IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v40y1992i6p1156-1179.html
   My bibliography  Save this article

Numerical Methods in Markov Chain Modeling

Author

Listed:
  • Bernard Philippe

    (IRISA, Rennes, France)

  • Youcef Saad

    (University of Minnesota, Minneapolis, Minnesota)

  • William J. Stewart

    (North Carolina State University, Raleigh, North Carolina)

Abstract

This paper describes and compares several methods for computing stationary probability distributions of Markov chains. The main linear algebra problem consists of computing an eigenvector of a sparse, nonsymmetric matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous, singular linear system. We present several methods based on combinations of Krylov subspace techniques, single vector power iteration/relaxation procedures and acceleration techniques. We compare the performance of these methods on some realistic problems.

Suggested Citation

  • Bernard Philippe & Youcef Saad & William J. Stewart, 1992. "Numerical Methods in Markov Chain Modeling," Operations Research, INFORMS, vol. 40(6), pages 1156-1179, December.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:6:p:1156-1179
    DOI: 10.1287/opre.40.6.1156
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.40.6.1156
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.40.6.1156?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. Abderezak Touzene, 2008. "A Tensor Sum Preconditioner for Stochastic Automata Networks," INFORMS Journal on Computing, INFORMS, vol. 20(2), pages 234-242, May.
    2. Lin, Yan-Hui & Yam, Richard C.M., 2017. "Uncertainty importance measures of dependent transition rates for transient and steady state probabilities," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 402-409.
    3. Moghaddass, Ramin & Zuo, Ming J. & Wang, Wenbin, 2011. "Availability of a general k-out-of-n:G system with non-identical components considering shut-off rules using quasi-birth–death process," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 489-496.
    4. Kirkavak, Nureddin & Dincer, Cemal, 1999. "The general behavior of pull production systems: The allocation problems," European Journal of Operational Research, Elsevier, vol. 119(2), pages 479-494, December.
    5. Amy N. Langville & William J. Stewart, 2004. "Testing the Nearest Kronecker Product Preconditioner on Markov Chains and Stochastic Automata Networks," INFORMS Journal on Computing, INFORMS, vol. 16(3), pages 300-315, August.
    6. Ahmad Hanbali & Roland Haan & Richard Boucherie & Jan-Kees Ommeren, 2012. "Time-limited polling systems with batch arrivals and phase-type service times," Annals of Operations Research, Springer, vol. 198(1), pages 57-82, September.

    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:40:y:1992:i:6:p:1156-1179. 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.