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Optimal control of a truncated general immigration process through total catastrophes

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

E. G. Kyriakidis
E. G. Kyriakidis*
Affiliation:
University of the Aegean
*
∗Postal address: Technological Educational Institute Heraklion, Branch of Chania, Department of Electronics, 3 Romanou Str., Chania 73133, Crete, Greece.
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Abstract

A Markov decision model is considered for the control of a truncated general immigration process, which represents a pest population, by the introduction of total catastrophes. The optimality criterion is that of minimizing the expected long-run average cost per unit time. Firstly, a necessary and sufficient condition is found under which the policy of never controlling is optimal. If this condition fails, a parametric analysis, in which a fictitious parameter is varied over the entire real line, is used to establish the optimality of a control-limit policy. Furthermore, an efficient Markov decision algorithm operating on the class of control-limit policies is developed for the computation of the optimal policy.

Keywords

Markov decision processcatastrophesminimum average costcontrol-limit policies

MSC classification

Primary: 90C40: Markov and semi-Markov decision processes
Secondary: 60J25: Continuous-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 2 , June 1999 , pp. 461 - 472
Copyright
Copyright © Applied Probability Trust 1999 

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