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Series Expansions for Continuous-Time Markov Processes

Author

Listed:
  • Bernd Heidergott

    (Department of Econometrics, Vrije Universiteit Amsterdam, and Tinbergen Institute, 1081 HV Amsterdam, The Netherlands)

  • Arie Hordijk

    (Mathematical Institute, Leiden University, 2300 RA Leiden, The Netherlands)

  • Nicole Leder

    (Department of Mathematics, University of Hamburg, 20146 Hamburg, Germany)

Abstract

We present update formulas that allow us to express the stationary distribution of a continuous-time Markov process with denumerable state space having generator matrix Q * through a continuous-time Markov process with generator matrix Q . Under suitable stability conditions, numerical approximations can be derived from the update formulas, and we show that the algorithms converge at a geometric rate. Applications to sensitivity analysis and bounds on perturbations are discussed as well. Numerical examples are presented to illustrate the efficiency of the proposed algorithm.

Suggested Citation

  • Bernd Heidergott & Arie Hordijk & Nicole Leder, 2010. "Series Expansions for Continuous-Time Markov Processes," Operations Research, INFORMS, vol. 58(3), pages 756-767, June.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:3:p:756-767
    DOI: 10.1287/opre.1090.0738
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    References listed on IDEAS

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    1. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    2. Ger Koole & Avishai Mandelbaum, 2002. "Queueing Models of Call Centers: An Introduction," Annals of Operations Research, Springer, vol. 113(1), pages 41-59, July.
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    Cited by:

    1. Badredine Issaadi & Karim Abbas & Djamil Aïssani, 2017. "Perturbation Analysis of the GI/M/s Queue," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 819-841, September.
    2. Touazi, A. & Benouaret, Z. & Aissani, D. & Adjabi, S., 2017. "Nonparametric estimation of the claim amount in the strong stability analysis of the classical risk model," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 78-83.
    3. Henry Lam, 2016. "Robust Sensitivity Analysis for Stochastic Systems," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1248-1275, November.
    4. Joost Berkhout & Bernd F. Heidergott, 2019. "Analysis of Markov Influence Graphs," Operations Research, INFORMS, vol. 67(3), pages 892-904, May.

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