Journal of Applied Mathematics and Stochastic Analysis
Volume 10 (1997), Issue 4, Pages 363-381
The theory of networks of single server queues and the tandem queue model
France Telecom, CNET, 4 Parc de la Bérengère, Saint-Cloud F-92210, France
Received 1 August 1997; Revised 1 October 1997
Copyright © 1997 Pierre Le Gall. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider the stochastic behavior of networks of single server queues
when successive service times of a given customer are highly correlated.
The study is conducted in two particular cases: 1) networks in heavy
traffic, and 2) networks in which all successive service times have the same
value (for a given customer), in order to avoid the possibility of breaking
up the busy periods. We then show how the local queueing delay (for an
arbitrary customer) can be derived through an equivalent tandem queue on
the condition that one other local queueing delay is added: the jitter delay
due to the independence of partial traffic streams.
We consider a practical application of the results by investigating the
influence of long packets on the queueing delay of short packets in modern
packet switched telecommunication networks. We compare these results
with the results given by traffic simulation methods to conclude that there
is good agreement between results of calculation and of traffic simulation.