Analysis of Loss Networks with Routing

Abstract : 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 have, in general, reversibility properties so that the explicit expression of their invariant distribution is not known. A heavy traffic limit 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 the limit, the associated rescaled Markov process converges to a deterministic dynamical system with a unique equilibrium point characterized by a non-standard fixed point equation.