Sharp estimates and a central limit theorem for the invariant law for a large star-shaped loss network.
An asymptotic behaviour of a star-shaped network is studied. The network is constituted of \(N\) links of capacity \(C\). Calls arrive on the network according to a Poisson process. Each call requires one channel on each of \(L\) distinct links chosen uniformly at random. The call is lost if any of the chosen route is full, else it holds one channel on each of these links for an exponential time, after which it releases the \(L\) channels simultaneously. Arrivals, choices, and holding times are independent. The invariant law for the route occupation process has a semi-explicit expression similar to that for a Gibbs measure. It involves a combinatorial normalizing factor, the partition function, which is very difficult to evaluate. The author studies the large \(N\) limit while keeping the arrival rate per link fixed. The Laplace asymptotic method is used to obtain a sharp asymptotics of the partition function, and to derive the central limit theorem for the empirical measure of the occupancies of the links under the invariant law. A sharp version for the large deviation principle proved in a previous paper is also obtained.
scientific article; zbMATH DE number 2138894
scientific article