Modelling and simulation of fractional ARIMA processes based on importance sampling

Multimedia services will be the major loading factor of the future high speed networks. Recent studies present that many applications exhibit long range dependence(LRD). Existing analytical results based on Fractional Gaussian Noise and large deviation theory are valid only under steady-state and very large buffer size conditions. However, theoretical approach to obtain transient queuing behaviour for small buffer size is now intractable. The approach in this paper is based on f-ARIMA process and importance sampling technique to study certain rare events such as cell losses with very small probability of occurrence. It can present the transient queuing behaviour of both long and short range dependence(SRD). The results of simulations show that bodi LRD and SRD play an important role in the queuing systems. Especially when LRD is strong, the more buffer solution is almost useless to improve the queuing performance.