Packet Queueing Delay in Resilient Packet Ring Network Nodes

TSINGHUA SCIENCE AND TECHNOLOGY
ISSN 1007-0214 07/21 pp406-409
Volume 9, Number 4, August 2004
Packet Queueing Delay in Resilient Packet Ring Network Nodes *
SHI Guowei (史国炜) ** , FANG Hongbo (方红波),
QU Jianling (曲建岭) , ZENG Lieguang (曾烈光)
State Key Laboratory on Microwave and Digital Communications,
Department of Electronic Engineering, Tsinghua University, Beijing 100084, China;
Naval Aeronautical Engineering Academy Qingdao Branch, Qingdao 266041, China
Abstract: The packet queueing delay is one of the most important performance measures of a data net-
work and is also a significant factor to be considered in the scheduling buffer design for a network node.
This paper presents a traffic queueing model for resilient packet ring (RPR) networks and a method for
quantitatively analyzing queueing delays in RPR nodes. The method was used to calculate the average
queueing delays of different priority traffic for different transit queue modes. The simulations show that, in
the transmit direction, lower priority traffic is delayed more than higher priority traffic, and that Class-A traffic
is delayed more in a single-queue ring than in a dual-queue ring. In the transit direction, the secondary tran-
sit buffer in the dual-queue ring contributes more to the traffic delay than the primary transit buffer in the sin-
gle-queue ring, which in turn causes more delay than the primary transit buffer in the dual-queue ring.
Key words: resilient packet ring; queueing model; queueing delay
Introduction
The IEEE 802.17 resilient packet ring (RPR) protocol
has been introduced as a novel medium access control
protocol for metropolitan area networks [1-3] . An RPR
network supports service level agreement, and different
priority traffic has different requirements for
queueing delay in the scheduling buffer. Packet queueing
delay is one of the most important performance
measures of a data network and is also a significant
factor to be considered in scheduling buffer design for
a network node. This paper based on the delay analysis
used for other packet networks [4-6] presents a traffic
queueing model for an RPR network node and a
method to quantitatively calculate the packet queueing
delay in the scheduling buffer, and analyzes packet
Received: 2003-01-18
* Supported by the National High-Tech Research and Development
(863) Program of China (No. 2002AA121041)
** To whom correspondence should be addressed.
E-mail: shigw@sohu.com; Tel: 86-10-62781409
queueing delays of different priority traffic in different
transit queue modes.
1 Data Path Structure of an RPR
Network Node
The RPR protocol uses a bi-directional ring as shown
in Fig. 1. The RPR node feeds the ring with local client
traffic and forwards the upstream traffic to the downstream
nodes. Each node can send data to other nodes
via either of the two ringlets. In general, for a given
destination, the shorter of the two possible paths is
used, based on an RPR topology discovery scheme [2] .
Fig. 1 Structure of RPR network

SHI Guowei (史国炜) et al:Packet Queueing Delay in Resilient Packet Ring Network Nodes 407
RPR protocol defines two types of transit queueing
models for network nodes: single-queue (SQ) and
dual-queue (DQ). Accordingly, an RPR node may have
two kinds of data path structures, as shown in Figs. 2
and 3. The difference between the two data path structures
is in the number of transit buffers. The transit
buffer (TB) is used exclusively to avoid collisions between
transmit and transit packets. The frame-header
checker determines the reception and transit conditions
for the upstream packets. The arbiter schedules the access
of transmit and transit packets to the outgoing link.
Fig. 2 Data path structure of a single-queue node
Fig. 3 Data path structure of a dual-queue node
An RPR network supports client traffic with three
priority classes: Class A, Class B, and Class C. In the
transmit direction, Class A traffic has higher precedence
than Class B which in turn has higher precedence
than Class C traffic. According to the priority,
the client traffic is inserted into three transmit buffers,
which are named Tx-A, Tx-B, and Tx-C, respectively.
In the SQ mode, the node places all transit traffic into a
primary transit queue (PTQ). In the DQ mode, the
node puts Class A transit traffic into a higher priority
PTQ, and puts Class B and Class C transit traffic into a
lower priority secondary transit queue (STQ). Neither
mode supports preemption of either transit or ingress
packets.
