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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.
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    7. 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.
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    Cited by:

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