A convergence proof for an iterative method for ATM networks

A flow model for evaluating the performance of a network of asynchronous transfer mode (ATM) switches is presented. The performance measures used include the link (nodal) and end-to-end cell loss probabilities as well as the link (nodal) and end-to-end cell delays. In the model, the routing assignments are assumed to be given. The assumed form of routing assignments may be used to represent either virtual circuit or datagram service. Due to the nonlinear relationship between cell losses and offered flows, the flow model is a system of nonlinear equations. The authors develop a sufficient condition for the existence of a unique solution to the nonlinear system of equations. They present an iterative model and prove that it converges to a unique fixed point provided the sufficient condition is satisfied. The unique fixed point corresponds to the unique solution to the flow model