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On the stability of queues with the dropping function

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  • Andrzej Chydzinski

Abstract

In this paper, the stability of the queueing system with the dropping function is studied. In such system, every incoming job may be dropped randomly, with the probability being a function of the queue length. The main objective of the work is to find an easy to use condition, sufficient for the instability of the system, under assumption of Poisson arrivals and general service time distribution. Such condition is found and proven using a boundary for the dropping function and analysis of the embedded Markov chain. Applicability of the proven condition is demonstrated on several examples of dropping functions. Additionally, its correctness is confirmed using a discrete-event simulator.

Suggested Citation

  • Andrzej Chydzinski, 2021. "On the stability of queues with the dropping function," PLOS ONE, Public Library of Science, vol. 16(11), pages 1-16, November.
    • Handle: RePEc:plo:pone00:0259186
    DOI: 10.1371/journal.pone.0259186
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    References listed on IDEAS

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    1. Ping Wang & Daji Zhu & Xiaohui Lu, 2017. "Active queue management algorithm based on data-driven predictive control," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 64(1), pages 103-111, January.
    2. Lukasz Chrost & Andrzej Chydzinski, 2016. "On the deterministic approach to active queue management," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 63(1), pages 27-44, September.
    3. Pawel Mrozowski & Andrzej Chydzinski, 2018. "Queues with Dropping Functions and Autocorrelated Arrivals," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 97-115, March.
    4. Andrzej Chydzinski & Blazej Adamczyk, 2019. "Queues with the dropping function and general service time," PLOS ONE, Public Library of Science, vol. 14(7), pages 1-21, July.
    5. Ladan Khoshnevisan & Farzad R. Salmasi, 2016. "A robust and high-performance queue management controller for large round trip time networks," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(7), pages 1586-1597, May.
    6. Andrzej Chydzinski & Pawel Mrozowski, 2016. "Queues with Dropping Functions and General Arrival Processes," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-23, March.
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