Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 3, Pages 377-390
Multiserver queueing networks and the tandem queue model
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
queue. 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.