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Optimality of threshold policies in single-server queueing systems with server vacations

Published online by Cambridge University Press:  01 July 2016

Awi Federgruen  and
Kut C. So
Awi Federgruen*
Affiliation:
Columbia University
Kut C. So*
Affiliation:
University of California, Irvine
*
∗Postal address: Graduate School of Business, Columbia University, New York, NY 10027, USA.
∗∗Postal address: Graduate School of Management, University of California, Irvine, CA 92717, USA.
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Abstract

In this paper we consider a class of single-server queueing systems with compound Poisson arrivals, in which, at service completion epochs, the server has the option of taking off for one or several vacations of random length. The cost structure consists of a holding cost rate specified by a general non-decreasing function of the queue size, fixed costs for initiating and terminating service, and a variable operating cost incurred for each unit of time that the system is in operation. We show under some weak conditions with respect to the holding cost rate function and the service time, vacation time and arrival batch size distributions that it is either optimal among all feasible (stationary and non-stationary) policies never to take a vacation, or it is optimal to take a vacation when the system empties out and to resume work when, upon completion of a vacation, the queue size is equal to or in excess of a critical threshold. These optimality results are generalized for several variants of this model.

Keywords

VACATION MODELSREMOVABLE SERVERMONOTONE POLICIESSEMI-MARKOV DECISION PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 2 , June 1991 , pp. 388 - 405
Copyright
Copyright © Applied Probability Trust 1991 

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