In this work, we consider an approximation of the so-called far-end-tail distribution of processes describing quality of service (QoS) performance of queueing systems. This approximation is based on the asymptotic equivalence between the excess distribution over a high threshold and the generalized Pareto distribution, for a wide class of the governing distributions. The numerical results based on the regenerative estimation of a large deviation of the maximal workload over the regeneration cycle, in the queueing system M/G/1 with Pareto service time, are also presented, which verify theoretical results.
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Proceedings of the XXXV International Seminar on Stability Problems for Stochastic Models, Perm, Russia, September 24–28, 2018. Part II.
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Morozov, E.V., Peshkova, I.V. & Rumyantsev, A.S. Far-End-Tail Estimation of Queueing System Performance. J Math Sci 248, 80–91 (2020). https://doi.org/10.1007/s10958-020-04857-3
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DOI: https://doi.org/10.1007/s10958-020-04857-3