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Optimal Multiserver Stochastic Scheduling of two Interconnected Priority Queues

Part of: Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Dimitrios G. Pandelis  and
Demosthenis Teneketzis
Dimitrios G. Pandelis
Affiliation:
University of Michigan
Demosthenis Teneketzis*
Affiliation:
University of Michigan
*
* Postal address for both authors: Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109-2122, USA.
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Abstract

A number of jobs on two interconnected queues are to be processed by m identical servers. The servers operate in parallel, so that every server can process any job. Jobs in queue i, i = 1, 2, incur an instantaneous holding cost Ci during the time they remain in the system. The service time for jobs in queue i, denoted by Xi, is a random variable with a general distribution. The interconnection process is independent of the service process. We establish sufficient conditions on the service times, the holding costs and the interconnection process under which the non-preemptive scheduling strategy that gives priority to queue 1 minimizes the total expected α -discounted cost. We call this strategy P1. We present counterexamples showing that if any of the sufficient conditions is not satisfied P1 may not be optimal, and that the optimal policy for the single-server problem is not necessarily optimal for the multiserver problem.

Keywords

MULTISERVER SCHEDULINGINTERCONNECTED QUEUESSTOCHASTIC ORDERING

MSC classification

Secondary: 90B35: Scheduling theory, deterministic
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 26 , Issue 1 , March 1994 , pp. 258 - 279
Copyright
Copyright © Applied Probability Trust 1994 

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