Analysis of loss networks with routing

Details Analysis of loss networks with routing Analysis of loss networks with routing

2005-12-22

arxiv.org/abs/cs/0512088v4

Annals of Applied Probability 16, 4 (2006) 2007-2026

Computer Science

Networking and Internet Architecture

Published at http://dx.doi.org/10.1214/105051606000000466 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

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.

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