IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v89y2018i3d10.1007_s11134-017-9560-z.html
   My bibliography  Save this article

Heavy traffic limit for a tandem queue with identical service times

Author

Listed:
  • H. Christian Gromoll

    (University of Virginia)

  • Bryce Terwilliger

    (University of Virginia)

  • Bert Zwart

    (Centrum Wiskunde & Informatica)

Abstract

We consider a two-node tandem queueing network in which the upstream queue is M/G/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. We investigate the amount of work in the second queue at certain embedded arrival time points, namely when the upstream queue has just emptied. We focus on the case of infinite-variance service times and obtain a heavy traffic process limit for the embedded Markov chain.

Suggested Citation

  • H. Christian Gromoll & Bryce Terwilliger & Bert Zwart, 2018. "Heavy traffic limit for a tandem queue with identical service times," Queueing Systems: Theory and Applications, Springer, vol. 89(3), pages 213-241, August.
    • Handle: RePEc:spr:queues:v:89:y:2018:i:3:d:10.1007_s11134-017-9560-z
    DOI: 10.1007/s11134-017-9560-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-017-9560-z
    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/s11134-017-9560-z?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. O. J. Boxma & Q. Deng, 2000. "Asymptotic behaviour of the tandem queueing system with identical service times at both queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(2), pages 307-323, 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. Gromoll, H. Christian & Terwilliger, Bryce & Zwart, Bert, 2020. "Heavy traffic limit for the workload plateau process in a tandem queue with identical service times," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1435-1460.

    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. S. Minkevičius & S. Steišūnas, 2006. "About the Sojourn Time Process in Multiphase Queueing Systems," Methodology and Computing in Applied Probability, Springer, vol. 8(2), pages 293-302, June.
    2. Saulius Minkevičius & Vladimiras Dolgopolovas & Leonidas L. Sakalauskas, 2016. "A Law of the Iterated Logarithm for the Sojourn Time Process in Queues in Series," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 37-57, March.

    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:89:y:2018:i:3:d:10.1007_s11134-017-9560-z. 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.