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OPTIMAL SWITCHING ON AND OFF THE ENTIRE SERVICE CAPACITY OF A PARALLEL QUEUE

Published online by Cambridge University Press:  09 October 2015

Eugene A. Feinberg  and
Xiaoxuan Zhang
Eugene A. Feinberg
Affiliation:
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA E-mail: eugene.feinberg@stonybrook.edu
Xiaoxuan Zhang
Affiliation:
IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA E-mail: zhangxiaoxuan@live.com
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Abstract

This paper studies optimal switching on and off of the entire service capacity of an M/M/∞ queue with holding, running and switching costs. The running costs depend only on whether the system is on or off, and the holding costs are linear. The goal is to minimize average costs per unit time. The main result is that an average-cost optimal policy either always runs the system or is an (M, N)-policy defined by two thresholds M and N, such that the system is switched on upon an arrival epoch when the system size accumulates to N and is switched off upon a departure epoch when the system size decreases to M. It is shown that this optimization problem can be reduced to a problem with a finite number of states and actions, and an average-cost optimal policy can be computed via linear programming. An example, in which the optimal (M, N)-policy outperforms the best (0, N)-policy, is provided. Thus, unlike the case of single-server queues studied in the literature, (0, N)-policies may not be average-cost optimal.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 29 , Issue 4 , October 2015 , pp. 483 - 506
Copyright
Copyright © Cambridge University Press 2015 

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