# Spatial homogenization in a stochastic network with mobility

Abstract : A stochastic model for a mobile network is studied. Users enter the network, and then perform independent Markovian routes between nodes, where they receive service according to the Processor-Sharing policy. Once their service requirement is satisfied, they leave the system. The stability region is identified via a fluid limit approach, and strongly relies on a spatial homogenization'' property: At the fluid level, customers are instantaneously distributed across the network according to the stationary distribution of their Markovian dynamics and stay distributed as such as long as the network is not empty. In the unstable regime, spatial homogenization almost surely holds asymptotically as time goes to infinity (on the normal scale), telling how the system fills up. One of the technical achievements of the paper is the construction of a family of martingales associated to the multidimensional process of interest, which makes it possible to get crucial estimates for certain exit times.
Keywords :
Type de document :
Pré-publication, Document de travail
2008
Domaine :

https://hal.archives-ouvertes.fr/hal-00293988
Contributeur : Florian Simatos <>
Soumis le : mardi 8 juillet 2008 - 11:20:41
Dernière modification le : mercredi 12 octobre 2016 - 01:23:51
Document(s) archivé(s) le : vendredi 28 mai 2010 - 21:33:30

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### Identifiants

• HAL Id : hal-00293988, version 1
• ARXIV : 0807.1205

### Citation

Florian Simatos, Danielle Tibi. Spatial homogenization in a stochastic network with mobility. 2008. <hal-00293988>

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