Asymptotic sojourn time analysis of finite-source M/M/1 retrial queueing system 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
Anna Kvach: National Research Tomsk State University
Ádám Tóth: University of Debrecen

Annals of Operations Research, 2020, vol. 288, issue 1, No 16, 417-434

Abstract: Abstract The aim of the present paper is to investigate the steady-state distribution of response and waiting time in a finite-source M / M / 1 retrial queuing system with collision of customers where the server is subjects to random breakdowns and repairs depending on whether it is idle or busy. An asymptotic method is applied under the condition that the number of sources tends to infinity, the primary request generation rate, retrial rate tend to zero while service rate, failure rates, repair rate are fixed. As the result of the analysis it is shown that the steady-state probability distribution of the number of transitions/retrials of the customer into the orbit is geometric with a given parameter, and the normalized sojourn time of the customer in the system follows a generalized exponential distribution. It is also proved that the limiting distributions of the normalized sojourn time of the customer in the system and the normalized sojourn/waiting time of the customer in the orbit coincide. The novelty of this investigation is the introduction of failure and repair of the server. Approximations of prelimit distributions obtained with the help of stochastic simulation by asymptotic one are considered and several illustrative examples show the accuracy and range 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 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10479-019-03463-0

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