IDEAS home Printed from https://ideas.repec.org/a/spr/indpam/v56y2025i3d10.1007_s13226-025-00814-5.html
   My bibliography  Save this article

Computational Procedure for System Length and Waiting-time Distribution in an $$M^{X}/D/c/N$$ M X / D / c / N Queue

Author

Listed:
  • Sitaram Barik

    (Indian Institute of Technology Bhubaneswar)

  • Abhijit Datta Banik

    (Indian Institute of Technology Bhubaneswar)

  • Mohan L. Chaudhry

    (Royal Military College of Canada)

  • Saroja Kumar Singh

    (Ravenshaw University)

Abstract

In this paper, we discuss a finite-buffer and multi-server queue wherein a batch of customers of random size arrive according to a Poisson process. Service time follows the deterministic distribution, and the queue capacity is N, excluding the number of customers with the servers. The probability generating function (pgf) of queue-length and system-length distribution at a random epoch has been derived using embedded Markov chain. The Laplace-Stieltjes transform (LST) of the waiting time of a random customer in a batch has been derived using the LST of the waiting time of the first customer of a batch. We also derive the probability density function (pdf) for the waiting-time distribution of a random customer in a batch. Performance measures, like mean queue length, mean waiting time, and the probability of blocking have been obtained. Such queueing systems find applications in the performance analysis of communication, manufacturing, and transportation systems.

Suggested Citation

  • Sitaram Barik & Abhijit Datta Banik & Mohan L. Chaudhry & Saroja Kumar Singh, 2025. "Computational Procedure for System Length and Waiting-time Distribution in an $$M^{X}/D/c/N$$ M X / D / c / N Queue," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(3), pages 973-988, September.
    • Handle: RePEc:spr:indpam:v:56:y:2025:i:3:d:10.1007_s13226-025-00814-5
    DOI: 10.1007/s13226-025-00814-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13226-025-00814-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13226-025-00814-5?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

    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:spr:indpam:v:56:y:2025:i:3:d:10.1007_s13226-025-00814-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.