IDEAS home Printed from https://ideas.repec.org/a/inm/ormoor/v46y2021i1p268-300.html
   My bibliography  Save this article

Heavy Traffic Limits for Join-the-Shortest-Estimated-Queue Policy Using Delayed Information

Author

Listed:
  • Rami Atar

    (Viterbi Faculty of Electrical Engineering Technion–Israel Institute of Technology, Haifa 32000, Israel)

  • David Lipshutz

    (Viterbi Faculty of Electrical Engineering Technion–Israel Institute of Technology, Haifa 32000, Israel)

Abstract

We consider a load-balancing problem for a network of parallel queues in which information on the state of the queues is subject to a delay. In this setting, adopting a routing policy that performs well when applied to the current state of the queues can perform quite poorly when applied to the delayed state of the queues. Viewing this as a problem of control under partial observations, we propose using an estimate of the current queue lengths as the input to the join-the-shortest-queue policy. For a general class of estimation schemes, under heavy traffic conditions, we prove convergence of the diffusion-scaled process to a solution of a so-called diffusion model, in which an important step toward this goal establishes that the estimated queue lengths undergo state-space collapse. In some cases, our diffusion model is given by a novel stochastic delay equation with reflection, in which the Skorokhod boundary term appears with delay. We illustrate our results with examples of natural estimation schemes, discuss their implementability, and compare their relative performance using simulations.

Suggested Citation

  • Rami Atar & David Lipshutz, 2021. "Heavy Traffic Limits for Join-the-Shortest-Estimated-Queue Policy Using Delayed Information," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 268-300, February.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:1:p:268-300
    DOI: 10.1287/moor.2020.1056
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/moor.2020.1056
    Download Restriction: no
    File URL: https://libkey.io/10.1287/moor.2020.1056?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
    ---><---

    References listed on IDEAS

    as
    1. Anton Braverman, 2020. "Steady-State Analysis of the Join-the-Shortest-Queue Model in the Halfin–Whitt Regime," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 1069-1103, August.
    2. Patrick Eschenfeldt & David Gamarnik, 2018. "Join the Shortest Queue with Many Servers. The Heavy-Traffic Asymptotics," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 867-886, August.
    3. Varun Gupta & Neil Walton, 2019. "Load Balancing in the Nondegenerate Slowdown Regime," Operations Research, INFORMS, vol. 67(1), pages 281-294, January.
    4. Jamol Pender & Richard Rand & Elizabeth Wesson, 2020. "A Stochastic Analysis of Queues with Customer Choice and Delayed Information," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 1104-1126, August.
    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. Debankur Mukherjee, 2022. "Rates of convergence of the join the shortest queue policy for large-system heavy traffic," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 317-319, April.
    2. 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.
    3. Anton Braverman, 2020. "Steady-State Analysis of the Join-the-Shortest-Queue Model in the Halfin–Whitt Regime," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 1069-1103, August.
    4. Kuang Xu & Yuan Zhong, 2020. "Information and Memory in Dynamic Resource Allocation," Operations Research, INFORMS, vol. 68(6), pages 1698-1715, November.
    5. 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.
    6. Jonatha Anselmi & Francois Dufour, 2020. "Power-of- d -Choices with Memory: Fluid Limit and Optimality," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 862-888, August.
    7. Sem Borst, 2022. "Load balancing in large-scale heterogeneous systems," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 397-399, April.
    8. Danielle Tibi, 2019. "Martingales and buffer overflow for the symmetric shortest queue model," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 153-190, October.
    9. Varun Gupta & Neil Walton, 2019. "Load Balancing in the Nondegenerate Slowdown Regime," Operations Research, INFORMS, vol. 67(1), pages 281-294, January.
    10. Zhong, Zhiheng & Cao, Ping, 2023. "Balanced routing with partial information in a distributed parallel many-server queueing system," European Journal of Operational Research, Elsevier, vol. 304(2), pages 618-633.
    11. Yuan, Xuchuan & Brian Hwarng, H., 2023. "Examining the dynamics of reactive capacity allocation through a chaos lens," European Journal of Operational Research, Elsevier, vol. 308(2), pages 912-928.
    12. Jiaqi Zhou & Ilya O. Ryzhov, 2021. "Equilibrium analysis of observable express service with customer choice," Queueing Systems: Theory and Applications, Springer, vol. 99(3), pages 243-281, December.

    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:inm:ormoor:v:46:y:2021:i:1:p:268-300. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.