Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 4, Pages 429-450
doi:10.1155/S1048953300000368
Single server queueing networks with varying service times and renewal input
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.
Abstract
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).