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

Pierre Le Gall

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.