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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
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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References

Baras, J. S., Dorsey, A. J. and Makowski, A. M. (1985) Two competing queues with linear costs and geometric service requirements: the µc-rule is often optimal. Adv. Appl. Prob. 17, 186–209.CrossRefGoogle Scholar
Buyukkoc, C., Varaiya, P. and Walrand, J. (1985) The cp rule revisited. Adv. Appl. Prob. 17, 237–238.CrossRefGoogle Scholar
Chang, C. S., Chao, X. L., Pinedo, M. and Weber, R. R. (1989) On the optimality of LEPT and cµ-rules for machines in parallel. J. Appl. Prob. 29(3).Google Scholar
Frederickson, G. N., Bruno, J. and Downey, P. (1981) Sequencing tasks with exponential service times to minimize the expected flow time or makespan. J. Assoc. Comput. Mach. 28, 100–113.Google Scholar
Kampke, T. (1987) On the optimality of static priority policies in stochastic scheduling on parallel machines. J. Appl. Prob. 24, 430–448.CrossRefGoogle Scholar
Kampke, T. (1989) Optimal scheduling of jobs with exponential service times on identical parallel processors. Operat. Res. 37, 126–133.CrossRefGoogle Scholar
Kawaguchi, T. and Kyan, S. (1986) Worst case of an LRF schedule for the mean weighted flow-time problem. SIAM J. Comput. 15, 1119–1129.CrossRefGoogle Scholar
Pinedo, M. (1983) Stochastic scheduling with release dates and due dates. Operat. Res. 31, 559–572.CrossRefGoogle Scholar
Ross, S. (1983) Introduction to Stochastic Dynamic Programming. Academic Press, New York.Google Scholar
Van Der Heyden, L. (1981) Scheduling jobs with exponential processing and arrival times on identical processors so as to minimize the expected makespan. Math. Operat. Res. 6, 305–312.CrossRefGoogle Scholar
Weber, R. R. (1982) Scheduling jobs with stochastic processing requirements on parallel machines to minimize makespan or flowtime. J. Appl. Prob. 19, 167–182.CrossRefGoogle Scholar
Weber, R. R. (1983) Scheduling stochastic jobs on parallel machines to minimize makespan or flowtime. In Proc. ORSA/TIMS Special Interest Meeting: Applied Probability–Computer Science, the Interface , ed. Disney, R., 327–338.Google Scholar
Weiss, G. (1982) Multiserver stochastic scheduling deterministic and stochastic scheduling. In Deterministic and Stochastic Scheduling , ed. Dempster, M. A. and Lenstra, J. K., pp. 157–179. Kluwer, Dordrecht.CrossRefGoogle Scholar