Abstract
We consider the logarithmic asymptotics of the large deviation probability in a single-server queue with Poisson input, where server, after completion of service, seeks a customer in a virtual orbit (retrial customer) for the next service, unless new arrival captures server. This system is described by a regenerative process, and under stability assumption, the logarithmic asymptotics of the stationary probability that the number of the customers in the system reaches a high threshold within a regeneration cycle is found. Some examples are given for particular retrieval time distributions.
The research is supported by the Russian Foundation for Basic Research, project No. 19-07-00303.
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Morozov, E., Zhukova, K. (2021). The Overflow Probability Asymptotics in a Single-Class Retrial System with General Retrieve Time. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2021. Lecture Notes in Computer Science(), vol 13144. Springer, Cham. https://doi.org/10.1007/978-3-030-92507-9_6
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