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Moment Solutions for the State Exiting Counting Processes of a Markov Renewal Process

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Listed:
  • Manuel D. Rossetti

    (University of Arkansas)

  • Gordon M. Clark

    (The Ohio State University)

Abstract

Important performance measures for many Markov renewal processes are the counts of the exits from each state. We present solutions for the conditional first, second, and covariance moments of the state exiting counting processes for a Markov renewal process, and solutions for the unconditional equilibrium versions of the moments. We demonstrate the relationship between the conditional first moments for the state exiting and the state entering counting processes. For analytical and illustrative purposes, we concentrate on the two state case. Two asymptotic expansions for the moment functions are proposed and evaluated both analytically and empirically. The two approximations are shown to be competitive in terms of absolute relative error, but the second approximation has a simpler analytical form which is useful in analyzing more complex stochastic processes having an underlying MRP structure.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:1:y:1999:i:3:d:10.1023_a:1010065426139
    DOI: 10.1023/A:1010065426139
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    References listed on IDEAS

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    1. Erhan Çinlar, 1975. "Exceptional Paper--Markov Renewal Theory: A Survey," Management Science, INFORMS, vol. 21(7), pages 727-752, March.
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