Solving product form stochastic networks with Monte Carlo summation

Multiclass queuing networks and stochastic loss networks often give rise to a product form solution for their equilibrium probabilities, but the product form solution typically involves a normalization constant calling for a multidimensional summation over an astronomical number of states. The authors propose the application of Monte Carlo summation to the problem of determining the normalization constant and related performance measures. It is shown that if the proper sampling technique is used then the computational effort of Monte Carlo summation is independent of link capacities for loss networks. The application of importance sampling and antithetic variates is then discussed. Importance sampling is shown to give significant variance reduction for a multirate loss network example.