Propagation of chaos for a fully connected loss network with alternate routing

We study a stochastic loss network of switched circuits with alternate routing. The processes of interest will be the loads of the links, forming a strongly interacting system which is neither exchangeable nor Markovian. We consider interaction graphs representing the past history of a collection of links and prove their convergence to a limit tree, using the notion of chain reactions. Thus we prove a propagation of chaos result in variation norm for the laws of the whole sample paths, for general initial conditions, and in the i.i.d. case we have speeds of convergence.