IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v50y1994i2p253-262.html
   My bibliography  Save this article

Ergodicity of a polling network

Author

Listed:
  • Borovkov, A. A.
  • Schassberger, R.

Abstract

The polling network considered here consists of a finite collection of stations visited successively by a single server who is following a Markovian routing scheme. At every visit of a station a positive random number of the customers present at the start of the visit are served, whereupon the server takes a positive random time to walk to the station to be visited next. The network receives arrivals of customer groups at Poisson instants, and all customers wait until served, whereupon they depart from the network. Necessary and sufficient conditions are derived for the server to be able to cope with the traffic. For the proof a multidimensional imbedded Markov chain is studied.

Suggested Citation

  • Borovkov, A. A. & Schassberger, R., 1994. "Ergodicity of a polling network," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 253-262, April.
    • Handle: RePEc:eee:spapps:v:50:y:1994:i:2:p:253-262
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(94)90122-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

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


    Cited by:

    1. Saffer, Zsolt & Telek, Miklós, 2009. "Stability of periodic polling system with BMAP arrivals," European Journal of Operational Research, Elsevier, vol. 197(1), pages 188-195, August.
    2. Menshikov, Mikhail & Zuyev, Sergei, 2001. "Polling systems in the critical regime," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 201-218, April.

    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:eee:spapps:v:50:y:1994:i:2:p:253-262. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.