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Preventing Large Sojourn Times Using SMART Scheduling

Author

Listed:
  • Misja Nuyens

    (Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands)

  • Adam Wierman

    (Computer Science Department, California Institute of Technology, Pasadena, California 91125)

  • Bert Zwart

    (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Abstract

Recently, the so-called class of SMART scheduling policies has been introduced to formalize the common heuristic of “biasing toward small jobs.” We study the tail of the sojourn-time (response-time) distribution under both SMART policies and the foreground-background policy (FB) in the GI/GI/1 queue. We prove that these policies behave very well under heavy-tailed service times. Specifically, we show that the sojourn-time tail under all SMART policies and FB is similar to that of the service-time tail, up to a constant, which makes the SMART class superior to first-come-first-served (FCFS). In contrast, for light-tailed service times, we prove that the sojourn-time tail under FB and SMART is larger than that under FCFS. However, we show that the sojourn-time tail for a job of size y under FB and all SMART policies still outperforms FCFS as long as y is not too large.

Suggested Citation

  • Misja Nuyens & Adam Wierman & Bert Zwart, 2008. "Preventing Large Sojourn Times Using SMART Scheduling," Operations Research, INFORMS, vol. 56(1), pages 88-101, February.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:1:p:88-101
    DOI: 10.1287/opre.1070.0504
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    References listed on IDEAS

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    1. P. Jelenković & P. Momčilović, 2003. "Large Deviation Analysis of Subexponential Waiting Times in a Processor-Sharing Queue," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 587-608, August.
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    Cited by:

    1. Bo Zhang & Bert Zwart, 2013. "Steady-State Analysis for Multiserver Queues Under Size Interval Task Assignment in the Quality-Driven Regime," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 504-525, August.
    2. Adam Wierman & Bert Zwart, 2012. "Is Tail-Optimal Scheduling Possible?," Operations Research, INFORMS, vol. 60(5), pages 1249-1257, October.
    3. Nikhil Bansal & Bart Kamphorst & Bert Zwart, 2018. "Achievable Performance of Blind Policies in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 949-964, August.
    4. Samuli Aalto & Ziv Scully, 2023. "Minimizing the mean slowdown in the M/G/1 queue," Queueing Systems: Theory and Applications, Springer, vol. 104(3), pages 187-210, August.
    5. Predrag Jelenković & Xiaozhu Kang & Jian Tan, 2009. "Heavy-tailed limits for medium size jobs and comparison scheduling," Annals of Operations Research, Springer, vol. 170(1), pages 133-159, September.

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