Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 4, Pages 429-450

Single server queueing networks with varying service times and renewal input

Pierre Le Gall

France Telecom, R&D, 4 Pare de la Bérengère, Saint-Cloud F-92210, France

Received 1 January 1999; Revised 1 December 1999

Copyright © 2000 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.


Using recent results in tandem queues and queueing networks with renewal input, when successive service times of the same customer are varying (and when the busy periods are frequently not broken up in large networks), the local queueing delay of a single server queueing network is evaluated utilizing new concepts of virtual and actual delays (respectively). It appears that because of an important property, due to the underlying tandem queue effect, the usual queueing standards (related to long queues) cannot protect against significant overloads in the buffers due to some possible “agglutination phenomenon” (related to short queues). Usual network management methods and traffic simulation methods should be revised, and should monitor the partial traffic streams loads (and not only the server load).