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Optimal Scheduling on Parallel Processors with Precedence Constraints and General Costs

Published online by Cambridge University Press:  27 July 2009

Zhen Liu  and
Rhonda Righter
Zhen Liu
Affiliation:
INRIA, Centre Sophia Antipolis, 2004 Route des Lucioles B.P. 93, 06902 Sophia-Antipolis, France
Rhonda Righter
Affiliation:
Department of Decision and Information Sciences, Santa Clara University, Santa Clara, California 95053
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Abstract

We consider preemptive and nonpreemptive scheduling of partially ordered tasks on parallel processors, where the precedence relations have an intervalorder, an in-forest, or a uniform out-forest structure. Processing times of tasks are random variables with an increasing in likelihood ratio distribution in the nonpreemptive case and an exponential distribution in the preemptive case. We consider a general cost that is a function of time and of the uncompleted tasks and show that the most successors (MS) policy stochastically minimizes the cost function when it satisfies certain agreeability conditions. A consequence is that the MS policy stochastically minimizes makespan, weighted flowtime, and the weighted number of late jobs.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 1 , January 1997 , pp. 79 - 93
Copyright
Copyright © Cambridge University Press 1997

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