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Optimal control of a flexible server

Part of: Operations research and management science Computer system organization Stochastic systems and control

Published online by Cambridge University Press:  01 July 2016

Hyun-Soo Ahn ,
Izak Duenyas  and
Rachel Q. Zhang
Hyun-Soo Ahn*
Affiliation:
University of California, Berkeley
Izak Duenyas*
Affiliation:
University of Michigan
Rachel Q. Zhang*
Affiliation:
Cornell University
*
∗ Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720-1777, USA.
∗∗ Postal address: University of Michigan Business School, Ann Arbor, MI 48109, USA. Email address: [email protected]
∗∗∗ Johnson Graduate School of Management, Cornell University, Ithaca, NY 14853, USA.
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Abstract

We consider the dynamic scheduling of a multiclass queueing system with two servers, one dedicated (server 1) and one flexible (server 2), with no arrivals. Server 1 is dedicated to processing type-1 jobs while server 2 is primarily responsible for processing type-2 jobs but can also aid server 1 with its work. We address when it is optimal for server 2 to aid server 1 with type-1 jobs rather than process type-2 jobs. The objective is to minimize the total holding costs incurred until all jobs in the system are processed and leave the system. We show that the optimal policy can exhibit one of three possible structures: (i) an exhaustive policy for type-2 jobs, (ii) a nonincreasing switching curve in the number of type-1 jobs and (iii) a nondecreasing switching curve in the number of type-1 jobs. We characterize the necessary and sufficient conditions under which each policy will be optimal. We also explore the use of the optimal policy for the problem with no arrivals as a heuristic for the problem with dynamic arrivals.

Keywords

Stochastic schedulingmultiserver queueflexible serverclearing system

MSC classification

Primary: 93E20: Optimal stochastic control
Secondary: 90B22: Queues and service 68M20: Performance evaluation; queueing; scheduling
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 36 , Issue 1 , March 2004 , pp. 139 - 170
Copyright
Copyright © Applied Probability Trust 2004 

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