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Optimality of index policies for stochastic scheduling with switching penalties

Part of: Stochastic systems and control Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Mark P. Van Oyen ,
Dimitrios G. Pandelis  and
Demosthenis Teneketzis
Mark P. Van Oyen*
Affiliation:
University of Michigan
Dimitrios G. Pandelis*
Affiliation:
University of Michigan
Demosthenis Teneketzis*
Affiliation:
University of Michigan
*
∗ Postal address for all authors: Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109–2122, USA.
∗ Postal address for all authors: Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109–2122, USA.
∗ Postal address for all authors: Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109–2122, USA.
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Abstract

We investigate the impact of switching penalties on the nature of optimal scheduling policies for systems of parallel queues without arrivals. We study two types of switching penalties incurred when switching between queues: lump sum costs and time delays. Under the assumption that the service periods of jobs in a given queue possess the same distribution, we derive an index rule that defines an optimal policy. For switching penalties that depend on the particular nodes involved in a switch, we show that although an index rule is not optimal in general, there is an exhaustive service policy that is optimal.

Keywords

OPTIMAL CONTROL OF QUEUESSWITCHING COSTSWITCHING TIMEMULTI-ARMED BANDITSCOUPLING

MSC classification

Primary: 93E20: Optimal stochastic control
Secondary: 90B35: Scheduling theory, deterministic
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 4 , December 1992 , pp. 957 - 966
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

The work of Mark Van Oyen was supported by a University of Michigan Regents Fellowship.

References

[1] Agrawal, R., Hegde, M. and Teneketzis, D. (1988) Asymptotically efficient adaptive allocation rules for the multi-armed bandit problem with switching cost. IEEE Trans. Autom. Control 33, 899–906.Google Scholar
[2] Agrawal, R., Hegde, M. and Teneketzis, D. (1990) Multi-armed bandit problems with multiple plays and switching cost. Stoch. Stoch. Rep. 29, 437–459.Google Scholar
[3] Baker, J. E. and Rubin, I. (1987) Polling with a general-service order table. IEEE Trans. Comm. 35, 283–288.Google Scholar
[4] Baras, J. S., Ma, D.-J. and Makowski, A. M. (1985) K competing queues with geometric service requirements and linear costs: the µc-rule is always optimal. Systems Control Lett. 6, 173–180.Google Scholar
[5] Browne, S. and Yechiali, U. (1989) Dynamic priority rules for cyclic-type queues. Adv. Appl. Prob. 21, 432–450.Google Scholar
[6] Buyukkoc, C., Varaiya, P. and Walrand, J. (1985) The cµ-rule revisited, Adv. Appl. Prob. 17, 237–238.Google Scholar
[7] Dempster, M. A. H., Lenstra, J. K. and Rinnooy Kan, A. M. G. (1982) Deterministic and Stochastic Scheduling. D. Reidel, Dordrecht.Google Scholar
[8] Eisenberg, M. (1972) Queues with periodic service and changeover time. Operat. Res. 20, 440–451.Google Scholar
[9] Ferguson, M. J. and Aminetzah, Y. J. (1985) Exact results for nonsymmetric token ring systems. IEEE Trans. Comm. 33, 223–231.Google Scholar
[10] Gittins, J. C. (1979) Bandit processes and dynamic allocation indices. J. R. Statist. Soc. B41, 148–177.Google Scholar
[11] Gittins, J. C. (1989) Multi-armed Bandit Allocation Indices. Wiley, New York.Google Scholar
[12] Gittins, J. C. and Jones, D. M. (1974) A dynamic allocation index for the sequential design of experiments. Progress in Statistics, ed. Gani, J. et al., pp. 241–266. North-Holland, Amsterdam.Google Scholar
[13] Glazebrook, K. D. (1980) On stochastic scheduling with precedence relations and switching cost. J. Appl. Prob. 17, 1016–1024.Google Scholar
[14] Glazebrook, K. D. and Gittins, J. C. (1981) On single-machine scheduling with precedence relations and linear or discounted costs. Operat. Res. 29, 161–173.Google Scholar
[15] Gupta, D., Gerchak, Y. and Buzacott, J. A. (1987) On optimal priority rules for queues with switchover costs. Preprint, Dept. of Management Sciences, University of Waterloo.Google Scholar
[16] Harrison, J. M. (1975) Dynamic scheduling of a multi-class queue: discount optimality. Operat. Res. 23, 270–282.Google Scholar
[17] Hofri, M. and Ross, K. W. (1987) On the optimal control of two queues with server setup times and its analysis. SIAM J. Comput. 16, 399–420.Google Scholar
[18] Klimov, G. P. (1974) Time sharing service systems I. Theory Prob. Appl. 19, 532–551.Google Scholar
[19] Klimov, G. P. (1978) Time sharing service systems II. Theory Prob. Appl. 23, 314–321.Google Scholar
[20] Lai, T. L. and Ying, Z. (1988) Open bandit processes and optimal scheduling of queueing networks. Adv. Appl. Prob. 20, 447–472.Google Scholar
[21] Monma, C. L. and Potts, C. N. (1989) On the complexity of scheduling with batch setup times. Operat. Res. 37, 798–804.Google Scholar
[22] Murata, M. and Takagi, H. (1986) Mean waiting times in nonpreemptive priority M/G/1 queues with server switchover time. In Teletraffic Analysis and Computer Performance Evaluation, ed. Boxma, O. J., Cohen, J. W., and Tijms, H. C., pp. 395–407, Elsevier, Amsterdam.Google Scholar
[23] Nain, P. (1989) Interchange arguments for classical scheduling problems in queues. Sys. Control Lett. 12, 177–184.Google Scholar
[24] Nain, P., Tsoucas, P. and Walrand, J. (1989) Interchange arguments in stochastic scheduling. J. Appl. Prob. 27, 815–826.Google Scholar
[25] Ross, S. (1983) Introduction to Stochastic Dynamic Programming. Academic Press, New York.Google Scholar
[26] Sidney, J. B. (1975) Decomposition algorithms for single-machine sequencing with precedence relations and deferral costs. Operat. Res. 23, 283–298.Google Scholar
[27] Sykes, J. S. (1970) Simplified analysis of an alternating priority queueing model with set up times. Operat. Res. 18, 1182–1192.Google Scholar
[28] Takagi, H. (1986) Analysis of Polling Systems. MIT Press, Cambridge, MA.Google Scholar
[29] Varaiya, P., Walrand, J. and Buyukkoc, C. (1985) Extensions of the multi-armed bandit problem. IEEE Trans. Autom. Control 30, 426–439.Google Scholar
[30] Walrand, J. (1988) An Introduction to Queueing Networks. Prentice Hall, Englewood Cliffs, NJ.Google Scholar
[31] Whittle, P. (1980) Multi-armed bandits and the Gittins index. J. R. Statist. Soc. B42, 143–149.Google Scholar
[32] Whittle, P. (1981) Arm-acquiring bandits. Ann. Prob. 9, 284–292.Google Scholar