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Optimal stochastic scheduling of forest networks with switching penalties

  • Mark P. Van Oyen (a1) and Demosthenis Teneketzis (a1)

Abstract

We present structural properties of optimal policies for the problem of scheduling a single server in a forest network of N queues (without arrivals) subject to switching penalties. In addition to linear holding costs, we impose either lump sum switching costs or batch set-up delays which are incurred at each instant the server processes a job in a queue different from the previous one. We use reward rate notions to unearth conditions on the holding costs and service distributions for which an exhaustive policy is optimal. For the case of two nodes connected probabilistically in tandem, we explicitly define an optimal policy under similar conditions.

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* Postal address: Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109-2122, USA.

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This work was supported in part by a Department of Electrical Engineering and Computer Science Graduate Fellowship and by NSF grant No. NCR-9204419.

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References

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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, 899906.
Agrawal, R., Hegde, M., and Teneketzis, D. (1990) Multi-armed bandit problems with multiple plays and switching cost. Stoch. Stoch. Rep. 29, 437459.
Browne, S. and Yechiali, U. (1989) Dynamic priority rules for cyclic-type queues. Adv. Appl. Prob. 21, 432450.
Bruno, J. and Downey, P. (1978) Complexity of task sequencing with deadlines, set-up times and changeover costs. SIAM J. Comput. 7, 393404.
Dempster, M. A. H., Lenstra, J. K., and Rinnooy Kan, A. M. G. (1982) Deterministic and Stochastic Scheduling. Reidel, Dordrecht.
Foss, S. G. (1984) Queues with customers of several types. In Advances in Probability Theory: Limit Theorems, and Related Problems, ed. Borovkov, A. A., pp. 348377. Springer-Verlag, New York.
Gittins, J. C. (1979) Bandit processes and dynamic allocation indices. J. R. Statist. Soc. B 41, 147177.
Gittins, J. C. (1989) Multi-armed Bandit Allocation Indices. Wiley, New York.
Gittins, J. C. and Jones, D. M. (1974) A dynamic allocation index for the sequential design of experiments. Read at the 1972 European Meeting of Statisticians, Budapest. In Progress in Statistics ed. Gani, J. et al., pp. 241266. North-Holland, Amsterdam.
Glazebrook, K. D. (1980) On stochastic scheduling with precedence relations and switching cost. J. Appl. Prob. 17, 10161024.
Glazebrook, K. D. and Gittins, J. C. (1981) On single-machine scheduling with precedence relations and linear or discounted costs. Operat. Res. 29, 161173.
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.
Harrison, J. M. (1975) Dynamic scheduling of a multi-class queue: discount optimality. Operat. Res. 23, 270282.
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, 399420.
Jo, K. Y. (1987) Decomposition approximation of queueing-network control models with tree structures. Ann. Operat. Res. 8, 117132.
Klimov, G. P. (1974) Time sharing service systems I. Theory Prob. Appl. 19, 532551.
Klimov, G. P. (1978) Time sharing service systems II. Theory Prob. Appl. 23, 314321.
Lai, T. L. and Ying, Z. (1988) Open bandit processes and optimal scheduling of queueing networks. Adv. Appl. Prob. 20, 447472.
Liu, Z., Nain, P., and Towsley, D. (1992) On optimal polling policies. QUESTA 11, 5984.
Magnanti, T. L. and Vachani, R. (1990) A strong cutting plane algorithm for production scheduling with changeover costs. Operat. Res. 38, 456473.
Monma, C. L. and Potts, C. N. (1989) On the complexity of scheduling with batch set up times. Operat. Res. 37, 798804.
Nain, P. (1989) Interchange arguments for classical scheduling problems in queues. Systems Control Lett. 12, 177184.
Nain, P., Tsoucas, P., and Walrand, J. (1989) Interchange arguments in stochastic scheduling. J. Appl. Prob. 27, 815826.
Perkins, J. R. and Kumar, P. R. (1989) Stable distributed real-time scheduling of flexible manufacturing/assembly/disassembly systems. IEEE Trans. Autom. Control 34, 139148.
Rajan, R. and Agrawal, R. (1991) Stochastic dominance in homogeneous queueing systems with switchover costs. Preprint.
Ross, S. (1983) Introduction to Stochastic Dynamic Programming. Academic Press, New York.
Santos, C. and Magazine, M. (1985) Batching in single operation manufacturing systems. Operat. Res. Lett. 4, 99103.
Van Oyen, M. P. (1992) Optimal Stochastic Scheduling of Queueing Networks: Switching Costs and Partial Information. Ph.D. Thesis, University of Michigan.
Van Oyen, M. P., Pandelis, D., and Teneketzis, D. (1992) Optimality of index policies for stochastic scheduling with switching penalties. J. Appl. Prob. 29, 957966.
Varaiya, P., Walrand, J., and Buyukkoc, C. (1985) Extensions of the multi-armed bandit problem. IEEE Trans. Autom. Control 30, 426439.
Walrand, J. (1988) An Introduction to Queueing Networks. Prentice-Hall, Englewood Cliffs, NJ.
Weber, R. R. and Weiss, G. (1990) On an index policy for restless bandits. J. Appl. Prob. 27, 637648.
Whittle, P. (1988) Restless bandits: activity allocation in a changing world. In A Celebration of Applied Probability, ed. Gani, J., J. Appl. Prob. 25A, 287298.

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Optimal stochastic scheduling of forest networks with switching penalties

  • Mark P. Van Oyen (a1) and Demosthenis Teneketzis (a1)

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