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Scheduling Jobs with Stochastically Ordered Processing Times on Parallel Machines to Minimize Expected Flowtime

R. R. Weber, P. Varaiya and J. Walrand
Journal of Applied Probability
Vol. 23, No. 3 (Sep., 1986), pp. 841-847
DOI: 10.2307/3214023
Stable URL: http://www.jstor.org/stable/3214023
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Scheduling Jobs with Stochastically Ordered Processing Times on Parallel Machines to Minimize Expected Flowtime
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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.

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