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

  • Jacqueline Loris-Teghem (a1)
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.

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* The author is Chargé de Recherches at the Fonds National Belge de la Recherche Scientifique.
References
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Cohen, J. W. (1967) On two integral equations of queueing theory. J. Appl. Prob. 4, 343355.
Kingman, J. F. C. (1966) On the algebra of queues. J. Appl. Prob. 3, 285326.
Loris-Teghem, J. (1971) On the waiting time distribution in a generalized GI/G/1 queueing system. J. Appl. Prob. 8, 241251.
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.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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