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Optimal control of random walks, birth and death processes, and queues

Published online by Cambridge University Press:  01 July 2016

Richard Serfozo
Richard Serfozo*
Affiliation:
Bell Laboratories
*
∗Postal address: Bell Laboratories, Holmdel, NJ 07733, U.S.A.
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Abstract

This is a study of simple random walks, birth and death processes, and M/M/s queues that have transition probabilities and rates that are sequentially controlled at jump times of the processes. Each control action yields a one-step reward depending on the chosen probabilities or transition rates and the state of the process. The aim is to find control policies that maximize the total discounted or average reward. Conditions are given for these processes to have certain natural monotone optimal policies. Under such a policy for the M/M/s queue, for example, the service and arrival rates are non-decreasing and non-increasing functions, respectively, of the queue length. Properties of these policies and a linear program for computing them are also discussed.

Keywords

RANDOM WALKBIRTH AND DEATH PROCESSM/M/s QUEUEMARKOV DECISION PROCESSDYNAMIC PROGRAMMINGMONOTONE OPTIMAL POLICYSUPERMODULARITY
Type
Research Article
Information
Advances in Applied Probability , Volume 13 , Issue 1 , March 1981 , pp. 61 - 83
Copyright
Copyright © Applied Probability Trust 1981 

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Footnotes

Part of this research was supported by Air Force Grant AFOSR-74-2627 and NSF Grant ENG-75-13653.

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