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Burst ratio for a versatile traffic model

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  • Andrzej Chydzinski

Abstract

We deal with a finite-buffer queue, in which arriving jobs are subject to loss due to buffer overflows. The burst ratio parameter, which reflects the tendency of losses to form long series, is studied in detail. Perhaps the most versatile model of the arrival stream is used, i.e. the batch Markovian arrival process (BMAP). Among other things, it enables modeling the interarrival time density function, the interarrival time autocorrelation function and batch arrivals. The main contribution in an exact formula for the burst ratio in a queue with BMAP arrivals and arbitrary service time distribution. The formula is presented in an explicite, ready-to-use form. Additionally, the impact of various system parameters on the burst ratio is demonstrated in numerical examples. The primary application area of the results is computer networking, where the complex nature of traffic has a deep impact on the burst ratio. However, due to the versatile arrival model, the results can be applied in other fields as well.

Suggested Citation

  • Andrzej Chydzinski, 2022. "Burst ratio for a versatile traffic model," PLOS ONE, Public Library of Science, vol. 17(8), pages 1-19, August.
    • Handle: RePEc:plo:pone00:0272263
    DOI: 10.1371/journal.pone.0272263
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    References listed on IDEAS

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    1. A. D. Banik & M. L. Chaudhry, 2017. "Efficient Computational Analysis of Stationary Probabilities for the Queueing System BMAP / G /1/ N With or Without Vacation(s)," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 140-151, February.
    2. Andrzej Chydzinski & Dominik Samociuk, 2019. "Burst ratio in a single-server queue," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 70(2), pages 263-276, February.
    3. 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.
    4. 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.
    5. Chydzinski, Andrzej & Samociuk, Dominik & Adamczyk, Blazej, 2018. "Burst ratio in the finite-buffer queue with batch Poisson arrivals," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 225-238.
    6. Lothar Breuer, 2002. "An EM Algorithm for Batch Markovian Arrival Processes and its Comparison to a Simpler Estimation Procedure," Annals of Operations Research, Springer, vol. 112(1), pages 123-138, April.
    7. Chydzinski, Andrzej, 2022. "On the structure of data losses induced by an overflowed buffer," Applied Mathematics and Computation, Elsevier, vol. 415(C).
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