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Approximating Nonrenewal Processes by Markov Chains: Use of Super-Erlang (SE) Chains

Author

Listed:
  • Gabriel R. Bitran

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • Sriram Dasu

    (University of California, Los Angeles, California)

Abstract

We study a class of point processes generated by transitions in Markov chains. We are primarily concerned with approximating superposed phase renewal processes by these point processes. We identify a subclass of Markov chains that we call Super-Erlang chains. These chains have special properties that facilitate the development of approximations. We outline an approximation procedure and provide computational results that demonstrate the potential of the approach. The primary motivation for this study is the analysis of open queueing networks.

Suggested Citation

  • Gabriel R. Bitran & Sriram Dasu, 1993. "Approximating Nonrenewal Processes by Markov Chains: Use of Super-Erlang (SE) Chains," Operations Research, INFORMS, vol. 41(5), pages 903-923, October.
    • Handle: RePEc:inm:oropre:v:41:y:1993:i:5:p:903-923
    DOI: 10.1287/opre.41.5.903
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    Cited by:

    1. Ira Gerhardt & Barry L. Nelson & Michael R. Taaffe, 2017. "Technical Note: The MAP t / Ph t /∞ Queueing System and Multiclass [ MAP t / Ph t /∞] K Queueing Network," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 367-376, May.
    2. Girish, Muckai K. & Hu, Jian-Qiang, 2000. "Higher order approximations for the single server queue with splitting, merging and feedback," European Journal of Operational Research, Elsevier, vol. 124(3), pages 447-467, August.

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