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Performance Analysis for Controlled Semi-Markov Systems with Application to Maintenance

Author

Listed:
  • Yonghui Huang

    (Sun Yat-Sen University
    Guangdong Province Key Laboratory of Computational Science)

  • Xianping Guo

    (Sun Yat-Sen University
    Guangdong Province Key Laboratory of Computational Science)

  • Xinyuan Song

    (Chinese University of Hong Kong)

Abstract

This paper concerns with the performance analysis for controlled semi-Markov systems in Borel state and action spaces. The performability of the system is defined as the probability that the system reaches a prescribed reward level during a first passage time to some target set. Under mild conditions, we develop a value iteration algorithm for computing the optimal value, and establish the existence of optimal policies with the maximal performability. Our main results are applied to a maintenance problem.

Suggested Citation

  • Yonghui Huang & Xianping Guo & Xinyuan Song, 2011. "Performance Analysis for Controlled Semi-Markov Systems with Application to Maintenance," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 395-415, August.
    • Handle: RePEc:spr:joptap:v:150:y:2011:i:2:d:10.1007_s10957-011-9813-7
    DOI: 10.1007/s10957-011-9813-7
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    References listed on IDEAS

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    1. A. Jaśkiewicz, 2009. "Zero-Sum Ergodic Semi-Markov Games with Weakly Continuous Transition Probabilities," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 321-347, May.
    2. Çekyay, B. & Özekici, S., 2010. "Mean time to failure and availability of semi-Markov missions with maximal repair," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1442-1454, December.
    3. Singh, Sumeetpal S. & Tadic, Vladislav B. & Doucet, Arnaud, 2007. "A policy gradient method for semi-Markov decision processes with application to call admission control," European Journal of Operational Research, Elsevier, vol. 178(3), pages 808-818, May.
    4. Manfred Schäl, 1992. "On the Second Optimality Equation for Semi-Markov Decision Models," Mathematics of Operations Research, INFORMS, vol. 17(2), pages 470-486, May.
    5. John W. Mamer, 1986. "Successive Approximations for Finite Horizon, Semi-Markov Decision Processes with Application to Asset Liquidation," Operations Research, INFORMS, vol. 34(4), pages 638-644, August.
    6. Diego Klabjan & Daniel Adelman, 2007. "An Infinite-Dimensional Linear Programming Algorithm for Deterministic Semi-Markov Decision Processes on Borel Spaces," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 528-550, August.
    7. 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.
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    Cited by:

    1. Bhabak, Arnab & Saha, Subhamay, 2022. "Risk-sensitive semi-Markov decision problems with discounted cost and general utilities," Statistics & Probability Letters, Elsevier, vol. 184(C).
    2. Liu, Qiuli & He, Yu & Wang, Junwei, 2018. "Optimal control for probabilistic Boolean networks using discrete-time Markov decision processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1297-1307.
    3. Xiangxiang Huang & Xianping Guo, 2020. "Nonzero-Sum Stochastic Games with Probability Criteria," Dynamic Games and Applications, Springer, vol. 10(2), pages 509-527, June.

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