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Scheduling two classes of exponential jobs on parallel processors: structural results and worst-case analysis

Published online by Cambridge University Press:  01 July 2016

Cheng-Shang Chang,
Randolph Nelson and
Michael Pinedo
Cheng-Shang Chang*
Affiliation:
IBM Research Division
Randolph Nelson*
Affiliation:
IBM Research Division
Michael Pinedo*
Affiliation:
Columbia University
*
∗Postal address: IBM Research Division, T. J. Watson Research Center, P.O. Box 704, Yorktown Heights, NY 10598, USA.
∗Postal address: IBM Research Division, T. J. Watson Research Center, P.O. Box 704, Yorktown Heights, NY 10598, USA.
∗∗Postal address: Department of Industrial Engineering and Operations Research, Columbia University, NY 10027, USA.
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Abstract

In this paper, we consider scheduling problems with m machines in parallel and two classes of job. We assume that all jobs are present at time 0 and there are no further arrivals. The service times of class 1 (2) jobs are independent and exponentially distributed with mean . Each class 1 (2) job incurs a cost c1 (c2) per unit of time until it leaves the system. The objective is to minimize the expected total cost, that is the expected weighted sum of completion times. We show that the optimal policy among all preemptive policies is of threshold type. Based on these structural results, we also show that the ratio of the expected weighted sum of completion times under the cµ-rule to that under the optimal rule is less than 1·71.

Keywords

THRESHOLD CONTROLcμ-RULE

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 4 , December 1991, pp. 925 - 944
Copyright
Copyright © Applied Probability Trust 1991 

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