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Time dependence of queues with semi-Markovian services

Published online by Cambridge University Press:  14 July 2016

Erhan Çinlar
Erhan Çinlar*
Affiliation:
Northwestern University, Evanston, Illinois
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Abstract

A single server queueing system with Poisson input is considered. There are a finite number of types of customers and the service time of the nth customers depends on the types of the nth and the (n – l)th customers. The time dependence of the queue size process will be studied, (it will be clear how the methods of the paper can be applied to other processes of interest,) and limiting as well as transient results will be given.

Type
Research Papers
Information
Journal of Applied Probability , Volume 4 , Issue 2 , August 1967 , pp. 356 - 364
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

Frobenius, G. (1912) Über Matrizen aus nicht-negativen Elementen. S.-B. Kgl. Preussischen Akad. Wiss. Berlin, 456–477.Google Scholar
Gantmacher, F. R. (1959) The Theory of Matrices. Chelsea, New York.Google Scholar
Loynes, R. M. (1962) Stationary waiting-time distributions for single-server queues. Ann. Math. Statist. 33, 1323–1339.CrossRefGoogle Scholar
Neuts, M. F. (1966) The single server queue with Poisson input and semi-Markov service times. J. Appl. Prob. 3, 202–230.CrossRefGoogle Scholar
Pyke, R. (1961) Markov renewal processes with finitely many states. Ann. Math. Statist. 32, 1243–1259.CrossRefGoogle Scholar
Smith, W. L. (1955) Regenerative stochastic processes. Proc. Roy. Soc. A 232, 6–31.Google Scholar
Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar
Wielandt, H. (1950) Unzerlegbare nicht-negative Matrizen. Math. Zeit. 52, 642–648.CrossRefGoogle Scholar