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 36000 in the considered examples