Abstract
The Approximating Sequence Method for computation of average cost optimal stationary policies in denumerahle state Markov decision chains, introduced in Sennott (1994), is reviewed. New methods for verifying the assumptions are given. These are useful for models with multidimensional state spaces that satisfy certain mild structural properties. The results are applied to four problems in the optimal routing of packets to parallel queues. Numerical results are given for one of the models.
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Arapostathis A, Borkar V, Fernandez-Gaucherand E, Ghosh M, Marcus S (1993) Discrete-time controlled Markov processes with average cost criterion: A survey. SIAM J Control Optim 31:282–344
Bertsekas D (1987) Dynamic programming. Prentice-Hall, Englewood Cliffs New Jersey
Ephremides A, Varaiya P, Walrand J (1980) A simple dynamic routing problem. IEEE Trans Auto Control 25:690–693
Hajek B (1984) Optimal control of two interacting service stations. IEEE Trans Auto Control 29:491–499
Puterman M (1994) Markov decision processes. John Wiley & Sons, New York
Rosberg Z (1986) Deterministic routing to buffered channels. IEEE Trans Comm 34:504–507
Sennott L (1989) Average cost optimal stationary policies in infinite state Markov decision processes with unbounded costs. Oper Res 37:626–633
Sennott L (1994) The computation of average optimal policies in denumerable state Markov decision chains. To appear, Adv Appl Prob
Sennott L (1995) Another set of conditions for average optimality in Markov control processes. Sys Control Lett 24:147–151
Stidham S Jr, Weber R (1993) A survey of Markov decision models for control of networks of queues. Queueing Sys 13:291–314
Winston W (1977) Optimality of the shortest line discipline. J Appl Prob 14:181–189
Weber R (1978) On the optimal assignment of customers to parallel servers. J. Appl Prob 15:406–413
Xu S, Righter R, Shanthikumar G (1992) Optimal dynamic assignment of customers to heterogeneous servers in parallel. Oper Res 40:1126–1138
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Sennott, L.I. On computing average cost optimal policies with application to routing to parallel queues. Mathematical Methods of Operations Research 45, 45–62 (1997). https://doi.org/10.1007/BF01194247
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DOI: https://doi.org/10.1007/BF01194247