in logging
process),owingtoitinfrastructureismoreresistanttoblocking
(e.g. by the Internet Service Provider). Every node in our
infrastructure has knowledge about other nodes and qualities
of paths between them - this knowledge is used for building
route tables. Nodes cooperate with the Logging Server by
exchanging information about paths. They report status of the
path between neighborsand receive information about the rest
of the infrastructure. Because in our system nodes have to
perform many tasks, we decided to use agents that will take
over some of them. That allowed us to decompose the code,
so it becomes more transparent. The system gains flexibility
- nodes can be easily upgraded just by changing agents
(even remotely). Additionally, different kinds of agents can
be used, e.g. intelligent agents with ability to learn and adapt
to different network conditions and by communicating with
each other they can share knowledge and make routing more
efficient. Each agent acts within the single node. Its main task
is to constantly control the quality of transmissions relayed
by this node. It analyzes such parameters as link bandwidth
usage, number of lost packets, time interval between packets
etc. Agents also test state of the other temporarily not being
used links for detecting any changes. More about agents and
routing mechanism is written in the next section.
From the security perspective, we distinguish two types of
nodes: standard and trusted. Every machine that has required
resources can join our network and become a standard node.
Nodes that had been previously verified as trusted can be used
for routing data that requires a higher level of security. Apart
from that, to ensure greater security and high reliability of the
presented VoIP application, we provide it with a reputation
mechanism. Every node has its own reputation index assigned
by Logging Server, based on node reliability and long time
behavior. Those reputation indexes are used for supporting
mechanisms for building routing tables.
End terminals
End terminals are applications installed on computers (or
smartphones) that are used for making and receiving calls.
Because application uses only two ports: TCP for signaling
and UDP for real-time data transfer, it is easy to configure
firewall to workwith it. After loggingin to the LoggingServer
Fig. 3. RTP/RTCP transmission schema.
(directly or if direct connection is unenviable/blocked by any
ofnodesbelongingto theinfrastructure– it hasalist oftrusted
nodes in memory) application connects to a node assigned by
Server and it is ready for use.
When user is logged in, or has just changed his/her status,
other users that have such a user on their contact lists are
informed about this change. This mechanism works due to
bilateral relation between users stored in the Login Server
database. After being added to someone’s contact list user is
asked for permission for checking his status. If permission is
granted, relation between those users is stored on server so
they can be immediately informed about status changes.
Other elements
Apart from mentioned elements, the presented application
can be easily extended with additional specialized nodes, like
public switched telephone network (PSTN) gateway or other
IP telephony standards (e.g. SIP or Skype) gateways.
III. DESIGN AND IMPLEMENTATION DETAILS
In this section we give an overview of design issues based
on our implementation.
A. Quality of Service
As it was said before, the standard best effort Internet is
not real time traffic friendly.Although there are techniquesfor
providing QoS like Intserv [10] or Diffserv [11] that reserve
certain network resources for handling real-time traffic; they
still depend on service providers policies and are often unable
to ensure requiredend-to-endquality. Method proposedin this
paper can be used to complement those existing mechanisms.
Our application combines traffic flow adjustment method and
path switching technique to ensure best possible connection
quality. Traffic flow adjustment method is popular and widely
usedincontrollingreal-timetraffic.Theessenceofthismethod
is to adjust codec configuration parameters (output rate, voice
frame size, etc.) and play buffer size to adapt to current
network state. To make proper adjustments it is necessary to
determine actual quality so feedback information is needed.
It can be provided by using additional feedback channel (like
in RTCP) or added into real-time traffic flow: into audio(e.g.
using watermarking techniques) or into packet header [12].
To make is simple, in this application we chose to add
feedback information about quality into real-time traffic packets
header, so if quality falls below desired level end user

