A Method of Moments for the Analysis of a Switched Communication Network's Performance

Abstract

The proposed method of moments is an approximation scheme consisting of a simple iteration algorithm which converges to the network's point-to-point blocking probabilities. The following are the key steps. First, the total traffic stream (obtained by combining the individually offered overflow and Poissonian streams under the assumption of independence) offered to any trunk (channel) group in the network is approximated by a renewal process of a specific type.The total overflow from the trunk group is obtained using the generalized Erlang loss function. After suitably apportioning the lost load among the individually offered streams, each stream's blocking on the trunk group is computed. Finally, a point-to-point probability linear graph is constructed from the alternate routing scheme and the point-point-to-point blocking is computed assuming independent blocking in the links. Numerical results are presented for a simple three-node network with Poissonian point-to-point demand and comparison is made between the three-moment methods and simulation. The results indicate that the three-moment method is sufficiently accurate for engineering purposes.