The RPR protocol defines the bandwidth allocation
and packet scheduling mechanisms. As shown in
Figs. 2 and 3, based on the RPR scheduling mechanism,
if we assume that the control packets are negligible in
amount and the capacity of all buffers is infinite, the
arbiter can schedule packets simply according to the
following priority order (from the highest to the
lowest):
● Dual-queue
① Packets from PTQ,
② Packets from Tx-A,
③ Packets from Tx-B,
④ Packets from Tx-C,
⑤ Packets from STQ.
● Single-queue
① Packets from PTQ,
② Packets from Tx-A,
③ Packets from Tx-B,
④ Packets from Tx-C.
2 Mathematic Analysis of Queueing
Delay
Assume that traffic arrival times and service times are
independent, that the arrival processes at each transmit
and transit buffer are of Poisson distribution, and that
all nodes have the same packet-length distribution.
Then the traffic queueing model of the RPR data path
can be regarded as a non-preemptive priority M/G/1
queueing system, based on the standard queueing
theory [7] .
In the following, we develop an equation for the average
delay for each priority class. The following symbols
are used in this paper: Wk is average queueing delay
for priority k; λk is average arrival rate for priority
k; X k is the first moment of service time for priority
2
k; X k is the second moment of service time for priority
k; ρk is the system utilization for priority k; R is mean
residual service time.
The queueing delay is the time span between the
time when the packet is assigned to a queue for transmission
and the time when it starts to be transmitted.
According to Little’s theorem and the Pollaczek-
Khintchine (P-K) formula [8] , the queueing delay for the
highest priority traffic is
R
W1
= (1)
1−
ρ
where the residual service time R is expressed as
1 n
2
R = ∑ λiX
i
(2)
2
i=
1
1

408 Tsinghua Science and Technology, August 2004, 9(4): 406–409
For the second priority class, the queueing delay W2
has a similar expression as W1 except that an additional
queueing delay has to be counted due to higher priority
customers arriving while a lower priority customer is
waiting in the queue. W2 is obtained,
R+ ρ1W1
W2
= (3)
1−ρ−ρ
1 2
The derivation is similar for all priority classes (k>1),
and the formula for the waiting time in the scheduling
buffer is
R
Wk= , k > 1
1−ρ −L−ρ 1−ρ
−L−ρ ( )( )
1 k−1 1
k
(4)
Suppose that all nodes have the same transmission
pattern. The average number of transit buffers traversed
by each packet is then obtained,
α
N −1
= ∑ q ( j−1)
j=
2
j
(5)
where N is the number of the nodes on the ring, and qj
is the probability of node i transmitting packets to its jth
neighbor node.
Assume that traffic of all priorities has the same arrival
rate in the transmit buffer. The relationship between
the traffic arrival rates in the transit buffer and
in the transmit buffer is [9]
λTB = αλTx
(6)
We assume that all packets have the same service
time X . The relationship between the system utilization
and the arrival rate for each priority class in a node
is then
ρ1 = αρA
(7)
For a DQ ring, we identify five priority traffic
classes as shown in Fig. 3. Using Eqs. (6) and (7), the
system utilization of each priority class can be expressed
as:
ρ1 = αρA
(8)
ρ = ρ
(9)
2 A
3 = B
ρ ρ
4 C
5 ( B C)
(10)
ρ = ρ
(11)
ρ = α ρ + ρ
(12)
From Eqs. (1), (3), and (8)-(12), the queueing delays
for each priority class in different buffers are obtained:
DQ R
