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.
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Acknowledgements
The authors are very grateful to the reviewers for their valuable comments and suggestions which improved the quality and the presentation of the paper. The publication was financially supported by the Ministry of Education and Science of the Russian Federation (The Agreement Number 02.a03.21.0008). The work of Tamás Bérczes was supported in part by the project EFOP-3.6.2-16-2017-00015 supported by the European Union, co-financed by the European Social Fund.
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Nazarov, A., Sztrik, J., Kvach, A. et al. Asymptotic analysis of finite-source M/M/1 retrial queueing system with collisions and server subject to breakdowns and repairs. Ann Oper Res 277, 213–229 (2019). https://doi.org/10.1007/s10479-018-2894-z
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DOI: https://doi.org/10.1007/s10479-018-2894-z