Asymptotic Analysis of Finite-Source M/GI/1 Retrial Queueing Systems with Collisions and Server Subject to Breakdowns and Repairs

Anatoly Nazarov (), János Sztrik (), Anna Kvach () and Ádám Tóth ()
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Anatoly Nazarov: National Research Tomsk State University
János Sztrik: University of Debrecen, Doctoral School of Informatics
Anna Kvach: National Research Tomsk State University
Ádám Tóth: University of Debrecen, Doctoral School of Informatics

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 3, 1503-1518

Abstract: Abstract This paper deals with a retrial queuing system with a finite number of sources and collision of the customers, where the server is subject to random breakdowns and repairs depending on whether it is idle or busy. A significant difference of this system from the previous ones is that the service time is assumed to follow a general distribution while the server’s lifetime and repair time is supposed to be exponentially distributed. The considered system is investigated by the method of asymptotic analysis under the condition of an unlimited growing number of sources. As a result, it is proved that the limiting probability distribution of the number of customers in the system follows a Gaussian distribution with given parameters. The Gaussian approximation and the estimations obtained by stochastic simulations of the prelimit probability distribution are compared to each other and measured by the Kolmogorov distance. Several examples are treated and figures show the accuracy and area of applicability of the proposed asymptotic method.

Keywords: Finite-source queueing system; Retrial queue; Collision; Server breakdowns and repairs; Asymptotic analysis; Limiting distribution; Approximation of distributions; Accuracy and area of applicability of approximations; 60K25; 68M20; 90B22 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-021-09870-w

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