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Fluid limits for shortest job first with aging

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  • Yonatan Shadmi

    (Technion-Israel Institute of Technology)

Abstract

We investigate fluid scaling of single-server queues operating under a version of shortest job first (SJF) where the priority level undergoes aging. That is, a job’s priority level is initialized by its size and varies smoothly in time according to an ordinary differential equation. Linear and exponential aging rules are special cases of this model. This policy can be regarded as an interpolation between FIFO and SJF. We use the measure-valued Skorokhod map to characterize the fluid model and establish convergence under fluid scale. We treat in detail examples of linear and exponential aging rules and provide a performance criterion based on our main result.

Suggested Citation

  • Yonatan Shadmi, 2022. "Fluid limits for shortest job first with aging," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 93-112, June.
    • Handle: RePEc:spr:queues:v:101:y:2022:i:1:d:10.1007_s11134-021-09723-w
    DOI: 10.1007/s11134-021-09723-w
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    References listed on IDEAS

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    1. Atar, Rami & Biswas, Anup & Kaspi, Haya, 2018. "Law of large numbers for the many-server earliest-deadline-first queue," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2270-2296.
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    6. Douglas G. Down & H. Christian Gromoll & Amber L. Puha, 2009. "Fluid Limits for Shortest Remaining Processing Time Queues," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 880-911, November.
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    Cited by:

    1. Atar, Rami & Shadmi, Yonatan, 2023. "Fluid limits for earliest-deadline-first networks," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 279-307.

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