Fluctuations for a fully connected loss network with alternate routing

We study a stochastic loss network of switched circuits with alternate routing. The loads of the links form a strongly interacting system which is neither exchangeable nor Markovian. The corresponding BBGKY hierarchy is nontrivial. By refining a random graph representation which gave us propagation of chaos in a previous paper, we show tightness for the fluctuation field and process. We then prove that the accumulation points for the fluctuation processes are continuous semimartingales. We show that the martingale part is Gaussian and unique, characterized by its Doob-Meyer bracket; for this we need to close a hierarchy coming from the simultaneous release of circuits in alternate routing.