Calculating blocking probabilities for loss networks based on probabilistic graphical models

Loss networks are a class of resource-sharing models which provide a powerful tool to the analysis and design of many communications and networking systems. For most loss networks of practical interest calculating the exact blocking probabilities is a difficult task. In this paper we present a new framework based on probabilistic graphical models to tackle this task. Specifically, we propose to use factor graphs to model the stationary distribution of product-form loss networks. We also propose to use the sum-product algorithm to compute the marginal distributions and the blocking probabilities of all call classes. Through extensive numerical experiments we show that the sum-product algorithm returns very accurate blocking probabilities and greatly outperforms the reduced load approximation for both single-service and multiservice loss networks with a variety of topologies. In addition, the sum-product algorithm converges very fast and can be implemented in a distributed way