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Optimal policies for scheduling repairs and allocating heterogeneous servers

Part of: Computer system organization Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Rhonda Righter
Rhonda Righter*
Affiliation:
Santa Clara University
*
∗Postal address: Department of Decision and Information Sciences, Santa Clara University, Santa Clara, CA 95053, USA.
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Abstract

We consider the machine repairman, or resource utilization, model in which there is a finite source of jobs with non-identically distributed exponential return times and a single server with job dependent service times. We also consider a related problem of scheduling jobs at heterogeneous servers. We construct a coupling framework that provides a simple unified proof that strengthens many of the results in the literature, and generalizes easily to prove several new results.

Keywords

MACHINE REPAIRMAN PROBLEMINVARIANCE RESULTSHETEROGENEOUS PROCESSORSSCHEDULING

MSC classification

Primary: 90B35: Scheduling theory, deterministic
Secondary: 68M20: Performance evaluation; queueing; scheduling
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 2 , September 1996 , pp. 536 - 547
Copyright
Copyright © Applied Probability Trust 1996 

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References

Buyukkoc, C, Varaiya, P. and Walrand, J. (1985) The cµ rule revisited. Adv. Appl. Prob. 17, 237–238.CrossRefGoogle Scholar
Chakka, R. and Mitrani, I. (1994) Heterogeneous multiprocessor systems with breakdowns: Performance and optimal repair strategies. Preprint. Google Scholar
Cooper, R. B. and Palakurthi, S. (1989) Heterogeneous-server loss systems with ordered entry: an anomaly. Operat. Res. Lett. 8, 347–349.CrossRefGoogle Scholar
Courcoubetis, C, Varaiya, P. and Walrand, J. (1982) Invariance in resource sharing problems. Proc. 21st IEEE Conf Dee. Cont. 861–863.Google Scholar
Courcoubetis, C., Varaiya, P. P. (1984) Serving process with least thinking time maximizes resource utilization. IEEE Trans. Aut. Cont. AC29, 1005–1008.CrossRefGoogle Scholar
Courcoubetis, C, Varaiya, P. and Walrand, J. (1984) Invariance in resource-sharing systems. J. Appl. Prob. 21, 777–785.Google Scholar
Derman, C, Lieberman, G. J. and Ross, S. M. (1980) On the optimal assignment of servers and a repairman. J. Appl. Prob. 17, 577–581.CrossRefGoogle Scholar
Frostig, E. (1993) Optimal policies for machine repairmen problems. J. Appl. Prob. 30, 703–715.Google Scholar
Horduk, A. and Koole, G. (1992) On the assignment of customers to parallel queues. Prob. Eng. Inf. Sci. 6, 495–512.Google Scholar
Kameda, H. (1982) A finite source queue with different customers. J. Assoc. Comp. Mach. 29, 478–491.Google Scholar
Kameda, H. (1984) Realizable performance vectors of a finite source queue. Operat. Res. 32, 1358–1367.Google Scholar
Katehakis, M. N. and Derman, C. (1984) Optimal repair allocation in a series system. Math. Operat. Res. 9, 615–623.CrossRefGoogle Scholar
Katehakis, M. N. and Melolidakis, C. (1992) A note on a problem of optimal repair of a series system. Preprint. Google Scholar
Koole, G. (1992) Stochastic Scheduling and Dynamic Programming. PhD thesis, Leiden University.Google Scholar
Nain, P., Tsoucas, P. and Walrand, J. (1989) Interchange arguments in stochastic scheduling. J. Appl. Prob. 27, 815–826.CrossRefGoogle Scholar
Nash, P. and Weber, R. R. (1982) Dominant strategies in stochastic allocation and scheduling problems. Deterministic and Stochastic Scheduling ed. Dempster, M. A. H. pp. 343–353. Dordrecht, Reidel.Google Scholar
Righter, R. (1988) Job scheduling to minimize expected weighted flowtime on uniform processors. Syst. Cont. Lett. 10, 211–216.Google Scholar
Righter, R. and Shanthikumar, J. G. (1989) Scheduling multiclass single server queueing systems to stochastically maximize the number of successful departures. Prob. Eng. Inf. Sci. 3, 323–333.Google Scholar
Righter, R. and Shanthikumar, J. G. (1992) Extremal properties of the FIFO discipline in queueing networks. J. Appl. Prob. 29, 867–978.Google Scholar
Seth, K. (1977) Optimal service policies, just after idle periods, in two-server heterogeneous queueing systems. Operat. Res. 25, 356–360.CrossRefGoogle Scholar
Shanthikumar, J. G. and Yao, D. (1987) Comparing ordered-entry queues with heterogeneous servers. QUESTA 2, 235–244.Google Scholar
Smith, D. R. (1978) Optimal repair of a series system. Operat. Res. 26, 653–662.Google Scholar
Sobel, M. J. (1982) The optimality of full service policies. Operat. Res. 30, 636–649.Google Scholar
Sobel, M. J. and Srivastava, C. (1991) Full-service policy optimality with heterogeneous servers. Preprint.Google Scholar
Yao, D. D. (1987) The arrangement of servers in an ordered-entry system. Operat. Res. 35, 759–763.CrossRefGoogle Scholar