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.

    References listed on IDEAS

    as
    1. Achyutha Krishnamoorthy & Anu Nuthan Joshua & Vladimir Vishnevsky, 2021. "Analysis of a k -Stage Bulk Service Queuing System with Accessible Batches for Service," Mathematics, MDPI, vol. 9(5), pages 1-16, March.
    2. A. Banik & U. Gupta, 2007. "Analyzing the finite buffer batch arrival queue under Markovian service process: GI X /MSP/1/N," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 146-160, July.
    3. Mohan Chaudhry & Abhijit Datta Banik & Sitaram Barik & Veena Goswami, 2023. "A Novel Computational Procedure for the Waiting-Time Distribution (In the Queue) for Bulk-Service Finite-Buffer Queues with Poisson Input," Mathematics, MDPI, vol. 11(5), pages 1-26, February.
    4. J. J. Kim & M. L. Chaudhry & V. Goswami & A. D. Banik, 2021. "A New and Pragmatic Approach to the GIX/Geo/c/N Queues Using Roots," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 273-289, March.
    5. Nobel, R. D., 1989. "Practical approximations for finite-buffer queueing models with batch arrivals," European Journal of Operational Research, Elsevier, vol. 38(1), pages 44-55, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Abhijit Datta Banik & Souvik Ghosh & M. L. Chaudhry, 2020. "On the optimal control of loss probability and profit in a GI/C-BMSP/1/N queueing system," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 144-162, March.
    2. van Dijk, Nico M., 1997. "An approximate solution and error bound for a discrete time queue with simultaneous servicing," European Journal of Operational Research, Elsevier, vol. 96(2), pages 289-298, January.
    3. Srinivas R. Chakravarthy & Serife Ozkar, 2024. "A Queueing Model with BMAP Arrivals and Heterogeneous Phase Type Group Services," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-30, December.
    4. Michiel De Muynck & Herwig Bruneel & Sabine Wittevrongel, 2023. "Analysis of a Queue with General Service Demands and Multiple Servers with Variable Service Capacities," Mathematics, MDPI, vol. 11(4), pages 1-21, February.
    5. Mohan Chaudhry & A. D. Banik & Soumyajit Dev & Sitaram Barik, 2025. "A simple derivation of the waiting-time distribution (in the queue) for the bulk-service $$M/G^{(a,b)}/1$$ queueing system," Annals of Operations Research, Springer, vol. 352(1), pages 1-24, September.
    6. M. L. Chaudhry & A. D. Banik & A. Pacheco, 2017. "A simple analysis of the batch arrival queue with infinite-buffer and Markovian service process using roots method: $$ GI ^{[X]}/C$$ G I [ X ] / C - $$ MSP /1/\infty $$ M S P / 1 / ∞," Annals of Operations Research, Springer, vol. 252(1), pages 135-173, May.

    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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.