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Exact Tail Asymptotics of a Queue with LRD Input Traffic

M. Lelarge 1, 2, 3 A. Villani 4
2 DYOGENE - Dynamics of Geometric Networks
CNRS - Centre National de la Recherche Scientifique : UMR8548, Inria Paris-Rocquencourt, DI-ENS - Département d'informatique de l'École normale supérieure
Abstract : In this work we compute the exact tail asymptotics of the stationary workload W, associated to a discretetime single server queue, with constant release rate, infinite buffer capacity, and with M/G/∞ input traffic exhibiting long-range dependence. We choose a regularly varying distribution with parameter α > 1 for the general distribution G. We show that the exact asymptotics of the workload is a specific regularly varying function under some assumptions on the parameters.
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https://hal.inria.fr/hal-01090582
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Submitted on : Wednesday, December 3, 2014 - 5:33:41 PM
Last modification on : Friday, October 15, 2021 - 1:40:29 PM

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M. Lelarge, A. Villani. Exact Tail Asymptotics of a Queue with LRD Input Traffic. International Journal of Applied Mathematical Sciences, Research India Publications, 2014, 196 (1), pp.12. ⟨10.1007/s10958-013-1636-7⟩. ⟨hal-01090582⟩

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