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Scheduling Multiclass Single Server Queueing Systems to Stochastically Maximize the Number of Successful Departures

Published online by Cambridge University Press:  27 July 2009

Rhonda Righter  and
J. George Shanthikumar
Rhonda Righter
Affiliation:
Department of Decision and In formation SciencesSanta Clara University Santa Clara, California 95053
J. George Shanthikumar
Affiliation:
School of Business AdministrationUniversity of California Berkeley, California 94720
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Abstract

We wish to schedule heterogeneous jobs on a single machine to stochastically maximize the number of jobs that are correctly completed before a random due date. Jobs arrive according to an arbitrary arrival process. Job i has probability ci, that it will be correctly completed, and a processing time that has distribution Fi. Jobs that are incorrectly processed cannot be reprocessed, and jobs that are not completed by the due date are assumed to be incorrectly processed. The machine is subject to breakdowns and repairs. Both premptive and non-preemptive policies are considered. We give conditions under which simple index rules are optimal. This generalizes and extends the results of Derman et al. [3], Pinedo and Rammouz [9], and Buyukkoc et al. [2], who derive policies that maximize the expected number of jobs correctly completed by the due date. We also consider policies that stochastically minimize the number of correct job completions. For single class systems, we give conditions under which FCFS (first-come-first-served) or LAST (least-attained-service-time) service disciplines stochastically minimize or maximize the number in the system.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 3 , July 1989 , pp. 323 - 333
Copyright
Copyright © Cambridge University Press 1989

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References

references

Bhattacharya, P.P. & Ephremides, A. (1988). Optimal scheduling of the transmission of messages with strict deadlines. Preprint.Google Scholar
Buyukkoc, C., Varaiya, P., & Walrand, J. (1985). The cμ rule revisited. Advances in Applied Probability 17: 237–238.CrossRefGoogle Scholar
Derman, C., Lieberman, G.J., & Ross, S.M. (1978). A renewal decision problem. Management Science 24: 554–561.CrossRefGoogle Scholar
Glazebrook, K.D. & Gittins, J.C. (1981). On single-machine scheduling with precedence relations and linear or discounted costs. Operations Research 29: 161–173.CrossRefGoogle Scholar
Glazebrook, K.D. (1984). Scheduling stochastic jobs on a single machine subject to breakdowns. Naval Research Logistics Quarterly 31: 251–264.CrossRefGoogle Scholar
Harrison, J.M. (1975). Dynamic scheduling of a multiclass queue: discount optimality. Operations Research 23: 270–282.CrossRefGoogle Scholar
Hirayama, T., Kijima, M., & Nishimura, S. (1988). Further results for dynamic scheduling of multiclass G/G/1 queues. Research Reports on Information Sciences B-202. Tokyo Institute of Technology.Google Scholar
Hirayama, T. & Kijima, M. (1988). An extremal property of FIFO discipline in G/G/1 queues. Research Reports on Information Sciences B-208. Tokyo Institute of Technology.Google Scholar
Pinedo, M. & Rammouz, E. (1988). A note on stochastic scheduling on a single machine subject to breakdown and repair. Probability in the Engineering and Informational Sciences 2: 41–49.CrossRefGoogle Scholar
Ross, S.M. (1983). Introduction to stochastic dynamic programming. New York: Academic Press.Google Scholar
Shanthikumar, J. G. & Sumita, U. (1987). Convex ordering of sojourn times in single-server queues: Extremal properties of FIFO and LIFO service disciplines. Journal of Applied Probability 24: 737–748.CrossRefGoogle Scholar
Wolff, R.W. (1970). Work-conserving priorities. Journal of Applied Probability 7: 327–337.CrossRefGoogle Scholar