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Scheduling Two-Point Stochastic Jobs to Minimize the Makespan on Two Parallel Machines

Published online by Cambridge University Press:  27 July 2009

Sem Borst ,
John Bruno ,
E. G. Coffman Jr  and
Steven Phillips
Sem Borst
Affiliation:
Bell Labs, Lucent Technologies Murray Hill, New Jersey 07974
John Bruno
Affiliation:
Department of Computer Science, University of California, Santa Barbara, California 93106
E. G. Coffman Jr
Affiliation:
Bell Labs, Lucent Technologies Murray Hill, New Jersey 07974
Steven Phillips
Affiliation:
AT&T Research Murray Hill, New Jersey 07974
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Abstract

Simple optimal policies are known for the problem of scheduling jobs to minimize expected makespan on two parallel machines when the job running-time distribution has a monotone hazard rate. But no such policy appears to be known in general. We investigate the general problem by adopting two-point running-time distributions, the simplest discrete distributions not having monotone hazard rates. We derive a policy that gives an explicit, compact solution to this problem and prove its optimality. We also comment briefly on first-order extensions of the model, but each of these seems to be markedly more difficult to analyze.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 1 , January 1997 , pp. 95 - 105
Copyright
Copyright © Cambridge University Press 1997

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