Abstract
In the paper, the retrial queueing system of M/M/1 type with negative calls is considered. The system of Kolmogorov equations for the system states process is derived. The method of asymptotic analysis is proposed for the system solving under the heavy load condition. The theorem about the gamma form of the asymptotic characteristic function of the number of calls in the orbit is formulated and proved. During the study, the expression for the system throughput is obtained. Also the exact characteristic function is derived. Numerical examples of comparison asymptotic and exact distributions are presented. The conclusion about the asymptotic method application area is made.
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The publication was financially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number 02.a03.21.0008) and by RFBR according to the research project No.16-31-00292mol-a.
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Farkhadov, M., Fedorova, E. (2017). Retrial Queue M/M/1 with Negative Calls Under Heavy Load Condition. 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_34
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DOI: https://doi.org/10.1007/978-3-319-66836-9_34
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