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Response time of the queue with the dropping function

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  • Chydzinski, Andrzej
  • Adamczyk, Blazej

Abstract

In many active queue management algorithms, the dropping function, which associates the probability of dropping a packet with the buffer occupancy, is used. Several different forms of the dropping function has been considered so far, from a simple linear one, to the newest three-range polynomials. In this paper, an analysis of the response time of the queue with the dropping function is presented. In particular, theorems on the distribution of the response time and its average value and variance are proven. The assumed model of the queue is general – it allows arbitrary form of the dropping function, arbitrary form of the service time distribution and infinite buffer. Theoretical results are illustrated with numerical results for five popular types of dropping functions.

Suggested Citation

  • Chydzinski, Andrzej & Adamczyk, Blazej, 2020. "Response time of the queue with the dropping function," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    • Handle: RePEc:eee:apmaco:v:377:y:2020:i:c:s0096300320301338
    DOI: 10.1016/j.amc.2020.125164
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    References listed on IDEAS

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    1. 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.
    2. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

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