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Scheduling Stochastic Jobs with a Two-Point Distribution on Two Parallel Machines

Published online by Cambridge University Press:  27 July 2009

E.G. Coffman Jr ,
M. Hofri  and
G. Weiss
E.G. Coffman Jr
Affiliation:
AT&T Bell Laboratories Murray Hill, New Jersey07974
M. Hofri
Affiliation:
Computer Science Department The Technion Haifa, Israel
G. Weiss
Affiliation:
School of ISyE Georgia Institute of Technology Atlanta, Georgia 30320
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Abstract

We analyze the optimal preemptive sequencing of n jobs on two machines to minimize expected total flow time. The running times of the jobs are independent samples from the distribution Pr(X = 1) = p, Pr(X = κ + 1) = 1 − p. We verify that the shortest-expected-remaining-processing-time (SERPT) policy, which is optimal for independent and identically distributed (i.i.d.) running times with a monotone hazard-rate distribution, is not optimal for this distribution. However, we prove that if p ≥ 1/κ, then the number of decisions where SERPT and an optimal policy disagree is bounded by a constant independent of n. For p < 1/k, we prove that the expected number of such decisions has a similar bound. In addition, bounds on the expected increase in flow times under SERPT are derived; these bounds are also independent of n.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 1 , January 1989 , pp. 89 - 116
Copyright
Copyright © Cambridge University Press 1989

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