Morozov E., Zhukova K.
The overflow probability asymptotics in a single-class retrial system with general retrieve time
// Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2021. Lecture Notes in Computer Science, vol 13144. Springer, Cham, 2021. P. 55–66
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.
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