Analysis of loss networks with routing

Antunes, Nelson; Fricker, Christine; Robert, Philippe; Tibi, Danielle

http://hdl.handle.net/10400.1/11814

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Resumo(s)

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.

Palavras-chave

Model Stochastic networks Heavy traffic limits Asymptotic dynamical systems Fixed point equations

URI

http://hdl.handle.net/10400.1/11814

Editora

Institute of Mathematical Statistics

DOI

10.1214/105051606000000466

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