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Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime

Published online by Cambridge University Press:  14 July 2016

R. R. Weber ,
P. Varaiya  and
J. Walrand
R. R. Weber*
Affiliation:
University of Cambridge
P. Varaiya*
Affiliation:
University of California, Berkeley
J. Walrand*
Affiliation:
University of California, Berkeley
*
∗Postal address: Department of Engineering, Control and Management Systems Division, Mill Lane, Cambridge, CB2 1RX, UK.
∗∗Postal address: Dept. of Electrical Engineering and Computer Sciences and Electronic Research Laboratory, University of California, Berkeley, CA 94720, USA.
∗∗Postal address: Dept. of Electrical Engineering and Computer Sciences and Electronic Research Laboratory, University of California, Berkeley, CA 94720, USA.
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Abstract

A number of jobs are to be processed using a number of identical machines which operate in parallel. The processing times of the jobs are stochastic, but have known distributions which are stochastically ordered. A reward r(t) is acquired when a job is completed at time t. The function r(t) is assumed to be convex and decreasing in t. It is shown that within the class of non-preemptive scheduling strategies the strategy SEPT maximizes the expected total reward. This strategy is one which whenever a machine becomes available starts processing the remaining job with the shortest expected processing time. In particular, for r(t) = – t, this strategy minimizes the expected flowtime.

Keywords

STOCHASTIC SCHEDULING
Type
Short Communications
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 841 - 847
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

Research supported by the Office of Naval Research Contract N00014-80-C-0507.

References

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