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Policy Improvement and the Newton–Raphson Algorithm for Renewal Reward Processes

Published online by Cambridge University Press:  27 July 2009

J. M. McNamara
J. M. McNamara
Affiliation:
School of MathematicsUniversity of Bristol University Walk Bristol, BS8 1 TW
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Abstract

We consider a renewal reward process in continuous time. The supremum average reward, γ* for this process can be characterised as the unique root of a certain function. We show how one can apply the Newton–Raphson algorithm to obtain successive approximations to γ*, and show that the successive approximations so obtained are the same as those obtained by using the policy improvement technique.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 3 , July 1989 , pp. 393 - 396
Copyright
Copyright © Cambridge University Press 1989

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References

Bather, J. A. (1971). Free boundary problems in the design of control charts. Transactions 6th Prague conference on information theory, statistical decision functions, random processes. Dordrecht: Riedel, pp. 89–106.Google Scholar
Howard, R.A. (1960). Dynamic programming and Markov processes. Cambridge, MA. MIT Press.Google Scholar
Johns, M. & Miller, R.G. (1963). Average renewal loss rate. Annals of Mathematical Statistics 34: 396–401.CrossRefGoogle Scholar
McNamara, J.M. (1985). An optimal sequential policy for controlling a Markov renewal process. Journal of Applied Probability 22: 324–335.CrossRefGoogle Scholar
Whittle, P. & Komarova, N. (1988). Policy improvement and the Newton–Raphson algorithm. Probability in the Engineering and Informational Sciences 2: 249–255.CrossRefGoogle Scholar