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Constrained continuous-time Markov decision processes with average criteria

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  • Lanlan Zhang
  • Xianping Guo

Abstract

In this paper, we study constrained continuous-time Markov decision processes with a denumerable state space and unbounded reward/cost and transition rates. The criterion to be maximized is the expected average reward, and a constraint is imposed on an expected average cost. We give suitable conditions that ensure the existence of a constrained-optimal policy. Moreover, we show that the constrained-optimal policy randomizes between two stationary policies differing in at most one state. Finally, we use a controlled queueing system to illustrate our conditions. Copyright Springer-Verlag 2008

Suggested Citation

  • Lanlan Zhang & Xianping Guo, 2008. "Constrained continuous-time Markov decision processes with average criteria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 323-340, April.
    • Handle: RePEc:spr:mathme:v:67:y:2008:i:2:p:323-340
    DOI: 10.1007/s00186-007-0154-0
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    References listed on IDEAS

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    1. Eugene A. Feinberg, 2000. "Constrained Discounted Markov Decision Processes and Hamiltonian Cycles," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 130-140, February.
    2. Masayuki Horiguchi, 2001. "Markov decision processes with a stopping time constraint," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(2), pages 279-295, June.
    3. Yasemin Serin & Vidyadhar Kulkarni, 2005. "Markov decision processes under observability constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(2), pages 311-328, June.
    4. Jorge Alvarez-Mena & Onésimo Hernández-Lerma, 2002. "Convergence of the optimal values of constrained Markov control processes," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 55(3), pages 461-484, June.
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    Cited by:

    1. Guo, Xianping & Ye, Liuer & Yin, George, 2012. "A mean–variance optimization problem for discounted Markov decision processes," European Journal of Operational Research, Elsevier, vol. 220(2), pages 423-429.
    2. Yonghui Huang & Qingda Wei & Xianping Guo, 2013. "Constrained Markov decision processes with first passage criteria," Annals of Operations Research, Springer, vol. 206(1), pages 197-219, July.

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