Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-14T17:26:42.115Z Has data issue: false hasContentIssue false
  • English
  • Français

On the waiting time distribution in a generalized queueing system with uniformly bounded sojourn times

Published online by Cambridge University Press:  14 July 2016

Jacqueline Loris-Teghem
Jacqueline Loris-Teghem*
Affiliation:
Université Libre de Bruxelles
*
*The author is Chargé de Recherches at the Fonds National Belge de la Recherche Scientifique.
Get access Rights & Permissions [Opens in a new window]

Abstract

A generalized queueing system with (N + 2) types of triplets (delay, service time, probability of joining the queue) and with uniformly bounded sojourn times is considered. An expression for the generating function of the Laplace-Stieltjes transforms of the waiting time distributions is derived analytically, in a case where some of the random variables defining the model have a rational Laplace-Stieltjes transform.

The standard Kl/Km/1 queueing system with uniformly bounded sojourn times is considered in particular.

Keywords

Kl/Km/1 TYPEUNIFORMLY BOUNDED SOJOURN TIMESTRANSIENTWAITING TIMESANALYTICAL
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 3 , June 1972 , pp. 642 - 649
Copyright
Copyright © Applied Probability Trust 1972 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Cohen, J. W. (1967) On two integral equations of queueing theory. J. Appl. Prob. 4, 343–355.CrossRefGoogle Scholar
Kingman, J. F. C. (1966) On the algebra of queues. J. Appl. Prob. 3, 285–326.CrossRefGoogle Scholar
Loris-Teghem, J. (1971) On the waiting time distribution in a generalized GI/G/1 queueing system. J. Appl. Prob. 8, 241–251.Google Scholar
Pollaczek, F. (1957) Problèmes stochastiques posés par le phénomène deformation d'une queue d'attente à un guichet et par des phénomènes apparentés. Mém. Sci. Math. 136.Google Scholar