IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v95y2020i3d10.1007_s11134-020-09656-w.html
   My bibliography  Save this article

Stability of JSQ in queues with general server-job class compatibilities

Author

Listed:
  • James Cruise

    (Heriot-Watt University)

  • Matthieu Jonckheere

    (Universidad de Buenos Aires and CONICET)

  • Seva Shneer

    (Heriot-Watt University)

Abstract

We consider Poisson streams of exponentially distributed jobs arriving at each edge of a hypergraph of queues. Upon arrival, an incoming job is routed to the shortest queue among the corresponding vertices. This generalizes many known models such as power-of-d load balancing and JSQ (join the shortest queue) on generic graphs. We prove that stability in this model is achieved if and only if there exists a stable static routing policy. This stability condition is equivalent to that of the JSW (join the shortest workload) policy. We show that some graph topologies lead to a loss of capacity, implying more restrictive stability conditions than in, for example, complete graphs.

Suggested Citation

  • James Cruise & Matthieu Jonckheere & Seva Shneer, 2020. "Stability of JSQ in queues with general server-job class compatibilities," Queueing Systems: Theory and Applications, Springer, vol. 95(3), pages 271-279, August.
    • Handle: RePEc:spr:queues:v:95:y:2020:i:3:d:10.1007_s11134-020-09656-w
    DOI: 10.1007/s11134-020-09656-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-020-09656-w
    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/s11134-020-09656-w?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. Alexander L. Stolyar, 2017. "Pull-based load distribution among heterogeneous parallel servers: the case of multiple routers," Queueing Systems: Theory and Applications, Springer, vol. 85(1), pages 31-65, February.
    2. Matthieu Jonckheere & Balakrishna J. Prabhu, 2018. "Asymptotics of insensitive load balancing and blocking phases," Queueing Systems: Theory and Applications, Springer, vol. 88(3), pages 243-278, April.
    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. Xiao-Yue Gong & Vineet Goyal & Garud N. Iyengar & David Simchi-Levi & Rajan Udwani & Shuangyu Wang, 2022. "Online Assortment Optimization with Reusable Resources," Management Science, INFORMS, vol. 68(7), pages 4772-4785, July.

    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. Kuang Xu & Yuan Zhong, 2020. "Information and Memory in Dynamic Resource Allocation," Operations Research, INFORMS, vol. 68(6), pages 1698-1715, November.
    2. Debankur Mukherjee & Sem C. Borst & Johan S. H. van Leeuwaarden & Philip A. Whiting, 2020. "Asymptotic Optimality of Power-of- d Load Balancing in Large-Scale Systems," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1535-1571, November.
    3. Seva Shneer & Alexander L. Stolyar, 2021. "Large-scale parallel server system with multi-component jobs," Queueing Systems: Theory and Applications, Springer, vol. 98(1), pages 21-48, June.
    4. Jazeem Abdul Jaleel & Sherwin Doroudi & Kristen Gardner & Alexander Wickeham, 2022. "A general “power-of-d” dispatching framework for heterogeneous systems," Queueing Systems: Theory and Applications, Springer, vol. 102(3), pages 431-480, December.
    5. Daniela Hurtado-Lange & Siva Theja Maguluri, 2022. "A load balancing system in the many-server heavy-traffic asymptotics," Queueing Systems: Theory and Applications, Springer, vol. 101(3), pages 353-391, August.

    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:95:y:2020:i:3:d:10.1007_s11134-020-09656-w. 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.