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Two queues in series with a finite, intermediate waitingroom

Published online by Cambridge University Press:  14 July 2016

Marcel F. Neuts
Marcel F. Neuts*
Affiliation:
Purdue University, Lafayette, Indiana
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Abstract

A service unit I, with Poisson input and general service times is in series with a unit II, with negative-exponential service times. The intermediate waitingroom can accomodate at most k persons and a customer cannot leave unit I when the waitingroom is full.

The paper shows that this system of queues can be studied in terms of an imbedded semi-Markov process. Equations for the time dependent distributions are given, but the main emphasis of the paper is on the equilibrium conditions and on asymptotic results.

Type
Research Papers
Information
Journal of Applied Probability , Volume 5 , Issue 1 , April 1968 , pp. 123 - 142
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

[1] Avi-Itzhak, B. and Yadin, M. (1965) A sequence of two servers with no intermediate queue. Management Sci. 11, 553–564.Google Scholar
[2] Çinlar, E. (1967) The time dependence of queues with semi-Markovian service times. J. Appl. Prob. 4, 356–364.CrossRefGoogle Scholar
[3] Neuts, M. F. (1966) The single server queue with Poisson input and semi-Markov service times. J. Appl. Prob. 3, 202–230.Google Scholar
[4] Neuts, M. F. (1967) A general class of bulk queues with Poisson input. Ann. Math. Statist. 38, 759–770.CrossRefGoogle Scholar
[5] Neuts, M. F. (1966) Semi-Markov analysis of a bulk queue. Bull. Soc. Math. Belg. 18, 28–42.Google Scholar
[6] Neuts, M. F. (1966) The queue with Poisson input and general service times treated as a branching process. Mimeo Series No. 92, Dept. of Statistics, Purdue University, Lafayette, Indiana.Google Scholar
[7] Prabhu, N. U. (1966) Transient behavior of a tandem queue. Management Sci. 13′ 631–639.Google Scholar
[8] Pyke, R. (1961) Markov renewal processes: definitions and preliminary properties. Ann. Math. Statist. 32, 1231–1242.Google Scholar
[9] Pyke, R. (1961) Markov renewal processes with finitely many states. Ann. Math. Statist. 32, 1243–1259.Google Scholar
[10] Pyke, R. and Schaufele, R. (1964) Limit theorems for Markov renewal processes. Ann. Math. Statist. 35, 1746–1765.Google Scholar
[11] Suzuki, T. (1964) On a tandem queue with blocking. J. Operations Res. Soc. Japan 6, 137–157.Google Scholar
[12] Takács, L. (1962) Introduction to the Theory of Queues. Oxford Univ. Press, New York, N.Y. Google Scholar
[13] Yadin, M. Private communication.Google Scholar