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Randomization Procedures in the Computation of Cumulative-Time Distributions over Discrete State Markov Processes

Author

Listed:
  • Benjamin Melamed

    (AT&T Bell Laboratories, Holmdel, New Jersey)

  • Micha Yadin

    (Technion, Haifa, Israel)

Abstract

This paper proposes a methodology for computing numerical bounds on cumulative-time (i.e., the time spent in a specified set of states before entering another specified set of states) distributions over discrete state Markov processes. The methodology uses randomization procedures to compute results for appropriately defined transient Markov processes; the transient distribution computed is equivalent to the requisite cumulative-time distribution. A queueing application of the methodology to delay times in queueing networks is outlined and its efficacy is appraised by comparing the results with a sojourn time for a problem with a known distribution.

Suggested Citation

  • Benjamin Melamed & Micha Yadin, 1984. "Randomization Procedures in the Computation of Cumulative-Time Distributions over Discrete State Markov Processes," Operations Research, INFORMS, vol. 32(4), pages 926-944, August.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:4:p:926-944
    DOI: 10.1287/opre.32.4.926
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    Citations

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    Cited by:

    1. Dijk, N.M. van, 1991. "Letters to the editor : on a simple proof of uniformization for continuous and discrete-state continuous-time Markov chains," Serie Research Memoranda 0002, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    2. Michel Mandjes & Birgit Sollie, 2022. "A Numerical Approach for Evaluating the Time-Dependent Distribution of a Quasi Birth-Death Process," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1693-1715, September.
    3. Chen, Weiwei & Kumcu, Gül Çulhan & Melamed, Benjamin & Baveja, Alok, 2023. "Managing resource allocation for the recruitment stocking problem," Omega, Elsevier, vol. 120(C).
    4. Juan A. Carrasco, 2013. "A New General-Purpose Method for the Computation of the Interval Availability Distribution," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 774-791, November.
    5. Papadopoulos, H. T., 1998. "An approximate method for calculating the mean sojourn time of K-station production lines with no intermediate buffers," International Journal of Production Economics, Elsevier, vol. 54(3), pages 297-305, May.
    6. Dijk, N.M. van, 1991. "On uniformization for nonhomogeneous Markov chains," Serie Research Memoranda 0006, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    7. Jamal Temsamani & Juan A. Carrasco, 2006. "Transient analysis of Markov models of fault‐tolerant systems with deferred repair using split regenerative randomization," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(4), pages 318-353, June.

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