Self-similar traffic generation and parameter estimation using wavelet transform

Previous studies of real network traffic have shown that packet traffic exhibits fractal properties such as self-similarity which are fundamentally different from features of traditional Poisson-based traffic models. Fractional Brownian motion (FBM) is a widely-used self-similar process which can be characterized by the Hurst parameter. To gain a better understanding of queueing and network-related performance issues with regard to FBM models, it is essential to be able to accurately and quickly generate traffic from FBM processes. In the mean time, it is of crucial importance to accurately estimate the Hurst parameter. In this paper we attack the above two problems by using the wavelet transform. Our analysis indicates that the wavelet approach is as fast or faster than existing methods and appears to generate a closer approximation to true self-similar sample paths than the other known fast method (random midpoint displacement). Moreover, the Hurst parameter can also be accurately estimated from the power-law behaviour of the wavelet coefficients variance.