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Optimal stationary policies for denumerable Markov chains in continuous time

Published online by Cambridge University Press:  01 July 2016

John Bather
John Bather*
Affiliation:
University of Sussex
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Abstract

This paper is concerned with the problem of selecting the transition intensities for a Markov chain in continuous time so as to minimise the long-term average cost. Sufficient conditions are established for an optimal stationary policy using unbounded solutions of the optimality equation. This is a development of recent work on Markovian decision processes in discrete time. The theory is illustrated by considering a simple birth and death process with controlled immigration.

Keywords

MARKOVIAN DECISION PROCESSMINIMUM AVERAGE COSTCONTINUOUS TIMEDYNAMIC PROGRAMMINGOPTIMALITY EQUATION
Type
Research Article
Information
Advances in Applied Probability , Volume 8 , Issue 1 , March 1976 , pp. 144 - 158
Copyright
Copyright © Applied Probability Trust 1976 

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References

[1] Bather, J. (1973) Optimal decision procedures for finite Markov chains. Adv. Appl. Prob. 5, 328–540, 541–553.CrossRefGoogle Scholar
[2] Derman, C. (1966) Denumerable state Markovian decision processes—average cost criterion. Ann. Math. Statist. 37, 1545–1554.Google Scholar
[3] Feller, W. (1966) An Introduction to Probability Theory and its Applications, Vol. II. Wiley, New York.Google Scholar
[4] Hordijk, A. (1974) Dynamic programming and Markov potential theory. Mathematical Centre Tracts. No. 51. Amsterdam.Google Scholar
[5] Howard, R. A. (1960) Dynamic Programming and Markov Processes. Wiley, New York.Google Scholar
[6] Miller, B. L. (1968) Finite state continuous time Markov decision processes with a finite planning horizon. SIAM J. Control 6, 266–280.Google Scholar
[7] Miller, B. L. (1968) Finite state continuous time Markov decision processes with an infinite planning horizon. J. Math. Anal. Appl. 22, 552–569.Google Scholar
[8] Robinson, D. R. (1976) Markov decision chains with unbounded costs and applications to the control of queues. Adv. Appl. Prob. 8, 159–176.Google Scholar
[9] Ross, S. M. (1970) Average cost semi-Markov decision processes. J. Appl. Prob. 7, 649–656.Google Scholar