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Heavy traffic analysis for single-server SRPT and LRPT queues via EDF diffusion limits

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  • Łukasz Kruk

    (Maria Curie-Skłodowska University)

Abstract

Extending the results of Kruk (Queueing theory and network applications. QTNA 2019. Lecture notes in computer science, vol 11688. Springer, Cham, pp 263–275, 2019), we derive heavy traffic limit theorems for a single server, single customer class queue in which the server uses the Shortest Remaining Processing Time (SRPT) policy from heavy traffic limits for the corresponding Earliest Deadline First queueing systems. Our analysis allows for correlated customer inter-arrival and service times and heavy-tailed inter-arrival and service time distributions, as long as the corresponding stochastic primitive processes converge weakly to continuous limits under heavy traffic scaling. Our approach yields simple, concise justifications and new insights for SRPT heavy traffic limit theorems of Gromoll et al. (Stoch Syst 1(1):1–16, 2011). Corresponding results for the longest remaining processing time policy are also provided.

Suggested Citation

  • Łukasz Kruk, 2022. "Heavy traffic analysis for single-server SRPT and LRPT queues via EDF diffusion limits," Annals of Operations Research, Springer, vol. 310(2), pages 411-429, March.
    • Handle: RePEc:spr:annopr:v:310:y:2022:i:2:d:10.1007_s10479-021-03929-0
    DOI: 10.1007/s10479-021-03929-0
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Thomas Kittsteiner & Benny Moldovanu, 2005. "Priority Auctions and Queue Disciplines That Depend on Processing Time," Management Science, INFORMS, vol. 51(2), pages 236-248, February.
    4. Linus E. Schrage & Louis W. Miller, 1966. "The Queue M / G /1 with the Shortest Remaining Processing Time Discipline," Operations Research, INFORMS, vol. 14(4), pages 670-684, August.
    5. Linus Schrage, 1968. "Letter to the Editor—A Proof of the Optimality of the Shortest Remaining Processing Time Discipline," Operations Research, INFORMS, vol. 16(3), pages 687-690, June.
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