SPATIAL HOMOGENIZATION IN A STOCHASTIC NETWORK WITH MOBILITY

• 成果类型: Article
• 署名作者: Simatos, Florian; Tibi, Danielle
• 署名单位: Inria; Universite Paris Cite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP613
• 发表日期: 2010
• 页码: 312-355
• 关键词: fluid models; CONVERGENCE; equilibria

摘要

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.