Analysis of loss networks with routing

• 成果类型: Article
• 署名作者: Antunes, Nelson; Fricker, Christine; Robert, Philippe; Tibi, Danielle
• 署名单位: Universidade do Algarve; Universite Paris Cite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000466
• 发表日期: 2006
• 页码: 2007-2026
• 关键词: model

摘要

This paper analyzes stochastic networks consisting of finite capacity nodes with different classes of requests which move according to some routing policy. The Markov processes describing these networks do not, in general, have reversibility properties, so the explicit expression of their invariant distribution is not known. Kelly's limiting regime is considered: the arrival rates of calls as well as the capacities of the nodes are proportional to a factor going to infinity. It is proved that, in limit, the associated rescaled Markov process converges to a deterministic dynamical system with a unique equilibrium point characterized by a nonstandard fixed point equation.