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Local edge minimality of SRPT networks with shared resources

Author

Listed:
  • Łukasz Kruk

    (Maria Curie-Skłodowska University)

  • Robert Gieroba

    (Maria Curie-Skłodowska University)

Abstract

We consider a general network with arbitrary topology and node capacities, in which users require simultaneous service from a number of shared resources. We study pathwise minimality of the shortest remaining processing time protocol with respect to suitable criteria based on the system’s cumulative transmission times of flows with residual service requirements not greater than any threshold value on the network routes. No distributional assumptions are made on the underlying stochastic primitives.

Suggested Citation

  • Łukasz Kruk & Robert Gieroba, 2022. "Local edge minimality of SRPT networks with shared resources," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(3), pages 459-492, December.
    • Handle: RePEc:spr:mathme:v:96:y:2022:i:3:d:10.1007_s00186-022-00801-0
    DOI: 10.1007/s00186-022-00801-0
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    References listed on IDEAS

    as
    1. Jing Dong & Rouba Ibrahim, 2021. "SRPT Scheduling Discipline in Many-Server Queues with Impatient Customers," Management Science, INFORMS, vol. 67(12), pages 7708-7718, December.
    2. Łukasz Kruk, 2017. "Edge minimality of EDF resource sharing networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 331-366, October.
    3. Łukasz Kruk, 2016. "Minimality of EDF networks with resource sharing," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(2), pages 259-283, October.
    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. 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.
    6. 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.
    7. Łukasz Kruk & Tymoteusz Chojecki, 2022. "Instability of SRPT, SERPT and SJF multiclass queueing networks," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 57-92, June.
    8. Samuli Aalto & Urtzi Ayesta, 2009. "SRPT applied to bandwidth-sharing networks," Annals of Operations Research, Springer, vol. 170(1), pages 3-19, September.
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