Loss networks under diverse routing: the symmetric star network

A highly symmetric loss network is considered, the symmetric star network previously considered by Whitt [12] and Ziedins and Kelly [14]. As the number of links, K, becomes large, the state space for this process also grows, so we consider a functional of the network, one which contains all information relevant to blocking probabilities within the network but which is easier to analyse. We show that this reduced process obeys a functional law of large numbers and a functional central limit theorem, the limit in this latter case being an Ornstein-Uhlenbeck diffusion process. Finally, by considering the network in equilibrium, we are able to prove that the well-known Erlang fixed point approximation for blocking probabilities is correct to within o(K −1/2 ) as K → ∞