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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.
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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 

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References

Cohen, J. W. (1967) On two integral equations of queueing theory. J. Appl. Prob. 4, 343–355.CrossRefGoogle Scholar
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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