Abstract
We consider a tandem queueing system consisting of two stations. The input flow at the single-server first station is described by a BMAP (batch Markovian arrival process). If a customer from this flow meets the busy server, it goes to the orbit of infinite size and tries its luck later on in exponentially distributed random time. The service time distribution at the first station is assumed to be semi-Markovian. After service at the first station a customer proceeds to the second station which is described by a multi-server queue without a buffer. The service time by the server of the second station is exponentially distributed. We derive the condition for the stable operation of the system and determine the stationary distribution of the system states. Some key performance measures are calculated and illustrative numerical results are presented.
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Acknowledgments
This work has been financially supported by the Russian Science Foundation and the Department of Science and Technology (India) via grant No 16-49-02021 (INT/RUS/RSF/16) for the joint research project by the V.A. Trapeznikov Institute of Control Sciences and the CMS College Kottayam.
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Klimenok, V., Dudina, O., Vishnevsky, V., Samouylov, K. (2017). Retrial Tandem Queue with BMAP-Input and Semi-Markovian Service Process. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2017. Communications in Computer and Information Science, vol 700. Springer, Cham. https://doi.org/10.1007/978-3-319-66836-9_14
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DOI: https://doi.org/10.1007/978-3-319-66836-9_14
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