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Evènements rares dans les réseaux.

Abstract : In this thesis, we study rare events in communication networks. We first introduce the class of monotone separable networks which will allow us to analyse networks regardless to their dimension. We will in particular apply our theory to (max,plus)-linear networks and to gene! ralized Jackson networks. The first step consists in understanding the dynamic of these networks. We describe their fluid limit and relate it to their stability condition. We construct the stationary version of their state variables. The sample-path study allows us to understand the stochastic behaviour of the network. We compute the asymptotics of the probability of rare events (that tends to 0) and describe "how" these events occur. We show that the behaviour of the network is quite different depending on the stochastic assumptions made on the distribution of the service time. In the case of subexponential distributions, one big service time is responsible for the rare event whereas in the light-tailed case, the rare event is due to many unusually long service times. These heuristics are made precise in the computation of the probability of the given event. We also study thanks to fractional Brownian motion. The impact of long range dependence on the performance of a (max,plus)-linear network.
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Submitted on : Thursday, July 29, 2010 - 4:33:18 PM
Last modification on : Thursday, October 29, 2020 - 3:01:38 PM
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  • HAL Id : pastel-00001536, version 1



Marc Lelarge. Evènements rares dans les réseaux.. Mathématiques [math]. Ecole Polytechnique X, 2005. Français. ⟨pastel-00001536⟩



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