Calculating the flow level performance of balanced fairness in tree networks

We consider a tree network whose resources are shared by a dynamically varying number of elastic flows. We present an efficient method for calculating performance metrics such as flow throughputs when the resource allocation is balanced fair. The method is based on a recursive algorithm for computing the normalization constant of the stationary distribution. Several examples are worked out. A proof is given for the Pareto efficiency of balanced fairness in tree networks.