Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-06-02T00:56:09.662Z Has data issue: false hasContentIssue false
  • English
  • Français

The optimality of LEPT in parallel machine scheduling

Part of: Computer system organization Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Cheng-Shang Chang  and
Rhonda Righter
Cheng-Shang Chang*
Affiliation:
IBM T. J. Watson Research Center
Rhonda Righter*
Affiliation:
Santa Clara University
*
∗ Postal address: IBM Research Division, T. J. Watson Research Center, P.O. Box 704, Yorktown Heights, NY 10598, USA.
∗∗ Postal address: Department of Decision and Information Sciences, Santa Clara University, Santa Clara, CA 95053, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider preemptive scheduling on parallel machines where the number of available machines may be an arbitrary, possibly random, function of time. Processing times of jobs are from a family of DLR (decreasing likelihood ratio) distributions, and jobs may arrive at random agreeable times. We give a constructive coupling proof to show that LEPT stochastically minimizes the makespan, and that it minimizes the expected cost when the cost function satisfies certain agreeability conditions.

Keywords

PARALLEL PROCESSORSMAKESPANLEPT RULECOUPLING

MSC classification

Primary: 90B35: Scheduling theory, deterministic
Secondary: 68M20: Performance evaluation; queueing; scheduling
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 3 , September 1994 , pp. 788 - 796
Copyright
Copyright © Applied Probability Trust 1994 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Bruno, J. and Downey, P. (1977) Sequencing tasks with exponential service times on two machines. Technical Report EECS, UC Santa Barbara.Google Scholar
[2] Bruno, J., Downey, P. and Frederickson, G. (1981) Sequencing tasks with exponential service times to minimize the expected flow time or makespan. J. Assoc. Comp. Mach. 28, 100–113.Google Scholar
[3] Chang, C.-S. (1992) A new ordering for stochastic majorization: theory and applications. Adv. Appl. Prob. 24, 604–634.Google Scholar
[4] Chang, C.-S., Chao, X. L., Pinedo, M. and Weber, R. R. (1992). On the optimality of LEPT and cµ rules for machines in parallel. J. Appl. Prob. 29, 667–681.Google Scholar
[5] Glazebrook, K. D. (1979) Scheduling tasks with exponential service times on parallel processors. J. Appl. Prob. 16, 685–689.CrossRefGoogle Scholar
[6] Glazebrook, K. D. and Nash, P. (1977) On multi-server stochastic scheduling. J. R. Statist. Soc. B38, 67–72.Google Scholar
[7] Hordijk, A. and Koole, G. (1991) Optimal policies in two stochastic scheduling problems with arrivals of customers. Preprint.Google Scholar
[8] Kämpke, T. (1987) On the optimality of static priority policies in stochastic scheduling on parallel machines. J. Appl. Prob. 24, 430–448.Google Scholar
[9] Kämpke, T. (1987) Necessary optimality conditions for priority policies in stochastic weighted flowtime scheduling problems. Adv. Appl. Prob. 19, 749–750.Google Scholar
[10] Kämpke, T. (1989) Optimal scheduling of jobs with exponential service times on identical parallel processors. Operat. Res. 37, 126–133.Google Scholar
[11] Nash, P. and Weber, R. R. (1982) Sequential open-loop scheduling strategies. Deterministic and Stochastic Scheduling, ed. Dempster, M. A. H., pp. 385–397. D. Reidel, Dordrecht.Google Scholar
[12] Pinedo, M. (1983) Stochastic scheduling with release dates and due dates. Operat. Res. 31, 559–572.Google Scholar
[13] Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
[14] Ross, S. M. (1983) Introduction to Stochastic Dynamic Programming. New York: Academic Press.Google Scholar
[15] 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.Google Scholar
[16] Weber, R. R. (1982) Scheduling jobs with stochastic processing requirements on parallel machines to minimize makespan or flowtime. J. Appl. Prob. 19, 167–182.Google Scholar
[17] Weiss, G. and Pinedo, M. (1980) Scheduling tasks with exponential service times on nonidentical processors to minimize various cost functions. J. Appl. Prob. 17, 187–202.CrossRefGoogle Scholar
[18] Weiss, G. (1982) Multiserver stochastic scheduling. Deterministic and Stochastic Scheduling, ed. Dempster, M. A. H., pp. 157–179, D. Reidel, Dordrecht.CrossRefGoogle Scholar