Contents Telektronikk - Telenor

102
According to our plans rerouting and circuit
reservation will be implemented in
1995, while the implementation of
Dynamic Alternative Routing is planned
for 1996.
At present, the work indicated in chapter
10 is continued in order to make optimal
use of protection mechanisms in the
physical network and its main user
PSTN/ ISDN. A review of the
dimensioning rules is part of this work.
As this article indicates, optimal grade of
service during failure is a complex subject
involving traffic theory, both physical
and logical network structure and
physical routing as well as traffic routing.
A major part of the problem is also the
evaluation of lost traffic. However, as the
models and the parameters used are not
very accurate and the cost ratio work/
equipment is increasing, emphasis should
be put on simple models with defined
interfaces between the physical and logical
network.
References
1 Parviala, A. Optimering av små overflow
vior. Nordic teletraffic seminar,
Helsinki, 1982.
2 Songhurst, D J. Protection against
traffic overload in hierarchical networks
employing alternative routing.
I: 1st international network planning
symposium, Paris, 1980.
3 Pettersen, H. Dirigering i fjernnettet
: en simuleringsstudie. Kjeller,
Norwegian Telecom Research, 1988.
(TF-report 53/88.)
4 Ash, G R, Huang, B D. Comparative
evaluation of dynamic routing strategies
for a worldwide intelligent network.
I: 14th international teletraffic
congress, ITC 14, France, 1994.
S
S
Appendix 1
A simple model for circuit
reservation
We will describe the properties of circuit
reservation through a simple model. Two
traffic streams A1 and A2 are offered a circuit
group of N circuits. The traffic
stream A1 is given priority by reserving
the last R free circuits for this traffic. This
means that call attempts from A2 are congested
when the number of free circuits
are equal to or less than R. When the traffic
streams are Poisson processes, e.g.
with exponential inter arrival times and
holding times, the traffic process can be
described by the state diagram in Figure
A1. The following symbols are used:
h mean holding time for calls (seizures)
of both type 1 and 2 (this
simplifies the model, but is not
necessary)
s1 mean arrival rate for call attempts
of type 1
s2 mean arrival rate for call attempts
of type 2
s total arrival rate, s = s1 + s2 A1 traffic offered of type 1 (A1 = s1h) A2 traffic offered of type 2 (A2 = s2h) A total traffic, A = A1 + A2 = sh
pj the probability of being in state j,
that means there are j simultaneous
calls leaving N-j circuits free.
In the state diagram a transition to the
next higher state occurs when a call arrives.
When a call terminates, a transition to
the next lower state takes place. The
arrival process is constant (s1 + s2 = s)in
all states, however calls of type two are
congested in the last R + 1 states of the
diagram, the termination rate (number of
calls terminating per time unit) is proportional
to the number of ongoing calls.
In the state diagram the number of transitions
per time unit between two neighbour
states must in average be the same
S
S 2 S 2 S 2 S
0 1 2 N-R-1 N-R N-R+1 N-1 N
1/h 2/h (N-R)/h (N-R+1)/h N/h
Figure A1 State diagram for one-level circuit reservation with two Poisson arrival processes with negative exponential holding times
S 1
in both directions. Thus, we have the following
equations:
p11/h = p0s p1 = p0sh = p0A p22/h = p1s p2 = p1sh/2 = p0A2 /2!
.
.
pjj/h = pj-1s pj = p0Aj /j!
.
.
pN-R (N-R)/h pN-R = pN-R-1s = p0AN-R /(N-R)!
pN-R+1 (N-R+1)/h pN-R+1 = pN-Rs1 = p0AN-RA1 /(N-R+1)!
.
.
pN N/h pN = pN-1s1 = p0AN-RA R
1 /N!
By using the normalising equation
N�
j=1
pj =1
the state probabilities may be explicitly
determined
⎧
⎨N−R
� � � j
p0 =1/ A /j!
⎩
+
j=1
j=0
R� �
A N−R A j
�
1 /(N − R + j)!
⎫ ⎬
⎭
The congestion for traffic stream A1 is
calculated directly as B1 = pN . The congestion
for traffic stream A2 is calculated
as
N�
B2 =
j=N−R
pj
In the case of no reservation, R = 0, the
formulas are, as expected, the same as
Erlang’s 1st formula:
B1 = B2 = pN = � A N /N ! � /
S 1
N� � �
j
A /j!
j=0