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Scheduling Independent Tasks to Minimize the Makespan on Identical Machines

Published online by Cambridge University Press:  27 July 2009

John Bruno ,
Edward G. Coffman Jr  and
Peter Downey
John Bruno
Affiliation:
Department of Computer Science, University of California, Santa Barbara, California 93106
Edward G. Coffman Jr
Affiliation:
AT&T Bell Laboratories, 600 Mountain Avenue, Murray Hill, New Jersey 07974
Peter Downey
Affiliation:
Department of Computer Science, University of Arizona, Tucson, Arizona 85721
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Abstract

In this paper we consider scheduling n tasks on m parallel machines where the task processing times are i.i.d. random variables with a common distribution function F. Scheduling is done by an a priori assignment of tasks to machines. We show that if the distribution function F is a Pólya frequency function of order 2 (decreasing reverse hazard rate) then the assignment that attempts to place an equal number of tasks on each machine achieves the stochastically smallest makespan among all assignments. The condition embraces many important distributions, such as the gamma and truncated normal distributions. Assuming that the task processing times have a common density that is a Pólya frequency function of order 2 (increasing likelihood ratio), then we find that flatter schedules have stochastically smaller makespans in the sense of the “joint” likelihood ratio.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 3 , July 1995 , pp. 447 - 456
Copyright
Copyright © Cambridge University Press 1995

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