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On almost optimal priority rules for preemptive scheduling of stochastic jobs on parallel machines

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Gideon Weiss
Gideon Weiss*
Affiliation:
Georgia Tech
*
* Present address: Department of Statistics, The University of Haifa, Haifa 31905, Israel.
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Abstract

We consider scheduling a batch of jobs with stochastic processing times on single or parallel machines, with the objective of minimizing the expected holding costs. Preemption of jobs is allowed, and the holding costs of preempted jobs may depend on the stage of completion. We provide a new proof of the optimality of a Gittins priority rule for the single machine and use the same proof to show that the Gittins priority rule is nearly optimal for parallel machines.

Keywords

STOCHASTIC PROCESSING TIMESHOLDING COSTSGITTINS PRIORITY RULE

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B35: Scheduling theory, deterministic 90C40: Markov and semi-Markov decision processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 3 , September 1995 , pp. 821 - 839
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Research supported by NSF grants DDM-8914863 and DDM-9215233, and the fund for the promotion of research at the Technion.

References

[1] Bruno, J., Downey, P. and Frederickson, G. (1981) Sequencing tasks with exponential service times to minimize the expected flowtime or makespan. J. ACM 28, 100–113.CrossRefGoogle Scholar
[2] Chazan, D., Konheim, A. G. and Weiss, B. (1968) A note on time sharing. J. Combinatorial Theory 5, 344–369.CrossRefGoogle Scholar
[3] Coffman, E. G., Hofri, M. and Weiss, G. (1989) Scheduling stochastic jobs with a two point distribution on two parallel machines. Prob. Eng. Inf. Sci. 3, 89–116.CrossRefGoogle Scholar
[4] Gittins, J. (1979) Bandit processes and dynamic allocation indices. J. R. Statist. Soc. B 14, 148–167.Google Scholar
[5] Gittins, J. (1989). Bandit Processes and Dynamic Allocation Indices. Wiley, New York.Google Scholar
[6] Gittins, J. (1982) Forward induction and dynamic allocation indices. In Deterministic and Stochastic Scheduling, Dempster, M. A. H. et al. pp. 125–156. Reidel, Dordrecht.Google Scholar
[7] Huang, C. C. and Weiss, G. (1992) Preemptive scheduling of stochastic jobs with a two stage processing time distribution on M + 1 parallel machines. Prob. Eng. Inf. Sci. 6, 171–191.Google Scholar
[8] Kawaguchi, T. and Kyan, S. (1986) Worst case bound for an LRF schedule for the mean weighted flowtime problem. SIAM J. Computing 15, 1119–1129.CrossRefGoogle Scholar
[9] Kleinrock, L. (1976) Queueing Systems, Vol. II: Computer Applications. Wiley, New York.Google Scholar
[10] Lawler, E. L., Lenstra, J. K., Rinnooy-Kan, A. H. G. and Shmoys, D. B. (1989) Sequencing and Scheduling: Algorithms and Complexity. Technical Report BS-R8909, Center for Mathematics and Computer Science, Amsterdam, The Netherlands.Google Scholar
[11] Lenstra, J. K., Rinnooy-Kan, A. H. G. and Brucker, P. (1977) Complexity of machine scheduling problems. Ann. Discrete Math. 1, 343–362.CrossRefGoogle Scholar
[12] Mcnaughton, R. (1959) Scheduling with deadlines and loss functions. Management Sci. 6, 1–12.CrossRefGoogle Scholar
[13] Pinedo, M. and Weiss, G. (1979) Scheduling of stochastic tasks on two parallel processors. Naval Res. Logist. Quart. 26, 527–535.Google Scholar
[14] Smith, W. E. (1956) Various optimizers for single stage production. Naval Res. Logist. Quart. 3, 59–66.CrossRefGoogle Scholar
[15] Spaccamela, A. M., Rhee, W. S., Stoughie, L. and Van De Geer, S. (1992) Probabilistic analysis of the minimum weighted flowtime problem. Operat. Res. Lett. 11, 67–71.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] Weber, R. R., Varaiya, P. and Walrand, J. (1986) Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime. J. Appl. Prob. 23, 841–847.Google Scholar
[18] Weiss, G. (1990) Approximation results in parallel machines stochastic scheduling. Ann. Operat. Res. Special Volume on Production Planning and Scheduling, ed. Queyranne, M., 26, 195–242.Google Scholar
[19] Weiss, G. (1992) Turnpike optimality of Smith's rule in parallel machines stochastic scheduling. Math. Operat. Res. 17, 255–270.CrossRefGoogle Scholar
[20] Weiss, G. and Pinedo, M. (1980) Scheduling tasks with exponential service times on non-identical processors to minimize various cost functions. J. Appl. Prob. 17, 187–202.Google Scholar
[21] Wolff, R. N. (1989) Stochastic Modeling and the Theory of Queues. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar