IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v36y2019i04ns0217595919500192.html
   My bibliography  Save this article

Performance Analysis of Joining the Shortest Queue Model Among a Large Number of Queues

Author

Listed:
  • Donald A. Dawson

    (School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada)

  • Jiashan Tang

    (School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada2College of Science, Nanjing University of Posts, and Telecommunications, Nanjing, Jiangsu 210023, P. R. China)

  • Yiqiang Q. Zhao

    (School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada)

Abstract

Consider a queueing network with a large number N nodes, in which each queue has a dedicated input stream, and, in addition, there is an extra input stream, balancing the network load by directing its arrivals to the shortest queue(s). A mean field interaction model is set up to study the performance of this network in terms of limiting results. One of our results shows that the stationary behavior of any of the queues is approximated by that of the M/M/1 queue with a modified arrival rate when the queue length is around zero.

Suggested Citation

  • Donald A. Dawson & Jiashan Tang & Yiqiang Q. Zhao, 2019. "Performance Analysis of Joining the Shortest Queue Model Among a Large Number of Queues," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(04), pages 1-23, August.
  • Handle: RePEc:wsi:apjorx:v:36:y:2019:i:04:n:s0217595919500192
    DOI: 10.1142/S0217595919500192
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0217595919500192
    Download Restriction: Access to full text is restricted to subscribers

    File URL: https://libkey.io/10.1142/S0217595919500192?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. Johri, Pravin K., 1989. "Optimality of the shortest line discipline with state-dependent service rates," European Journal of Operational Research, Elsevier, vol. 41(2), pages 157-161, July.
    2. Yang Zhang & Edwin K. P. Chong & Jan Hannig & Donald Estep, 2013. "Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-16, April.
    Full references (including those not matched with items on IDEAS)

    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. Blanc, J.P.C., 2009. "Bad luck when joining the shortest queue," European Journal of Operational Research, Elsevier, vol. 195(1), pages 167-173, May.
    2. Hung T. Do & Masha Shunko, 2020. "Constrained Load-Balancing Policies for Parallel Single-Server Queue Systems," Management Science, INFORMS, vol. 66(8), pages 3501-3527, August.
    3. Maria E. Mayorga & Emmett J. Lodree & Justin Wolczynski, 2017. "The optimal assignment of spontaneous volunteers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(9), pages 1106-1116, September.
    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. Esther Frostig & Benny Levikson, 1999. "Optimal Routing of Customers to Two Parallel Heterogeneous Servers: The Case of IHR Service Times," Operations Research, INFORMS, vol. 47(3), pages 438-444, June.
    6. P S Ansell & K D Glazebrook & C Kirkbride, 2003. "Generalised ‘join the shortest queue’ policies for the dynamic routing of jobs to multi-class queues," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(4), pages 379-389, April.
    7. Cao, Ping & Zhong, Zhiheng & Huang, Junfei, 2021. "Dynamic routing in a distributed parallel many-server service system: The effect of ξ-choice," European Journal of Operational Research, Elsevier, vol. 294(1), pages 219-235.

    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:wsi:apjorx:v:36:y:2019:i:04:n:s0217595919500192. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/apjor/apjor.shtml .

    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.