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Optimal Scheduling of Multiclass Stochastic Systems

Published online by Cambridge University Press:  27 July 2009

Rhonda Righter
Rhonda Righter
Affiliation:
Department of Decision and Information Sciences, Santa Clara University, Santa Clara, California 95053
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Abstract

We study the problem of scheduling multiclass parallel server queues where the cost for each job is a general class-dependent function of the job's completion time and a second random variable. We characterize the structure of the optimal policy under fairly general conditions on the random variables.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 2 , April 1996 , pp. 229 - 241
Copyright
Copyright © Cambridge University Press 1996

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References

1.Baccelli, F., Liu, Z., & Towsley, D. (1993). Extremal scheduling of parallel processing with and without real-time constraints. Journal of the Association of Computing Machinery 40: 1209–1237.CrossRefGoogle Scholar
2.Chang, C.-S. & Yao, D.D. (1993). Rearrangement, majorization and stochastic scheduling. Mathematics of Operations Research 18: 658–684.CrossRefGoogle Scholar
3.Daley, D.J. (1987). Certain optimality properties of the first come first served discipline for G/G/s queues. Stochastic Processes and Their Applications 25: 301–308.CrossRefGoogle Scholar
4.Forst, F.G. (1993). Stochastic sequencing on one machine with earliness and tardiness penalties. Probability in the Engineering and Informational Sciences 7: 291–300.CrossRefGoogle Scholar
5.Foss, S.G. (1980). Approximation of multichannel queueing systems. Siberian Mathematics Journal 21: 851–857.CrossRefGoogle Scholar
6.Foss, S.G. (1981). Comparison of servicing strategies in multichannel queueing systems. Siberian Mathematics Journal 22: 142–147.CrossRefGoogle Scholar
7.Hirayama, T. & Kijima, M. (1989). An extremal property of FIFO discipline in G/IFR/I queues. Advances in Applied Probability 21: 481–484.CrossRefGoogle Scholar
8.Huang, C.-C. & Weiss, G. (1992). Scheduling jobs with stochastic processing times and due dates to minimize total tardiness. Preprint.Google Scholar
9.Kingman, J.F.C. (1970). Inequalities in the theory of queues. Journal of the Royal Statistical Society B 32: 102–110.Google Scholar
10.Liu, Z. & Righter, R. (1995). Optimal scheduling on parallel processors with precedence constraints. Preprint.Google Scholar
11.Liu, Z. & Towsley, D. (1994). Effects of service disciplines in G/G/s queueing systems. Annals of Operations Research 48 (Special Issue on Queueing Networks) (to appear).CrossRefGoogle Scholar
12.Liu, Z. & Towsley, D. (1994). Stochastic scheduling in in-forest networks. Advances in Applied Probability 26: 222–241.CrossRefGoogle Scholar
13.Marshall, A.W. & Olkin, I. (1979). Inequalities: Theory of majorization and its application. New York: Academic Press.Google Scholar
14.Pandelis, D.G. & Teneketzis, D. (1994). Optimal stochastic dynamic scheduling in multi-class queues with tardiness and/or earliness penalties. Probability in the Engineering and Informational Sciences 8: 491–509.CrossRefGoogle Scholar
15.Ross, S.M. (1983). Stochastic processes. New York: J. Wiley & Sons.Google Scholar
16.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
17.Towsley, D. & Baccelli, F. (1991). Comparisons of service disciplines in a tandem queueing network with real time constraints. Operations Research Letters 10: 49–55.CrossRefGoogle Scholar
18.Towsley, D. & Panwar, S.S. (1991). Optimality of the stochastic earliest deadline policy for the G/M/c queue serving customers with deadlines. COINS Technical Report 91–61.Google Scholar
19.Vasicek, O.A. (1997). An inequality for the variance of waiting time under a general queueing discipline. Operations Research 25: 879–884.CrossRefGoogle Scholar
20.Wolff, R.W. (1977). An upper bound for multi-channel queues. Journal of Applied Probability 14: 884–888.CrossRefGoogle Scholar
21.Wolff, R.W. (1987). Upper bounds on work in system for multichannel queues. Journal of Applied Probability 24: 547–551.CrossRefGoogle Scholar