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Exceptional Paper--Markov Renewal Theory: A Survey

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  • Erhan Çinlar

    (Northwestern University)

Abstract

The objective is to survey the major results and applications in an informal setting. The exposition is restricted to finite state spaces; some real problems are modelled and the lines of attack are indicated; and an extensive bibliography is provided to get a further glimpse of the variety of applications. Throughout, the parallels with renewal theory are brought out, and the unity of thought afforded by the formalism of Markov renewal equations is stressed.

Suggested Citation

  • Erhan Çinlar, 1975. "Exceptional Paper--Markov Renewal Theory: A Survey," Management Science, INFORMS, vol. 21(7), pages 727-752, March.
    • Handle: RePEc:inm:ormnsc:v:21:y:1975:i:7:p:727-752
    DOI: 10.1287/mnsc.21.7.727
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    File URL: http://dx.doi.org/10.1287/mnsc.21.7.727
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    Citations

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    Cited by:

    1. Manuel D. Rossetti & Gordon M. Clark, 1999. "Moment Solutions for the State Exiting Counting Processes of a Markov Renewal Process," Methodology and Computing in Applied Probability, Springer, vol. 1(3), pages 247-275, October.
    2. Mark, Brian L. & Ephraim, Yariv, 2013. "An EM algorithm for continuous-time bivariate Markov chains," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 504-517.
    3. Hau L. Lee & Kamran Moinzadeh, 1987. "Operating characteristics of a two‐echelon inventory system for repairable and consumable items under batch ordering and shipment policy," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 365-380, June.
    4. Aleka Papadopoulou & George Tsaklidis, 2007. "Some Reward Paths in Semi-Markov Models with Stochastic Selection of the Transition Probabilities," Methodology and Computing in Applied Probability, Springer, vol. 9(3), pages 399-411, September.
    5. Zhou, Yifan & Zhang, Zhisheng & Lin, Tian Ran & Ma, Lin, 2013. "Maintenance optimisation of a multi-state series–parallel system considering economic dependence and state-dependent inspection intervals," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 248-259.
    6. Riccardo De Blasis, 2023. "Weighted-indexed semi-Markov model: calibration and application to financial modeling," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-16, December.
    7. Erhan Bayraktar & Ulrich Horst & Ronnie Sircar, 2006. "A Limit Theorem for Financial Markets with Inert Investors," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 789-810, November.
    8. Soltani, A.R. & Ghasemi, H., 2014. "Semi-Markov and reward fields," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 71-76.
    9. Huynh, K.T., 2021. "An adaptive predictive maintenance model for repairable deteriorating systems using inverse Gaussian degradation process," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    10. Erhan Bayraktar & Ulrich Horst & Ronnie Sircar, 2007. "Queueing Theoretic Approaches to Financial Price Fluctuations," Papers math/0703832, arXiv.org.
    11. Ganeshan, Ram, 1999. "Managing supply chain inventories: A multiple retailer, one warehouse, multiple supplier model," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 341-354, March.
    12. Shelby Brumelle & Darius Walczak, 2003. "Dynamic Airline Revenue Management with Multiple Semi-Markov Demand," Operations Research, INFORMS, vol. 51(1), pages 137-148, February.
    13. Süleyman Özekici & Talin Papazyan, 1988. "Inspection policies and processes for deteriorating systems subject to catastrophic failure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(4), pages 481-492, August.
    14. D. A. Elkins & M. A. Wortman, 2001. "On Numerical Solution of the Markov Renewal Equation: Tight Upper and Lower Kernel Bounds," Methodology and Computing in Applied Probability, Springer, vol. 3(3), pages 239-253, September.

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