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Analyse stochastique des réseaux spatiaux.

Charles Bordenave 1 
1 TREC - Theory of networks and communications
DI-ENS - Département d'informatique - ENS Paris, Inria Paris-Rocquencourt
Abstract : In a spatial network, the vertices of the network have a position in the Euclidean space. The interactions in the network are determined by the underlying geometry of the vertices. Communication networks is large field of application and a source of new models for this topic of research. The thesis tackles three topics in different fields. The first concerns the study of a class of geometric spanning trees of Poisson point processes. Thes work deals in particular with the small world phenomenon, the radial spanning tree and the minimal spanning tree. Another topic concerns the stability of stochastic processes of queueing networks where the queues have spatial interactions. The last part of the thesis deals with themes related to stochastic geometry: a study of the dead leaves model and a work on the sensitivity of functionals of Poisson point processes.
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Submitted on : Wednesday, July 28, 2010 - 2:43:06 PM
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  • HAL Id : pastel-00001902, version 1



Charles Bordenave. Analyse stochastique des réseaux spatiaux.. Analyse fonctionnelle [math.FA]. Ecole Polytechnique X, 2006. Français. ⟨pastel-00001902⟩



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