Large deviations at equilibrium for a large star-shaped loss network

We consider a symmetric network composed of N links, each with capacity C. Calls arrive according to a Poisson process, and each call concerns L disti nct links chosen uniformly at random. If each of these links has free capac ity, the call is held for an exponential time; otherwise it is lost. The se miexplicit stationary distribution for this process is similar to a Gibbs m easure: it involves a normalizing factor, the partition function, which is very difficult to evaluate. We let N go to infinity and keep fixed the rate of call attempts concerning any link. We use asymptotic combinatorics and recent techniques involving the law of large numbers to obtain the asymptot ic equivalent fur the logarithm of the partition function and then the larg e deviation principle for the empirical measure of the occupancies of the l inks. We give an explicit formula for the rate function and examine its pro perties.