Abstract
We consider retrial queue with Markov-modulated Poisson input process and exponential probability distribution of service durations. The object of our research is output flow of the system. We use asymptotic analysis method under low rate of retrials limit condition to obtain probability distribution of the number of served customers at the moment t. The obtained formulae has explicit expression and contains matrix exponential. Furthermore, we show that the output belongs to the class of Markovian arrival processes.
The reported study was funded by RFBR according to the research project No 18-01-00277.
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Lapatin, I., Nazarov, A. (2019). Asymptotic Analysis of the Output Process in Retrial Queue with Markov-Modulated Poisson Input Under Low Rate of Retrials Condition. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2019. Communications in Computer and Information Science, vol 1141. Springer, Cham. https://doi.org/10.1007/978-3-030-36625-4_25
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