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Edge minimality of EDF resource sharing networks

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  • Łukasz Kruk

    (Maria Curie-Skłodowska University)

Abstract

We consider a general real-time network with soft customer deadlines, in which users require service from several shared resources simultaneously. We call the service protocol for such a network edge minimal (locally edge minimal) if it minimizes globally (resp., locally) in time, in a suitable sense, the system resource idleness with respect to customers with lead times not greater than any given threshold value on all the routes of the network. We show that the preemptive Earliest-Deadline-First (EDF) service discipline is edge minimal. Moreover, we characterize the preemptive EDF policy as a protocol making the underlying network locally edge minimal. Our arguments are pathwise, independent on the network topology and requiring very mild assumptions, or even no assumptions, on the model stochastic primitives. Application of our characterization to fluid model analysis for EDF resource sharing networks is also discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:86:y:2017:i:2:d:10.1007_s00186-017-0598-9
    DOI: 10.1007/s00186-017-0598-9
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    References listed on IDEAS

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    1. Heng-Qing Ye & Jihong Ou & Xue-Ming Yuan, 2005. "Stability of Data Networks: Stationary and Bursty Models," Operations Research, INFORMS, vol. 53(1), pages 107-125, February.
    2. 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.
    3. H. Christian Gromoll & Philippe Robert & Bert Zwart, 2008. "Fluid Limits for Processor-Sharing Queues with Impatience," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 375-402, May.
    4. 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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    Cited by:

    1. 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.
    2. Łukasz Kruk, 2020. "Continuity and monotonicity of solutions to a greedy maximization problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(1), pages 33-76, August.

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