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An approximation approach to ergodic semi-Markov control processes

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  • Anna Jaśkiewicz

Abstract

We consider semi-Markov control models (SMCMs) with a Borel state space satisfying certain stochastic stability assumptions on the transition structure which imply the so-called V-uniform geometric ergodicity of the state process. We deal with a class of ε-perturbations of transition probability functions of the original model. First, we determine the rate of convergence of the optimal expected costs in in perturbed models to the optimal expected cost in the orginal SMCM. Next, we present a new algorithm for finding the solution to the average cost optimality equation (ACOE). The algorithm makes use of a sequence of solutions to the ACOE for the perturbed models, which can be found by a simple iterative procedure. Copyright Springer-Verlag Berlin Heidelberg 2001

Suggested Citation

  • Anna Jaśkiewicz, 2001. "An approximation approach to ergodic semi-Markov control processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(1), pages 1-19, October.
    • Handle: RePEc:spr:mathme:v:54:y:2001:i:1:p:1-19
    DOI: 10.1007/s001860000079
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    Cited by:

    1. Huang, Yonghui & Guo, Xianping, 2011. "Finite horizon semi-Markov decision processes with application to maintenance systems," European Journal of Operational Research, Elsevier, vol. 212(1), pages 131-140, July.
    2. C. Drent & S. Kapodistria & J. A. C. Resing, 2019. "Condition-based maintenance policies under imperfect maintenance at scheduled and unscheduled opportunities," Queueing Systems: Theory and Applications, Springer, vol. 93(3), pages 269-308, December.
    3. Qingda Wei & Xianping Guo, 2012. "New Average Optimality Conditions for Semi-Markov Decision Processes in Borel Spaces," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 709-732, June.

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