IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v104y2023i1d10.1007_s11134-023-09871-1.html
   My bibliography  Save this article

Stability of a cascade system with multiple stations

Author

Listed:
  • Bara Kim

    (Korea University)

  • Jeongsim Kim

    (Chungbuk National University)

Abstract

This paper considers an m-station cascade system with renewal arrival processes and general service time distributions. Miyazawa and Morozov (Queueing Syst 100:225–227, 2022a; Stability of a cascade system with two stations and its extension for multiple stations, 2022b. arXiv:2203.14294v1 ) formulated a conjecture on the stability of this cascade system. In this paper, we show that this conjecture is not true for $$m\ge 3$$ m ≥ 3 . We also show that when $$m\ge 3$$ m ≥ 3 , the stability condition is not determined solely by the moments of the interarrival and service times, but also depends on their distributions. In addition, we provide the necessary and sufficient condition for the stability of this cascade system by modifying a result of Miyazawa and Morozov (2022).

Suggested Citation

  • Bara Kim & Jeongsim Kim, 2023. "Stability of a cascade system with multiple stations," Queueing Systems: Theory and Applications, Springer, vol. 104(1), pages 53-64, June.
    • Handle: RePEc:spr:queues:v:104:y:2023:i:1:d:10.1007_s11134-023-09871-1
    DOI: 10.1007/s11134-023-09871-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-023-09871-1
    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/s11134-023-09871-1?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.

    References listed on IDEAS

    as
    1. Masakiyo Miyazawa & Evsey Morozov, 2022. "Stability condition of a cascade system with a general number of stations," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 225-227, April.
    2. E. Morozov & B. Steyaert, 2013. "Stability analysis of a two-station cascade queueing network," Annals of Operations Research, Springer, vol. 202(1), pages 135-160, January.
    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. Masakiyo Miyazawa & Evsey Morozov, 2023. "Stability of a cascade system with two stations and its extension for multiple stations," Queueing Systems: Theory and Applications, Springer, vol. 104(3), pages 155-174, August.

    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. Masakiyo Miyazawa & Evsey Morozov, 2023. "Stability of a cascade system with two stations and its extension for multiple stations," Queueing Systems: Theory and Applications, Springer, vol. 104(3), pages 155-174, August.
    2. Masakiyo Miyazawa & Evsey Morozov, 2022. "Stability condition of a cascade system with a general number of stations," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 225-227, April.
    3. Hong Zhang & Saviour Worlanyo Akuamoah & Wilson Osafo Apeanti & Prince Harvim & David Yaro & Paul Georgescu, 2021. "The Stability Analysis of a Double-X Queuing Network Occurring in the Banking Sector," Mathematics, MDPI, vol. 9(16), pages 1-21, August.
    4. Rosario Delgado, 2016. "A two-queue polling model with priority on one queue and heavy-tailed On/Off sources: a heavy-traffic limit," Queueing Systems: Theory and Applications, Springer, vol. 83(1), pages 57-85, June.
    5. K. Avrachenkov & E. Morozov & B. Steyaert, 2016. "Sufficient stability conditions for multi-class constant retrial rate systems," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 149-171, February.

    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:queues:v:104:y:2023:i:1:d:10.1007_s11134-023-09871-1. 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.