Efficient Importance Sampling for Monte Carlo Simulation of Multicast Networks

We consider the problem of estimating blocking probabilities in a multicast loss system via simulation, applying the static Monte Carlo method with importance sampling. An approach is introduced where the original estimation problem is first decomposed into independent simpler sub-problems, each roughly corresponding to estimating the blocking probability contribution from a single link. Then we apply importance sampling to solve each sub-problem. The importance sampling distribution is the original distribution conditioned on that the state is in the blocking state region of a single link. Samples can be generated from this distribution using the so called inverse convolution method. Finally, a dynamic control algorithm is used for optimally allocating the samples between different sub-problems. The numerical results demonstrate that the variance reduction obtained with the method is remarkable, between 400 and 36 000 in the considered examples. Keywords—Multicast, loss systems, simulation, Monte Carlo methods, variance reduction, importance sampling.