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Some explicit formulas for the steady-state behavior of the queue with semi-Markovian service times

Published online by Cambridge University Press:  01 July 2016

Marcel F. Neuts
Marcel F. Neuts*
Affiliation:
Purdue University
*
∗ Now at the University of Delaware.
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Abstract

This paper discusses a number of explicit formulas for the steady-state features of the queue with Poisson arrivals in groups of random sizes and semi-Markovian service times. Computationally useful formulas for the expected duration of the various busy periods, for the mean numbers of customers served during them, as well as for the lower order moments of the queue lengths, both in discrete and in continuous time, and of the virtual waiting time are obtained. The formulas are recursive matrix expressions, which generalize the analogous but much simpler results for the classical M/G/1 model.

Keywords

QUEUESSEMI-MARKOV SERVICE TIMESM/SM/1 QUEUECOMPUTATIONAL PROBABILITYQUEUE LENGTHWAITING TIME

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 9 , Issue 1 , March 1977, pp. 141 - 157
Copyright
Copyright © Applied Probability Trust 1977 

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Footnotes

This paper was prepared for presentation as an invited address at the Statistics Days at Ball State University, Muncie, Indiana, 9-10 April 1976. This research was sponsored by the Air Force Office of Scientific Research Air Force Sytems Command USAF, under Grant No. AFOSR-72-2350 B.

References

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