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Queues with Dropping Functions and Autocorrelated Arrivals

Author

Listed:
  • Pawel Mrozowski

    (Avio Polska Sp. z o.o.)

  • Andrzej Chydzinski

    (Silesian University of Technology)

Abstract

We present an analysis of the queueing system in which arriving jobs are dropped with probability depending on the queue size. The arrivals are assumed to be autocorrelated and they are modeled by the Markov-modulated Poisson process. Both transient and stationary distributions of the queue size, as well as the system loss ratio and throughput are obtained. The analytical results are accompanied with numerical examples based on the autocorrelated traffic recorded in an IP computer network.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:1:d:10.1007_s11009-016-9534-3
    DOI: 10.1007/s11009-016-9534-3
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    References listed on IDEAS

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    1. Ryden, Tobias, 1996. "An EM algorithm for estimation in Markov-modulated Poisson processes," Computational Statistics & Data Analysis, Elsevier, vol. 21(4), pages 431-447, April.
    2. António Pacheco & Helena Ribeiro, 2008. "Consecutive customer losses in oscillating GI X /M//n systems with state dependent services rates," Annals of Operations Research, Springer, vol. 162(1), pages 143-158, September.
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    Cited by:

    1. Marek Barczyk & Andrzej Chydzinski, 2022. "AQM based on the queue length: A real-network study," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-21, February.
    2. 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.
    3. Konovalov, Mikhail & Razumchik, Rostislav, 2023. "Finite capacity single-server queue with Poisson input, general service and delayed renovation," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1075-1083.
    4. Chydzinski, Andrzej & Adamczyk, Blazej, 2020. "Response time of the queue with the dropping function," Applied Mathematics and Computation, Elsevier, vol. 377(C).

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