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Computation of the Optimal Policy for the Control of a Compound Immigration Process through Total Catastrophes

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  • Epaminondas G. Kyriakidis

    (University of the Aegean)

  • Theodosis D. Dimitrakos

    (University of the Aegean)

Abstract

In this paper we consider a Markov decision model introduced by Economou (2003), in which it was proved that the optimal policy in the problem of controlling a compound immigration process through total catastrophes is of control-limit type. We show that the average cost of a control-limit policy is unimodal as a function of the critical point. This result enables us to design very efficient algorithms for the computation of the optimal policy as the bisection procedure and a special-purpose policy iteration algorithm that operates on the class of control-limit policies.

Suggested Citation

  • Epaminondas G. Kyriakidis & Theodosis D. Dimitrakos, 2005. "Computation of the Optimal Policy for the Control of a Compound Immigration Process through Total Catastrophes," Methodology and Computing in Applied Probability, Springer, vol. 7(1), pages 97-118, March.
    • Handle: RePEc:spr:metcap:v:7:y:2005:i:1:d:10.1007_s11009-005-6657-3
    DOI: 10.1007/s11009-005-6657-3
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    References listed on IDEAS

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    1. Richard F. Serfozo, 1979. "Technical Note—An Equivalence Between Continuous and Discrete Time Markov Decision Processes," Operations Research, INFORMS, vol. 27(3), pages 616-620, June.
    2. D. J. White, 1988. "Further Real Applications of Markov Decision Processes," Interfaces, INFORMS, vol. 18(5), pages 55-61, October.
    3. Love, C. E. & Zhang, Z. G. & Zitron, M. A. & Guo, R., 2000. "A discrete semi-Markov decision model to determine the optimal repair/replacement policy under general repairs," European Journal of Operational Research, Elsevier, vol. 125(2), pages 398-409, September.
    4. Economou, Antonis, 2003. "On the control of a compound immigration process through total catastrophes," European Journal of Operational Research, Elsevier, vol. 147(3), pages 522-529, June.
    5. Nobel, Rein D. & Tijms, Henk C., 1999. "Optimal control for an MX/G/1 queue with two service modes," European Journal of Operational Research, Elsevier, vol. 113(3), pages 610-619, March.
    6. Douglas J. White, 1985. "Real Applications of Markov Decision Processes," Interfaces, INFORMS, vol. 15(6), pages 73-83, December.
    7. Kyriakidis, E. G., 1993. "A Markov decision algorithm for optimal pest control through uniform catastrophes," European Journal of Operational Research, Elsevier, vol. 64(1), pages 38-44, January.
    8. Van der Duyn Schouten, F. A. & Vanneste, S. G., 1995. "Maintenance optimization of a production system with buffer capacity," European Journal of Operational Research, Elsevier, vol. 82(2), pages 323-338, April.
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    Cited by:

    1. Antonio Di Crescenzo & Virginia Giorno & Balasubramanian Krishna Kumar & Amelia G. Nobile, 2018. "A Time-Non-Homogeneous Double-Ended Queue with Failures and Repairs and Its Continuous Approximation," Mathematics, MDPI, vol. 6(5), pages 1-23, May.
    2. Zhang Xiaoyan & Liu Liwei & Jiang Tao, 2015. "Analysis of an M/G/1 Stochastic Clearing Queue in a 3-Phase Environment," Journal of Systems Science and Information, De Gruyter, vol. 3(4), pages 374-384, August.
    3. Antonis Economou & Athanasia Manou, 2013. "Equilibrium balking strategies for a clearing queueing system in alternating environment," Annals of Operations Research, Springer, vol. 208(1), pages 489-514, September.
    4. Nitin Kumar & Umesh Chandra Gupta, 2022. "Markovian Arrival Process Subject to Renewal Generated Binomial Catastrophes," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2287-2312, December.
    5. F. P. Barbhuiya & Nitin Kumar & U. C. Gupta, 2019. "Batch Renewal Arrival Process Subject to Geometric Catastrophes," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 69-83, March.

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