Analyzing Product-Form Stochastic Networks Via Factor Graphs and the Sum-Product Algorithm

A large number of stochastic networks including loss networks and certain queueing networks have product-form steady-state probabilities. However, for most practical networks, evaluating the system performance is a difficult task due to the presence of a normalization constant. We propose a new framework based on probabilistic graphical models to tackle this task. Specifically, we use factor graphs to model the stationary distribution of a network. 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 related performance measures such as 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 loss networks with a variety of topologies. The factor graph model also provides a promising approach for analyzing product-form queueing networks.