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Instability of SRPT, SERPT and SJF multiclass queueing networks

Author

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  • Łukasz Kruk

    (Maria Curie- Skłodowska University)

  • Tymoteusz Chojecki

    (Maria Curie- Skłodowska University)

Abstract

We provide two examples of strictly subcritical multiclass queueing networks which are unstable under the shortest remaining processing time (SRPT) service protocol. Both of them are reentrant lines with two servers and eight customer classes. The customer service times in our first system are deterministic, yielding an example of an unstable shortest remaining expected processing time (SERPT) network. In the second one, the service times in one customer class are randomized. Both our examples show also system instability under the shortest job first (SJF) discipline. A simulation study of robustness of our results with respect to changes in the customer interarrival and service times is also provided. Our results indicate that size-based service policies may not use the available resources efficiently in a multiserver network setting and in fact cause instability effects. This is in sharp contrast with their satisfactory performance for single-server queues.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:queues:v:101:y:2022:i:1:d:10.1007_s11134-021-09733-8
    DOI: 10.1007/s11134-021-09733-8
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    References listed on IDEAS

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    1. J. G. Dai & G. Weiss, 1996. "Stability and Instability of Fluid Models for Reentrant Lines," Mathematics of Operations Research, INFORMS, vol. 21(1), pages 115-134, February.
    2. Samuli Aalto & Urtzi Ayesta, 2009. "SRPT applied to bandwidth-sharing networks," Annals of Operations Research, Springer, vol. 170(1), pages 3-19, September.
    3. Łukasz Kruk, 2018. "Stability of linear EDF networks with resource sharing," Queueing Systems: Theory and Applications, Springer, vol. 88(1), pages 167-203, February.
    4. 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.
    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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    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.

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