Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 3, Pages 377-390

Multiserver queueing networks and the tandem queue model

Pierre Le Gall

France Telecom, CNET, 4 Parc de la Bérengère, Saint-Cloud F-92210, France

Received 1 November 1997; Revised 1 May 1998

Copyright © 1998 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 a tandem queue model we evaluate the local “endogenous” (= internal) queueing delay in single server and multiserver queueing networks. The new concept of the apparent overall upstream queueing delay(as perceived by the downstream network) allows us to analyze the distribution of this local queue by interpolating between the distributions of the tandem queue (generated by a concentration tree) and the isolated G/G/squeue. The interpolation coefficients depend on the proportion of “premature departures”, typically interfering in the upstream stage and leaving the considered path without being offered to the considered local queue. On the other hand, local “exogenous” arrivals (from outside the network) require the introduction of the “interference delay” concept. Finally, in the case of single server queueing networks, we stress the need to extend the capacities of the buffers, by considering the “worst case” scenario and by using an “equivalent tandem queue” model.