IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i19p3575-d930381.html
   My bibliography  Save this article

Analysis of a Queueing Model with MAP Arrivals and Heterogeneous Phase-Type Group Services

Author

Listed:
  • Srinivas R. Chakravarthy

    (Department of Industrial and Manufacturing Engineering and Mathematics, Kettering University, Flint, MI 48504, USA)

Abstract

Queueing models have proven to be very useful in real-life applications to enable the practitioners to optimize the limited resources to conduct their businesses as well as offer services efficiently. In general, we can group such applications into two sectors: manufacturing and service. These two sectors cover everything we deal with on a day-to-day basis. Queues in which the services are offered in blocks (or groups or batches) are well established in the literature and have a wide variety of applications in practice. In this paper, we look at one such queueing model in which the arrivals occur according to a Markovian arrival process and the services are offered in batches of varying sizes from 1 to a finite pre-determined constant, say, b . The service times are assumed to be of phase type with representation depending on the size of the group. Thus, the distributions considered are heterogeneous from both the representation and rate points of view. The model can be studied as a G I / M / 1 -type queue or as a Q B D -model. The model is analyzed in steady state by establishing results including on the rate matrix and the waiting time distribution and providing a number of illustrative examples.

Suggested Citation

  • Srinivas R. Chakravarthy, 2022. "Analysis of a Queueing Model with MAP Arrivals and Heterogeneous Phase-Type Group Services," Mathematics, MDPI, vol. 10(19), pages 1-30, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3575-:d:930381
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/19/3575/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/19/3575/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. S. R. Chakravarthy & Arunava Maity & U. C. Gupta, 2017. "An ‘(s, S)’ inventory in a queueing system with batch service facility," Annals of Operations Research, Springer, vol. 258(2), pages 263-283, November.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. 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.

    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. Achyutha Krishnamoorthy & Anu Nuthan Joshua & Dmitry Kozyrev, 2021. "Analysis of a Batch Arrival, Batch Service Queuing-Inventory System with Processing of Inventory While on Vacation," Mathematics, MDPI, vol. 9(4), pages 1-29, February.
    2. Karumbathil Rasmi & Machuveettil Joseph Jacob & Alexander S. Rumyantsev & Achyutha Krishnamoorthy, 2021. "A Multi-Server Heterogeneous Queuing-Inventory System with Class-Dependent Inventory Access," Mathematics, MDPI, vol. 9(9), pages 1-23, May.
    3. Agassi Melikov & Ramil Mirzayev & Sajeev S. Nair, 2022. "Double Sources Queuing-Inventory System with Hybrid Replenishment Policy," Mathematics, MDPI, vol. 10(14), pages 1-16, July.
    4. T. Harikrishnan & K. Jeganathan & S. Selvakumar & N. Anbazhagan & Woong Cho & Gyanendra Prasad Joshi & Kwang Chul Son, 2022. "Analysis of Stochastic M / M / c / N Inventory System with Queue-Dependent Server Activation, Multi-Threshold Stages and Optional Retrial Facility," Mathematics, MDPI, vol. 10(15), pages 1-37, July.

    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:gam:jmathe:v:10:y:2022:i:19:p:3575-:d:930381. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.