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Optimal Multiserver Stochastic Scheduling of two Interconnected Priority Queues

Part of: Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Dimitrios G. Pandelis  and
Demosthenis Teneketzis
Dimitrios G. Pandelis
Affiliation:
University of Michigan
Demosthenis Teneketzis*
Affiliation:
University of Michigan
*
* Postal address for both authors: Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109-2122, USA.
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Abstract

A number of jobs on two interconnected queues are to be processed by m identical servers. The servers operate in parallel, so that every server can process any job. Jobs in queue i, i = 1, 2, incur an instantaneous holding cost Ci during the time they remain in the system. The service time for jobs in queue i, denoted by Xi, is a random variable with a general distribution. The interconnection process is independent of the service process. We establish sufficient conditions on the service times, the holding costs and the interconnection process under which the non-preemptive scheduling strategy that gives priority to queue 1 minimizes the total expected α -discounted cost. We call this strategy P1. We present counterexamples showing that if any of the sufficient conditions is not satisfied P1 may not be optimal, and that the optimal policy for the single-server problem is not necessarily optimal for the multiserver problem.

Keywords

MULTISERVER SCHEDULINGINTERCONNECTED QUEUESSTOCHASTIC ORDERING

MSC classification

Secondary: 90B35: Scheduling theory, deterministic
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 26 , Issue 1 , March 1994 , pp. 258 - 279
Copyright
Copyright © Applied Probability Trust 1994 

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References

Agrawal, R., Hegde, M. and Teneketzis, D. (1990) Multi-armed bandit problems with multiple plays and switching costs. Stoch. Stoch. Rep. 29, 437–459.Google Scholar
Bruno, J., Downey, P. and Frederickson, G. N. (1981) Sequencing tasks with exponential service times to minimize the expected flowtime or makespan. J. Assoc. Comp. Mach. 28, 100–113.Google Scholar
Chang, C. S., Nelson, R. and Pinedo, M. (1991) Scheduling two classes of exponential jobs on parallel processors: structural results and worst-case analysis. Adv. Appl. Prob. 23, 925–944.Google Scholar
Coffman, E. G., Flatto, L., Garey, M. R. and Weber, R. R. (1987) Minimizing expected makespans on uniform processor systems. Adv. Appl. Prob. 19, 177–201.Google Scholar
Glazebrook, K. D. (1979) Scheduling tasks with exponential service times on parallel processors. J. Appl. Prob. 16, 685–689.Google Scholar
Glazebrook, K. D. and Nash, P. (1976) On multi-server stochastic scheduling. J. R. Statist. Soc. B 38, 67–72.Google Scholar
Kampke, T. (1987) On the optimality of static priority policies in stochastic scheduling on parallel machines. J. Appl. Prob. 24, 430–448.Google Scholar
Kampke, T. (1989) Optimal scheduling of jobs with exponential service times on identical parallel processors. Operat. Res. 37, 126–133.Google Scholar
Lehtonen, T. (1988) Scheduling jobs with exponential processing times on parallel machines. J. Appl. Prob. 25, 752–762.Google Scholar
Ross, S. (1983a) Introduction to Stochastic Dynamic Programming. Academic Press, New York.Google Scholar
Ross, S. (1983b) Stochastic Processes. Wiley, 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. (1980) Optimal Organization of Multi-server Systems. Ph.D. Thesis, University of Cambridge.Google 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.Google Scholar
Weber, R. R. and Weiss, G. (1990) On an index policy for restless bandits. J. Appl. Prob. 27, 637–648.Google Scholar
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.CrossRefGoogle Scholar
Weiss, G. (1982) Multiserver stochastic scheduling. In Deterministic and Stochastic Scheduling, ed. Dempster, M. A. and Lenstra, J. K., pp. 157–179. Kluwer, Dordrecht.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Whittle, P. (1988) Restless bandits: activity allocation in a changing world. In A Celebration of Applied Probability, ed. Gani, J., J. Appl. Prob. 25A, 287–298.Google Scholar
Xu, S. H., Mirchandani, P. B., Kumar, S. P. R. and Weber, R. R. (1990) Stochastic dispatching of multi-priority jobs to heterogeneous processors. J. Appl. Prob. 27, 852–861.CrossRefGoogle Scholar