Rare event probabilities in stochastic networks

The paper is dealing with estimation of rare event probabilities in stochastic networks. The well known variance reduction technique, called Importance Sampling (IS) is an effective tool for doing this. The main idea of IS is to simulate the random system under a modified set of parameters, so as to make the occurrence of the rare event more likely. The major problem of the IS technique is that the optimal modified parameters, called reference parameters to be used in IS are usually very difficult to obtain. Rubinstein (1997) developed the Cross Entropy (CE) method for the solution of this problem of IS technique and then he and his collaborators applied this for estimation of rare event probabilities in stochastic networks with exponential distribution [see De Boer et al. (2005)]. In this paper, we test this simulation technique also for medium sized stochastic networks and compare its effectiveness to the simple crude Monte Carlo (CMC) simulation.