IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v85y2017i3d10.1007_s11134-016-9512-z.html
   My bibliography  Save this article

Large deviations for the total queue size in non-Markovian tandem queues

Author

Listed:
  • Anne Buijsrogge

    (Universiteit Twente)

  • Pieter-Tjerk Boer

    (Universiteit Twente)

  • Karol Rosen
  • Werner Scheinhardt

    (Universiteit Twente)

Abstract

We consider a d-node tandem queue with arrival process and light-tailed service processes at all queues i.i.d. and independent of each other. We consider three variations of the probability that the number of customers in the system reaches some high level N, namely during a busy cycle, in steady state, and upon arrival of a new customer. We show that their decay rates for large N have the same value and give an expression for this value.

Suggested Citation

  • Anne Buijsrogge & Pieter-Tjerk Boer & Karol Rosen & Werner Scheinhardt, 2017. "Large deviations for the total queue size in non-Markovian tandem queues," Queueing Systems: Theory and Applications, Springer, vol. 85(3), pages 305-312, April.
    • Handle: RePEc:spr:queues:v:85:y:2017:i:3:d:10.1007_s11134-016-9512-z
    DOI: 10.1007/s11134-016-9512-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-016-9512-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/s11134-016-9512-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. A.J. Ganesh, 1998. "Large deviations of the sojourn time for queues in series," Annals of Operations Research, Springer, vol. 79(0), pages 3-26, 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. Anne Buijsrogge & Pieter-Tjerk Boer & Werner R. W. Scheinhardt, 2019. "Importance sampling for non-Markovian tandem queues using subsolutions," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 31-65, October.

    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. O'Connell, Neil & Yor, Marc, 2001. "Brownian analogues of Burke's theorem," Stochastic Processes and their Applications, Elsevier, vol. 96(2), pages 285-304, December.
    2. Marcos Singer & Patricio Donoso & José Noguer, 2005. "Optimal Planning of a Multi-Station System with Sojourn Time Constraints," Annals of Operations Research, Springer, vol. 138(1), pages 203-222, September.

    More about this item

    Keywords

    GG1 queue; Tandem queue; Decay rate; Large deviations;
    All these keywords.

    JEL classification:

    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:queues:v:85:y:2017:i:3:d:10.1007_s11134-016-9512-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.