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On a decomposition result for a class of vacation queueing systems

Published online by Cambridge University Press:  14 July 2016

Jacqueline Loris-Teghem
Jacqueline Loris-Teghem*
Affiliation:
Université de l'Etat à Mons
*
∗Postal address: Faculté des Sciences Economiques et Sociales, Place Warocqué, 17 — B 7000 Mons, Belgium.
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Abstract

We consider a single-server infinite-capacity queueing sysem with Poisson arrivals of customer groups of random size and a general service time distribution, the server of which applies a general exhaustive service vacation policy. We are concerned with the steady-state distribution of the actual waiting time of a customer arriving while the server is active.

Keywords

BULK ARRIVALSVACATION POLICYWAITING TIMEDECOMPOSITION FORMULA
Type
Short Communications
Information
Journal of Applied Probability , Volume 27 , Issue 1 , March 1990 , pp. 227 - 231
Copyright
Copyright © Applied Probability Trust 1990 

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References

[1] Cox, D. R. and Lewis, P. A. W. (1968) The Statistical Analysis of Series of Events. Methuen, London.Google Scholar
[2] Heyman, D. P. and Sobel, M. (1982) Stochastic Models in Operations Research, Vol. I. McGraw-Hill, New York.Google Scholar
[3] Keilson, J. and Ramaswamy, R. (1988) The backlog and deflection-time process for M/G/1 vacation models with exhaustive service discipline. J. Appl. Prob. 25, 404–412.CrossRefGoogle Scholar
[4] Loris-Teghem, J. (1988) Waiting time distribution in some queueing systems with server vacations. In Operational Research '87, ed. Rand, G. K., North-Holland, Amsterdam.Google Scholar
[5] Loris-Teghem, J. (1988) On vacation models with bulk arrivals. Submitted.Google Scholar