IDEAS home Printed from https://ideas.repec.org/a/ids/ijmore/v34y2026i3p354-381.html

Bernoulli vacation bulk queue with essential, optional service, unreliable server and state dependent arrival rates

Author

Listed:
  • R. Kalyanaraman
  • R.V. Sivasuprajha

Abstract

This paper presents the steady state analysis of a single server, bulk arrival, fixed batch service, Bernoulli vacation queue. The arrival follows compound Poisson process with state dependent arrival rates. The service time follows general distribution and services are given in batches of fixed size. The server provides two types of services called, essential and optional service to each batch. At each service completion point, the server takes vacation of Bernoulli type. The vacation period is generally distributed. In addition, during the server's busy state, the server may breakdown immediately, the server is sent for repair. The number of breakdowns follows Poisson process whereas the repair period follows general distribution. For this queueing system the steady state probabilities are derived in terms of probability generating function. The expected number of customers and mean waiting times at various server states are derived. Numerical illustrations are given.

Suggested Citation

  • R. Kalyanaraman & R.V. Sivasuprajha, 2026. "Bernoulli vacation bulk queue with essential, optional service, unreliable server and state dependent arrival rates," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 34(3), pages 354-381.
    • Handle: RePEc:ids:ijmore:v:34:y:2026:i:3:p:354-381
    as

    Download full text from publisher

    File URL: https://www.inderscience.com/link.php?id=155541
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    More about this item

    Keywords

    ;

    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:ids:ijmore:v:34:y:2026:i:3:p:354-381. 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: Sarah Parker (email available below). General contact details of provider: http://www.inderscience.com/browse/index.php?journalID=320 .

    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.