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Technical Note—A New Proof of the Optimality of the Shortest Remaining Processing Time Discipline

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  • Donald R. Smith

    (Columbia University, New York, New York)

Abstract

We present a new proof of the fact that for a work-conserving queue, the queuing discipline that always serves a job with the shortest remaining processing time minimizes the number of jobs in the system. A key feature of the proof is a definition of work dominance, allowing comparison of two systems based on the remaining service times of jobs present. Work dominance is both necessary and sufficient for stochastic comparison of the number of jobs present under identical but arbitrary arrival processes.

Suggested Citation

  • Donald R. Smith, 1978. "Technical Note—A New Proof of the Optimality of the Shortest Remaining Processing Time Discipline," Operations Research, INFORMS, vol. 26(1), pages 197-199, February.
    • Handle: RePEc:inm:oropre:v:26:y:1978:i:1:p:197-199
    DOI: 10.1287/opre.26.1.197
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    Cited by:

    1. Łukasz Kruk & Ewa Sokołowska, 2016. "Fluid Limits for Multiple-Input Shortest Remaining Processing Time Queues," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1055-1092, August.
    2. Samuli Aalto & Ziv Scully, 2022. "On the Gittins index for multistage jobs," Queueing Systems: Theory and Applications, Springer, vol. 102(3), pages 353-371, December.
    3. 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.
    4. Samuli Aalto & Urtzi Ayesta, 2009. "SRPT applied to bandwidth-sharing networks," Annals of Operations Research, Springer, vol. 170(1), pages 3-19, September.
    5. Chen, Rubing & Yuan, Jinjiang & Ng, C.T. & Cheng, T.C.E., 2021. "Single-machine hierarchical scheduling with release dates and preemption to minimize the total completion time and a regular criterion," European Journal of Operational Research, Elsevier, vol. 293(1), pages 79-92.
    6. Yonatan Shadmi, 2022. "Fluid limits for shortest job first with aging," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 93-112, June.
    7. Jin Xu & Natarajan Gautam, 2020. "On competitive analysis for polling systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(6), pages 404-419, September.

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