Abstract
In this paper we study the extreme behavior of waiting time in steady-state GI/G/1 systems with Exponential-Pareto service times. We show that this distribution belongs to the subclass of subexponential distributions, that allows to apply known tail asymptotic for stationary waiting times via the equilibrium distribution of service times. We propose the expressions for the normalizing constants and derive the limiting distribution of waiting time maxima (Frechet-type distribution). Simulation results show that approximation by Frechet-type distribution works well for GI/G/2 systems as well.
The publication has been prepared with the support of Russian Science Foundation according to the research project No. 21-71-10135, https://rscf.ru/en/project/21-71-10135/..
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Peshkova, I., Golovin, A., Maltseva, M. (2023). On Waiting Time Maxima in Queues with Exponential-Pareto Service Times. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks. DCCN 2022. Communications in Computer and Information Science, vol 1748. Springer, Cham. https://doi.org/10.1007/978-3-031-30648-8_12
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