WPTQ
= (13)
1−
αρ
A
W
W
DQ
B
DQ
C
=
=
W
DQ
A
=
R
(1 −αρ ) 1 − 1 + α ρ
( ( ) )
A A
R
( )
( 1− ( 1+ α) ρA) 1− ( ( 1+
α) ρA + ρB)
R
( 1− ( ( 1+ α) ρA + ρB) ) 1− ( ( 1+
α) ρA + ρB + ρC)
W
DQ
STQ
=
( )
R
( 1− ( ( 1+
α) ρA + ρB + ρC)
)
1
( 1− ( ( 1+ α) ρA + ( 1+
α)( ρB + ρC)
) )
( 1 )( )
A B C
(14)
(15)
(16)
(17)
R = X + α ρ + ρ + ρ (18)
For the SQ ring, four priorities are identified as
shown in Fig. 2. Similar derivations to those used for
the DQ ring can be made. The equations for the system
utilization and queueing delay for each traffic class in
an SQ ring are obtained:
ρ = α ρ + ρ + ρ
(19)
W
SQ
A
W
=
W
SQ
PTQ
1
( )
A
B
C
ρ2 = ρA
(20)
ρ3 = ρB
(21)
ρ4 = ρC
(22)
R
=
1−
α ρ + ρ + ρ
( )
A B C
R
( )
( 1− α( ρA + ρB + ρC) ) 1−
( α( ρA + ρB + ρC) + ρA)
W
SQ
C
SQ
B
=
R
( 1−
( α( ρA + ρB + ρC) + ρA)
)
1
( 1− ( α( ρA + ρB + ρC) + ρA + ρB)
)
=
R
( 1−
( α( ρA + ρB + ρC) + ρA + ρB)
)
1
( 1− ( α + 1)(
ρA + ρB + ρC)
)
3 Simulation Results
(23)
(24)
(25)
(26)
In the normal operation state, the packets are routed on
a minimum hop basis in an RPR network. Therefore, it

SHI Guowei (史国炜) et al:Packet Queueing Delay in Resilient Packet Ring Network Nodes 409
is simple to deduce that
2
q j = ,
N − 1
for N is odd (27)
2
qj= ,
N
for N is even (28)
Combined with Eq. (5), the average number of transit
buffers traversed by each packet can be obtained:
N −1
N − 3
α=
∑ qj( j− 1 ) = , for N is odd (29)
4
j=
2
N −1
N − 2
α=
∑ qj( j− 1 ) = , for N is even (30)
4
j=
2
From Eq. (26), the maximum total system utilization
of the ring is obtained,
max N
ρtotal
= (31)
1+
α
We now analyze the queueing delay of different
priority traffic in the two different transit queue modes.
We assume that N = 63, the ring is loaded with Class B
traffic of 1 ρ and with Class C traffic of 1 ρ ,
3 3
max
total
and Class A traffic is varied from 0 to
max
total
1 max
ρ
3 total . The
queueing delay is normalized by the average service
time X ( X = 14.7 µs for a 2.5-Mbps link bit rate) to
mask the effect of different link rates. The function w
given in Figs. 4-7 is the scaled time. The actual
simulation time W can be obtained by multiplying the
factor X
W = wX
(32)
Figures 4 and 5 show the average transmit queueing
delays for the three classes of traffic in the SQ and DQ
modes, respectively. It is obvious that the queueing delays
for all three classes of traffic in transmit buffers
increase with increasing system utilization of Class A
traffic, and that Class A traffic has the shortest queueing
delay.
Fig. 4 Queueing delay in transmit buffers
(in the SQ mode)
Fig. 5 Queueing delay in transmit buffers
(in the DQ mode)
Figure 6 shows the queueing delays of Class A traffic
in transmit buffers for both the DQ and SQ rings. It
is clear that Class A traffic is delayed more in an SQ
ring than in a DQ ring.
Fig. 6 Comparison of queueing delays in transmit
buffers in the SQ and DQ modes
Figure 7 shows the traffic queueing delays in transit
buffers for the two kinds of transit queue modes.
Figure 7 shows that the STQ buffer in the DQ ring
contributes more traffic delay than the PTQ buffer in
the SQ ring which in turn causes more delay than the
PTQ buffer in the DQ ring.
Fig. 7 Queueing delay in transit buffers STQ and PTQ
4 Conclusions
The packet queueing delay is one of the most important
performance measures of a data network and is a
key factor to be considered in the scheduling buffer
(Continued on page 415)