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The number of departures from a semi-Markov queue

Published online by Cambridge University Press:  14 July 2016

D. C. McNickle
D. C. McNickle*
Affiliation:
University of Auckland
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Abstract

In this note an identity due to Arjas (1972) is used to express the distribution of the number of departures from a single server queue in which both service and interarrival times may depend on customer type in terms of the busy period and busy cycle processes.

Keywords

SEMI-MARKOV QUEUENUMBER OF DEPARTURESSM/M/1 QUEUE
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 825 - 828
Copyright
Copyright © Applied Probability Trust 1974 

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References

Arjas, E. (1972) On the use of a fundamental identity in the theory of semi-Markov queues. Adv. Appl. Prob. 4, 271–284.Google Scholar
Çinlar, E. (1967) Queues with semi-Markovian arrivals. J. Appl. Prob. 4, 365–379.Google Scholar
Cohen, J. W. (1969) The Single Server Queue. North-Holland, Amsterdam.Google Scholar