A technique for the fast simulation of broadband communications systems is proposed, which is based on regenerative Importance Sampling techniques. Our algorithm is applicable to estimate the probability of rare events when modeling the offered traffic using Fractional Stable Noise (FSN) processes (including Fractional Brownian Noise as a particular case), which have been recently proved to be able to capture both the long-range dependence and the burstiness of today's aggregate network traffic. An exact description of FSN processes is given, as well as an approximation that allows for the application of Importance Sampling techniques. The results obtained for a simple example are also included.