IDEAS home Printed from https://ideas.repec.org/a/taf/lstaxx/v53y2024i21p7491-7504.html
   My bibliography  Save this article

Analysis of M/M/1 queueing systems with negative customers and unreliable repairers

Author

Listed:
  • Ruiling Tian
  • Yao Zhang

Abstract

In this article, we study the M/M/1 queueing systems with negative customers and unreliable repairers. The arrival of a negative customer causes the failure of the server, and the server is repaired immediately. The repairers may successfully repair the server with probability p, and the server continues to serve customers in the system. Otherwise, once the repair fails, the system will be cleared and all customers are forced to leave the system. By analyzing the quasi-birth-and-death process and using the probability generating function method, we obtain the steady-state probability and some performance measures of the system. Then, based on the reward-cost structure, we discuss the strategic behavior of customers and consider the equilibrium strategy. Finally, the effects of system parameters on the performance measures, individual benefit, and social benefit are analyzed by numerical examples.

Suggested Citation

  • Ruiling Tian & Yao Zhang, 2024. "Analysis of M/M/1 queueing systems with negative customers and unreliable repairers," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(21), pages 7491-7504, November.
  • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:21:p:7491-7504
    DOI: 10.1080/03610926.2023.2265000
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/03610926.2023.2265000
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/03610926.2023.2265000?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
    ---><---

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

    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:taf:lstaxx:v:53:y:2024:i:21:p:7491-7504. 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 Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/lsta .

    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.