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Monotonicity of Optimal Performance Measures for Polling Systems

Published online by Cambridge University Press:  27 July 2009

Mark P. Van Oyen
Mark P. Van Oyen
Affiliation:
Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208–3119
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Abstract

We consider scheduling a single server in a multiclass queue subject to setup times and setup costs. We examine the issue of whether or not reductions in the mean and variance of the setup time distributions can lead to degraded system performance. Provided that setups are reduced according to a stochastically smaller ordering, we show that if an optimal policy is used both for the original system and for the system with reduced setup times, then an improvement in performance is guaranteed. Even in cases for which a truly optimal policy is unknown, idling can be employed to avoid degradation of performance as setup times are cut. We extend this approach to show that system performance is monotonic with respect to service time distributions, switching costs, holding costs, and uniform reductions in the arrival rates. Extensions to sequencedependent setups and job feedback are noted.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 2 , April 1997 , pp. 219 - 228
Copyright
Copyright © Cambridge University Press 1997

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