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Optimal control of batch service queues

Published online by Cambridge University Press:  01 July 2016

Rajat K. Deb  and
Richard F. Serfozo
Rajat K. Deb
Affiliation:
State University of New York, Oswego
Richard F. Serfozo
Affiliation:
Syracuse University
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Abstract

A batch service queue is considered where each batch size and its time of service is subject to control. Costs are incurred for serving the customers and for holding them in the system. Viewing the system as a Markov decision process (i.e., dynamic program) with unbounded costs, we show that policies which minimize the expected continuously discounted cost and the expected cost per unit time over an infinite time horizon are of the form: at a review point when x customers are waiting, serve min {x, Q} customers (Q being the, possibly infinite, service capacity) if and only if x exceeds a certain optimal level M. Methods of computing M for both the discounted and average cost contexts are presented.

Keywords

BATCH SERVICE QUEUESBULK QUEUESDYNAMIC PROGRAMMINGMARKOV DECISION PROCESSESSTOCHASTIC CONTROL
Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 2 , August 1973 , pp. 340 - 361
Copyright
Copyright © Applied Probability Trust 1973 

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