Bordenave, Charles (2006) Stochastic analysis of spatial networks. PhD thesis ENS et INRIA, INRIA / ENS, EP/X p.253.
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Alternative Locations: http://www.imprimerie.polytechnique.fr/Theses/Files/Bordenave.pdf
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.
| Item Type: | PhD Thesis (PhD) |
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| Thesis Supervisor: | Baccelli, François |
| Date: | July 2006 |
| Board of examiners: | David, Aldous and Nicholas, Bambos and Sergei, Foss and Jean-François, Le Gall and René, Schott |
| Ecole Doctorale: | ED 447 ECOLE DOCTORALE DE L'ECOLE POLYTECHNIQUE |
| Discipline: | ENS et INRIA |
| Collection (Fonds): | EP/X |
| Institution: | EP/X |
| Department: | INRIA / ENS |
| Subjects: | 1. Mathematics and Applications |
| Uncontrolled Keywords: | Spanning trees, Geometric graphs, Poisson point process, Stability of stochastic process, Communication networks, Arbres couvrants, Graphes géométriques, procesus ponctuel de Poisson, Stabilité de processus stochastique, Réseaux de communication |
| ID Code: | 1902 |
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| Deposited By: | Laurence Vidament |
| Deposited On: | 15 September 2006 |
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