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An algebraic approach to the waiting time process in GI/M/S

Published online by Cambridge University Press:  14 July 2016

Jacqueline Loris-Teghem
Jacqueline Loris-Teghem*
Affiliation:
Université Libre de Bruxelles∗
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Abstract

The transient behaviour of the waiting time process in GI/M/S is studied algebraically by means of a two-dimensional Markovian process {(vn, ln} , where the variables vn denote the times of full occupation immediately after the arrival instants Tn and where ln = max {0,– 1 + number of idle servers at (Tn + 0)}.

Keywords

GI/M/S QUEUEWAITING TIMESTRANSIENT BEHAVIOURTWO-DIMENSIONAL MARKOV PROCESSWENDEL PROJECTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 1 , March 1973 , pp. 181 - 191
Copyright
Copyright © Applied Probability Trust 1973 

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References

Kingman, J. F. C. (1966) On the algebra of queues. J. Appl. Prob. 3, 285–326.Google Scholar
Loris-Teghem, J. (1971a) On the waiting time distribution in a generalized GI/G/1 queueing system. J . Appl. Prob. 8, 241–251.CrossRefGoogle Scholar
Loris-Teghem, J. (1971b) Un traitement algébrique du modèle d'attente GI/M/2. Cah. Centre Et. Rech. Op. 13, 57–62.Google Scholar
Loris-Teghem, J. (1973) On the waiting time distribution in some generalized queueing systems. Bull. Soc. Math. Belgique. To appear.Google Scholar
Pollaczek, F. (1961) Théorie analytique des problèmes stochastiques relatifs à un groupe de lignes téléphoniques avec dispositif d'attente. Mémor. Sci. Math. 150.Google Scholar
Wendel, J. G. (1958) Spitzer's formula; a short proof. Proc. Amer. Math. Soc. 9, 905–908.Google Scholar