Abstract
Main objective of this article is waiting time in M/GI/1 RQ system. We investigate this process by the use of asymptotic analysis method under heavy load condition. As the main result of our research we obtain asymptotic characteristic function of the waiting time distribution. Within the framework of the problem posed, the asymptotic probability distribution of the number of returns of the request to the orbit in the considered RQ system was obtained, and also an analytical expression for the asymptotic conditional characteristic function of the limiting number of returns of the request to the orbit was obtained, which has the form of the characteristic function of exponential distribution with a random parameter, the distribution of which is determined by the value of the limiting number of requests in the orbit that has a gamma distribution.
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Nazarov, A., Samorodova, M.V. (2021). Asymptotic Waiting Time Analysis of a M/GI/1 RQ System. 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_12
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DOI: https://doi.org/10.1007/978-3-030-92507-9_12
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