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A queue with Markov-dependent service times

Published online by Cambridge University Press:  14 July 2016

Gerold Pestalozzi
Gerold Pestalozzi*
Affiliation:
Department of Public Works, Canton of Zurich
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Abstract

A queueing system is considered where each item has a property associated with it, and where the service time interposed between two items depends on the properties of both of these items. The steady state of a single-channel queue of this type, with Poisson input, is investigated. It is shown how the probability generating function of the number of items waiting can be found. Easily applied approximations are given for the mean number of items waiting and for the average waiting time.

Type
Research Papers
Information
Journal of Applied Probability , Volume 5 , Issue 2 , August 1968 , pp. 461 - 466
Copyright
Copyright © Applied Probability Trust 1968 

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References

[1] Gaver, D. P. Jr. (1963) A comparison of queue disciplines when service orientation times occur. Naval Res. Logist. Quart. 10.CrossRefGoogle Scholar
[2] Neuts, M. F. (1966) The single server queue with Poisson input and semi-Markov service times. J.Appl. Prob. 3, 202–230.CrossRefGoogle Scholar
[3] Kendall, D. G. (1951) Some problems in the theory of queues. J.R. Statist. Soc. B 13, No. 2, 151–185.Google Scholar
[4] Cox, D. R. and Smith, W. L. (1961) Queues. Methuen & Co. Ltd., London. John Wiley & Sons, Inc., New York.Google Scholar