This paper has two parts: Firstly, we investigate today's ATM network, especially the most load NFS applications. Secondly, we propose a fast simulation based on fractional ARIMA processes and an importance sampling scheme. In our collected data, we have found the traffic characteristics of today's ATM network present both long range dependence (LRD) and short range dependence (SRD) structures. Because of the strong SRD and LRD of the empirical traces, models which can present both LRD and SRD are necessary to simulate the traffic of today's networks. However, traditional Monte Carlo simulations with long range dependent structure make the cost of the computation very large and for CLP (cell loss probability)<10-9 traditional Monte Carlo simulations are almost impossible to achieve it. The proposed fast ARIMA simulation based on importance sampling efficient to simulate the queuing performance with self-similar inputs which exhibit both SRD and LRD properties.