IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v32y1984i4p926-944.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.32.4.926
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.32.4.926?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Chen, Weiwei & Kumcu, Gül Çulhan & Melamed, Benjamin & Baveja, Alok, 2023. "Managing resource allocation for the recruitment stocking problem," Omega, Elsevier, vol. 120(C).
    6. 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.
    7. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:32:y:1984:i:4:p:926-944. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.