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Load Balancing in the Nondegenerate Slowdown Regime

Author

Listed:
  • Varun Gupta

    (Booth School of Business, University of Chicago, Chicago, Illinois 60637)

  • Neil Walton

    (Alan Turing Building, University of Manchester, Manchester M13 9PL, United Kingdom)

Abstract

We analyze join-the-shortest-queue (JSQ) in a contemporary scaling regime known as the nondegenerate slowdown (NDS) regime. Join-the-shortest-queue is a classical load-balancing policy for queueing systems with multiple parallel servers. Parallel server queueing systems are regularly analyzed and dimensioned by diffusion approximations achieved in the Halfin–Whitt scaling regime. However, when jobs must be dispatched to a server upon arrival, we advocate the nondegenerate slowdown regime to compare different load-balancing rules. In this paper we identify novel diffusion approximation and timescale separation that provides insights into the performance of JSQ. We calculate the price of irrevocably dispatching jobs to servers and prove this to be within 15% (in the NDS regime) of the rules that may maneuver jobs between servers. We also compare our results for the JSQ policy with the NDS approximations of many modern load-balancing policies such as idle-queue-first and power-of-d-choices policies that act as low information proxies for the JSQ policy. Our analysis leads us to construct new rules that have identical performance to JSQ but require less communication overhead than power of two choices.

Suggested Citation

  • Varun Gupta & Neil Walton, 2019. "Load Balancing in the Nondegenerate Slowdown Regime," Operations Research, INFORMS, vol. 67(1), pages 281-294, January.
    • Handle: RePEc:inm:oropre:v:67:y:2019:i:1:p:281-294
    DOI: 10.1287/opre.2018.1768
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    References listed on IDEAS

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    1. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    2. Rami Atar, 2012. "A Diffusion Regime with Nondegenerate Slowdown," Operations Research, INFORMS, vol. 60(2), pages 490-500, April.
    3. 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.
    4. Lawrence Brown & Noah Gans & Avishai Mandelbaum & Anat Sakov & Haipeng Shen & Sergey Zeltyn & Linda Zhao, 2005. "Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 36-50, March.
    5. Sem Borst & Avi Mandelbaum & Martin I. Reiman, 2004. "Dimensioning Large Call Centers," Operations Research, INFORMS, vol. 52(1), pages 17-34, February.
    6. Hunt, P. J. & Kurtz, T. G., 1994. "Large loss networks," Stochastic Processes and their Applications, Elsevier, vol. 53(2), pages 363-378, October.
    7. Ward Whitt, 2003. "How Multiserver Queues Scale with Growing Congestion-Dependent Demand," Operations Research, INFORMS, vol. 51(4), pages 531-542, August.
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    Cited by:

    1. 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.
    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. 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.
    4. 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.
    5. Sem Borst, 2022. "Load balancing in large-scale heterogeneous systems," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 397-399, April.
    6. 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.
    7. 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.

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