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Retrial queue \(M/M/1\) with negative calls under heavy load condition. (English) Zbl 1459.60187
Vishnevskiy, Vladimir M. (ed.) et al., Distributed computer and communication networks. 20th international conference, DCCN 2017, Moscow, Russia, September 25–29, 2017. Proceedings. Cham: Springer. Commun. Comput. Inf. Sci. 700, 406-416 (2017).
Summary: 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.
For the entire collection see [Zbl 1393.68018].

60K25 Queueing theory (aspects of probability theory)
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