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Optimal control of arrivals to multiserver queues in a random environment

Published online by Cambridge University Press:  14 July 2016

Werner E. Helm  and
Karl-Heinz Waldmann
Werner E. Helm*
Affiliation:
Technische Hochschule Darmstadt
Karl-Heinz Waldmann*
Affiliation:
Freie Universität Berlin
*
∗Present address: Abt. Wiss. Datenverarbeitung, E. Merck, Postfach 4119, D-6100 Darmstadt 1, W. Germany.
∗∗Postal address: Institut für Quantitative Ökonomik und Statistik, Freie Universität Berlin, Garystr. 21, D-1000 Berlin 33, W. Germany.
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Abstract

We study the problem of optimal customer admission to multiserver queues. These queues are assumed to live in an extraneous environment which changes in a semi-Markovian way. Arrivals, service mechanism and random reward/cost structure may all depend on these surroundings. Included as special cases are SM/M/c queues, in particular G/M/c queues, in a random environment. By a direct inductive approach we establish optimality of a generalized control-limit rule depending on the actual environment. Particular emphasis is laid on different applications that show the versatility of the proposed setup.

Keywords

SM/M/c QUEUESMARKOV DECISION PROCESSESDYNAMIC PROGRAMMING
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 3 , September 1984 , pp. 602 - 615
Copyright
Copyright © Applied Probability Trust 1984 

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