A simple upper bound for blocking probabilities in large multi-rate loss networks

We consider large loss networks with fixed routing and multi-rate traffic. We use the Laplace method and standard results of multidimensional Gaussian distribution to obtain the upper bounds for the blocking probabilities of new calls under uniform light loading conditions. This is the loading regime of interest for many practical applications such as admission control in ATM networks. The main advantage of our approach is that the complexity does not scale with the capacity of the system, so computation are extremely rapid in any case. We verify our method on a small network example. Comparison with simulation results show that we get good upper bounds.