IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v85y2017i1d10.1007_s11134-016-9508-8.html
   My bibliography  Save this article

Pull-based load distribution among heterogeneous parallel servers: the case of multiple routers

Author

Listed:
  • Alexander L. Stolyar

    (Lehigh University)

Abstract

The model is a service system, consisting of several large server pools. A server’s processing speed and buffer size (which may be finite or infinite) depend on the pool. The input flow of customers is split equally among a fixed number of routers, which must assign customers to the servers immediately upon arrival. We consider an asymptotic regime in which the total customer arrival rate and pool sizes scale to infinity simultaneously, in proportion to a scaling parameter n, while the number of routers remains fixed. We define and study a multi-router generalization of the pull-based customer assignment (routing) algorithm PULL, introduced in Stolyar (Queueing Syst 80(4): 341–361, 2015) for the single-router model. Under the PULL algorithm, when a server becomes idle it sends a “pull-message” to a randomly uniformly selected router; each router operates independently—it assigns an arriving customer to a server according to a randomly uniformly chosen available (at this router) pull-message, if there is any, or to a randomly uniformly selected server in the entire system otherwise. Under Markov assumptions (Poisson arrival process and independent exponentially distributed service requirements), and under subcritical system load, we prove asymptotic optimality of PULL: as $$n\rightarrow \infty $$ n → ∞ , the steady-state probability of an arriving customer experiencing blocking or waiting vanishes. Furthermore, PULL has an extremely low router–server message exchange rate of one message per customer. These results generalize some of the single-router results in Stolyar (2015).

Suggested Citation

  • 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.
    • Handle: RePEc:spr:queues:v:85:y:2017:i:1:d:10.1007_s11134-016-9508-8
    DOI: 10.1007/s11134-016-9508-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-016-9508-8
    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/s11134-016-9508-8?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Kuang Xu & Yuan Zhong, 2020. "Information and Memory in Dynamic Resource Allocation," Operations Research, INFORMS, vol. 68(6), pages 1698-1715, November.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

    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:1:d:10.1007_s11134-016-9508-8. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.