Analyzing an M|M| N Queueing System with Feedback by the Method of Asymptotic Analysis

Abstract

In the paper, we consider a mathematical model for repeated customers in the form of a queuing system with N servers, instant and delayed feedback, and an orbit. It is believed that the orbit size for repeated customers is infinite. The input flow is Poisson. To find the joint probability distribution of the number of occupied servers in the system and the number of customers in the orbit, the asymptotic analysis method is used. The results of a numerical experiment are presented.

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Correspondence to A. Nazarov.

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Translated from Kibernetyka ta Systemnyi Analiz, No. 1, January–February, 2021, pp. 67–76.

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Nazarov, A., Melikov, A., Pavlova, E. et al. Analyzing an M|M| N Queueing System with Feedback by the Method of Asymptotic Analysis. Cybern Syst Anal 57, 57–65 (2021). https://doi.org/10.1007/s10559-021-00329-x

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Keywords

  • multi-server queueing system
  • instant feedback
  • delayed feedback
  • orbit
  • asymptotic
  • analysis method.