Asymptotic 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 Tamás Bérczes ()
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Anatoly Nazarov: National Research Tomsk State University
János Sztrik: University of Debrecen
Anna Kvach: National Research Tomsk State University
Tamás Bérczes: University of Debrecen

Annals of Operations Research, 2019, vol. 277, issue 2, No 5, 213-229

Abstract: Abstract The aim of the present paper is to investigate a finite-source M/M/1 retrial queuing system with collision of the 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 while the primary request generation rate, retrial rate tend to zero and service rate, failure rates, repair rate are fixed. It is proved that in steady state the limiting distribution of the centered and normalized number of customers in the system (orbit and service) follows a normal law with given parameters. The novelty of this investigation is the introduction of failure and repair of the service. Approximations of prelimiting distribution by asymptotic one are obtained and several illustrative examples show the accuracy and range of applicability of the proposed 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: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10479-018-2894-z

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