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Queues with Dropping Functions and General Arrival Processes

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  • Andrzej Chydzinski
  • Pawel Mrozowski

Abstract

In a queueing system with the dropping function the arriving customer can be denied service (dropped) with the probability that is a function of the queue length at the time of arrival of this customer. The potential applicability of such mechanism is very wide due to the fact that by choosing the shape of this function one can easily manipulate several performance characteristics of the queueing system. In this paper we carry out analysis of the queueing system with the dropping function and a very general model of arrival process—the model which includes batch arrivals and the interarrival time autocorrelation, and allows for fitting the actual shape of the interarrival time distribution and its moments. For such a system we obtain formulas for the distribution of the queue length and the overall customer loss ratio. The analytical results are accompanied with numerical examples computed for several dropping functions.

Suggested Citation

  • 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.
    • Handle: RePEc:plo:pone00:0150702
    DOI: 10.1371/journal.pone.0150702
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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. 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.
    2. Chydzinski, Andrzej & Adamczyk, Blazej, 2020. "Response time of the queue with the dropping function," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    3. Chydzinski, Andrzej, 2022. "Per-flow structure of losses in a finite-buffer queue," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    4. 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.
    5. 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.
    6. Chanintorn Jittawiriyanukoon & Vilasinee Srisarkun, 2020. "Cost Minimization for Unstable Concurrent Products in Multi-stage Production Line Using Queueing Analysis," International Journal of Economics & Business Administration (IJEBA), International Journal of Economics & Business Administration (IJEBA), vol. 0(1), pages 230-238.
    7. 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.

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