IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v97y2021i1d10.1007_s11134-020-09678-4.html
   My bibliography  Save this article

Workload distributions in ASIP queueing networks

Author

Listed:
  • Onno Boxma

    (Eindhoven University of Technology)

  • Offer Kella

    (The Hebrew University of Jerusalem)

  • Uri Yechiali

    (Tel Aviv University)

Abstract

The workload of a generalized n-site asymmetric simple inclusion process (ASIP) is investigated. Three models are analyzed. The first model is a serial network for which the steady-state Laplace–Stieltjes transform (LST) of the total workload in the first k sites ( $$k\le n$$ k ≤ n ) just after gate openings and at arbitrary epochs is derived. In a special case, the former (just after gate openings) turns out to be an LST of the sum of k independent random variables. The second model is a 2-site ASIP with leakage from the first queue. Gate openings occur at exponentially distributed intervals, and the external input processes to the stations are two independent subordinator Lévy processes. The steady-state joint workload distribution right after gate openings, right before gate openings and at arbitrary epochs is derived. The third model is a shot-noise counterpart of the second model where the workload at the first queue behaves like a shot-noise process. The steady-state total amount of work just before a gate opening turns out to be a sum of two independent random variables.

Suggested Citation

  • Onno Boxma & Offer Kella & Uri Yechiali, 2021. "Workload distributions in ASIP queueing networks," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 81-100, February.
    • Handle: RePEc:spr:queues:v:97:y:2021:i:1:d:10.1007_s11134-020-09678-4
    DOI: 10.1007/s11134-020-09678-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-020-09678-4
    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/s11134-020-09678-4?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. Onno Boxma & Offer Kella & Michel Mandjes, 2019. "Infinite-server systems with Coxian arrivals," Queueing Systems: Theory and Applications, Springer, vol. 92(3), pages 233-255, August.
    2. Onno Boxma & Offer Kella & Uri Yechiali, 2016. "An ASIP model with general gate opening intervals," Queueing Systems: Theory and Applications, Springer, vol. 84(1), pages 1-20, October.
    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. Uri Yechiali & Yaron Yeger, 2022. "Matrix Approach for Analyzing n -Site Generalized ASIP Systems: PGF and Site Occupancy Probabilities," Mathematics, MDPI, vol. 10(23), pages 1-33, 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. Ivo Adan & Onno Boxma & Jacques Resing, 2022. "Functional equations with multiple recursive terms," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 7-23, October.
    2. Onno Boxma & Michel Mandjes, 2021. "Shot-noise queueing models," Queueing Systems: Theory and Applications, Springer, vol. 99(1), pages 121-159, October.
    3. Uri Yechiali & Yaron Yeger, 2022. "Matrix Approach for Analyzing n -Site Generalized ASIP Systems: PGF and Site Occupancy Probabilities," Mathematics, MDPI, vol. 10(23), pages 1-33, December.
    4. Yiran Liu & Harsha Honnappa & Samy Tindel & Nung Kwan Yip, 2021. "Infinite server queues in a random fast oscillatory environment," Queueing Systems: Theory and Applications, Springer, vol. 98(1), pages 145-179, June.
    5. Yaron Yeger & Uri Yechiali, 2022. "Performance Measures in a Generalized Asymmetric Simple Inclusion Process," Mathematics, MDPI, vol. 10(4), pages 1-25, 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:97:y:2021:i:1:d:10.1007_s11134-020-09678-4. 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.