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The busy period of the Ek/G/1 queue by finite waiting room

Published online by Cambridge University Press:  01 July 2016

A. L. Truslove
A. L. Truslove*
Affiliation:
Monash University
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Abstract

For the Ek/G/1 queue with finite waiting room the phase technique is used to analyse the Markov chain imbedded in the queueing process at successive instants at which customers complete service, and the distribution of the busy period, together with the number of customers who arrive, and the number of customers served, during that period, is obtained. The limit as the size of the waiting room becomes infinite is found.

Keywords

FINITE WAITING ROOMBUSY PERIODERLANG INPUTPHASE TECHNIQUE
Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 2 , June 1975 , pp. 416 - 430
Copyright
Copyright © Applied Probability Trust 1975 

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References

Pollaczek, F. (1952) Sur la répartition des périodes d'occupation interrompue d'un guichet. C. R. Acad. Sci. Paris 234, 2042–2044.Google Scholar
Takács, L. (1961) Transient behavior of single server queueing processes with Erlang input. Trans. Amer. Math. Soc. 100, 1–28.CrossRefGoogle Scholar