IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v21y1975i9p1040-1048.html
   My bibliography  Save this article

A Graph Theoretic Formula for the Steady State Distribution of Finite Markov Processes

Author

Listed:
  • James J. Solberg

    (Purdue University)

Abstract

This paper presents a formula which expresses the solution to the steady-state equations of a finite irreducible Markov process in terms of subgraphs of the transition diagram of the process. The formula is similar in spirit to well-known flowgraph formulas, but possesses several unique advantages. The formula is the same whether the process is discrete or continuous in time; it is efficient in the sense that no cancellation of terms can occur (it is a simple sum of positive terms); and it is both conceptually and computationally simple. Because these advantages are gained by exploiting properties of Markov processes, the formula is not applicable to linear equations in general, as are the flowgraph methods. The paper states and proves the theorem for both the discrete and continuous cases, gives examples of each, and cites computational experience with the formula.

Suggested Citation

  • James J. Solberg, 1975. "A Graph Theoretic Formula for the Steady State Distribution of Finite Markov Processes," Management Science, INFORMS, vol. 21(9), pages 1040-1048, May.
    • Handle: RePEc:inm:ormnsc:v:21:y:1975:i:9:p:1040-1048
    DOI: 10.1287/mnsc.21.9.1040
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.21.9.1040
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.21.9.1040?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. N. Vijayamohanan Pillai, 2004. "Causality and error correction in Markov chain: Inflation in India revisited," Centre for Development Studies, Trivendrum Working Papers 366, Centre for Development Studies, Trivendrum, India.

    More about this item

    Statistics

    Access and download statistics

    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:ormnsc:v:21:y:1975:i:9:p:1040-1048. 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.