ORYŃCZAK AND KOTULSKI: AGENT BASED VOIP APPLICATION WITH REPUTATION MECHANISMS 91
terminal will modify audio parameters. Also every node on
the path is informing its neighbor about the quality of links
between them. It is done by inserting additional information,
like number of sent and received packets, average delay and
jitter, into header. By analyzing that data, the agent within the
node has knowledge about the current quality of the link, and
if it detects any changes, it may decide to re-route traffic by
choosing another nodes to relay data. Logging Server is also
informed about these changes and it passes this information
to other nodes. Additionally, frequent changes in link quality
affect on this link reputation by decreasing it. Temporary not
being used links are also regularly tested by agents, they
are sending (with desired time interval) series of test packets
to simulate real-time traffic and analyze the responses. For
performingroutingdecisions every node is building graph that
represent current network state, then Dijkstra’s shortest path
algorithm[13]is applied,butinstead ofshortestpathcounting,
paths with best end-to-end quality are chosen. It is done by
assigning to each edge in the graph its cost index, which is
calculated by multiplying the correspondinglink quality index
by its reputation. If any link state has changed, graph needs
to be updated and Dijkstra’s algorithm applied again.
B. Security
In case of designing security mechanism for real-time
traffic, it is very important to select appropriate security level.
It must be chosen so that it ensures safety of transmission but
also is not too demanding for resources (additional bandwidth
and CPU power).If toomanysecuritymechanismsare applied
it can affects on QoS, so call quality may be degraded. It
is also possible that VoIP users may choose to disable these
mechanisms to get better call quality. In this application we
used following security schema:
User logging – for logging process TLS connection is
established. The user verifies the authenticity of the Logging
Server using his CA certificate (with was previously delivered
with client program, or downloaded from WWW page). Next,
Digest method is used for user authentication. Afterward,
serverchoosesnodethatwillhandlethisclient,andwithserver
assist (server-node connection is also secure) node and client
exchange their public keys, client updates information about
his contact list, connection ends.
User to node connection – secure TLS connection is
established, for two-way authentication previously exchanged
with Login Sever assist keys are used.
Signaling and real-time traffic. Nodes are used to assist
in signaling between end-users. Main reason of choosing
this signaling method is willingness to provide mechanism
for maintaining secrecy of end-users location, so IP address
needs to be hidden from other users. In order to establish
phone-to-phonecall, only user names and indexes of nodes to
with they are attached are needed (indexes are not necessary
- they can be retrieved for the Login Server, but in this
schema server load and time needed to establish connection is
reduced). Node, to which calling user is connected establishes
TLS connection with destination user node, then they forward
signaling data between users. Diffie-Hellman key exchange
Fig. 4. User logging schema.
protocol is used to establish encrypting key for real-time
transmission. To avoid problems related with maintaining the
Public Key Infrastructure (PKI) users do not use certificates
for authentication. But in case additional security is needed,
we providedmechanism for to-way user authentication: Login
Server as a trusted intermediary is used.
For real-time transfer TLS cannot be used because it is
based on TCP, so it can cause additional delays. In this
application we used AES in integer counter mode [14] (with
the key agreed within signaling process) as a stream cipher.
Bits from cipherare XORed with sounddata, and SHA-1 hash
function is used to ensure packet integrity.
Apart from that, because nodes are participating in data
transmission, we have greater control over the data flow route.
If higher security level is required, it is possible to specify the
desired route, so regardlessof the external routingprotocolwe
can avoid paths that are vulnerable to eavesdropping.
C. Implementation and testing
Our system was written in C# and uses DirectSound to
access the sound device. Also, we created a simple agent
platform for our needs: agents can be run as separate threads
and communicate with each other using sockets.
For testing our infrastructure in many different network
configurations additional simulation software was written.
This simulator allows to graphically create desired network
infrastructureby adding nodes and connectionsbetween them,
real-time data flow is created by streaming audio files, then
links parameters and nodes behaviors can be changed in order
to simulate different cases. For simplicity, simulator is using
the same software that is running on nodes: it is running
them as threads, and configuring by assigning different port
numbers on the same IP. Node state, link delay, jitter, and
packet dropping percentage can be set.
IV. CONCLUSIONS AND FUTURE WORK
In this paper we presented new, based on Peer-to-Peer
network model, IP telephony system. The system model,
infrastructure elements and some implementation details were

92 ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, VOL. 2, NO. 3, SEPTEMPBER 2011
be controlledby agentsand will work betweeneach two nodes
that participate in data routing and are directly connected in
the overlay network.
Fig. 5. Infrastructure simulator.
described. Also benefits of using P2P networks for building
real-time infrastructures have been mentioned. Additionally,
by placing an agent on each infrastructure node and indicating
the advantages of this approach, we showed that agent
based programming could be a valuable tool for designing
this kind of systems. In our application we implemented
mechanisms for ensuring the highest possible call quality,
and security. In particular, a mechanism for improving QoS
throughcontinuousmeasurementofsoundqualityateachnode
in the overlay network, building dynamic routing tables and
path switching technique. System security is guaranteed by
using secure connection with authentication for login process,
AES encryption of real-time data and SHA-1 hash function
for packets integrality. Additionally, owing to P2P model,
maintaining the secrecy of users location is possible, and by
using internal routing protocols we can avoid unsafe paths.
So far,we havebuilt a workingimplementationofpresented
VoIP system, but it is still in its early testing phase. Many
changes and improvements are still being made, so many
elements, like i.e. reputation mechanism behavior or quality
drops tolerance before path switch occurs, still needs to be
tweaked and validated by simulations. Also, besides software
simulations, we are planning to build real infrastructure and
test system behavior in real environment.
In parallel, we are testing new features, like for example
fast retransmission mechanism for real-time packets, that will
REFERENCES
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Zbigniew Kotulski received his M.Sc. in applied mathematics from Warsaw
University of Technology and Ph.D. and D.Sc. Degrees from Institute of
Fundamental Technological Research of the Polish Academy of Sciences.
He is currently professor at IFTR PAS and professor and head of Security
Research Group at Department of Electronics and Information Technology of
Warsaw University of Technology, Poland.
Grzegorz Oryńczak received his M.Scin computer science from Jagiellonian
University. He is currently a Ph.D. student in computer science at the
Jagiellonian University and Institute of Fundamental Technological Research
of the Polish Academy of Sciences. He also works as a senior specialist at
the National Center for Nuclear Research, Świerk.

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