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Preemptive Scheduling of Stochastic Jobs with a Two-Stage Processing Time Distribution on M + 1 Parallel Machines

Published online by Cambridge University Press:  27 July 2009

Chueng-Chiu Huang
Affiliation:
School of Industrial and System Engineering Georgia Institute of Technology Atlanta, Georgia 30332
Gideon Weiss
Affiliation:
School of Industrial and System Engineering Georgia Institute of Technology Atlanta, Georgia 30332

Abstract

We analyze the optimal preemptive sequencing of n jobs on M + 1 parallel identical machines to minimize expected total flowtime. The running times of the jobs are independent samples from the distribution Pr(X = H) = p, Pr(X = H + T) = 1 − p, where H, T are random variables of general distribution. Preemption of a job is allowed when H is completed. This problem does not have a simple optimal solution. We show that the scheme of shortest expected remaining processing time first (SERPT) is close to optimal in two senses. The expected flowtime under SERPT and under the optimal policy differ by no more than a constant, independent of the number of jobs, and the expected number of optimal decisions that are not according to SERPT is bounded by a constant, independent of the number of jobs.

Type
Articles
Copyright
Copyright © Cambridge University Press 1992

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References

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