Réseaux Stochastiques et Algorithmes

Abstract : In this document, scaling methods used to analyze stochastic networks are presented. Ths first class of scaling investigated is the fluid limit regime, Markov jump processes are scaled in time and space in order to get a kind of functional law of large numbers for these processes. Several aspects of these scalings are discussed: non-deterministic fluid limits and the infinite dimensional case when the Markov processes are string valued. Studies concerning large networks with either a large number of nodes (thermodynamic limit regime) or with links of large capacity (Kelly's scaling) are also discussed.
The mathematical studies of several distributed algorithms used in these stochastic networks are presented. The emphasis is on the probabilistic methods used in a context which is not necessarily probabilistic. It is shown in particular how they can extend and simplify the results previously known in this domain.
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Habilitation à diriger des recherches
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Contributor : Philippe Robert <>
Submitted on : Friday, August 10, 2007 - 11:33:56 AM
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  • HAL Id : tel-00166813, version 1


Philippe Robert. Réseaux Stochastiques et Algorithmes. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2006. ⟨tel-00166813⟩



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