Performance Evaluation of Loss Networks via Factor Graphs and the Sum-Product Algorithm

Loss networks provide a powerful tool for the analysis and design of many communication and networking systems. It is well known that a large number of loss networks have product-form steady-state probabilities. However, for most networks of practical interest, evaluating the system performance is a difficult task due to the presence of a normalization constant. 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 a network. Based on the factor graph model, we can easily derive recursive formulas for symmetric networks. Most importantly, for networks with arbitrary topology, we can apply efficient message-passing algorithms like the sum-product algorithm to compute the exact or approximate marginal distributions of all state variables and the related performance measures such as call blocking probabilities. 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.