On-Line Segmentation of Non-stationary Fractal Network Traffic with Wavelet Transforms and Log-Likelihood-Based Statistics

Abstract

Network traffic exhibits fractal characteristics, such as self-similarity and long-range dependence. Traffic fractality and its associated burstiness have important consequences for the performance of computer networks, such as higher queue delays and losses than predicted by classical models. There are several estimators of the fractal parameters, and those based on the discrete wavelet transform (DWT) are the best in terms of efficiency and accuracy. The DWT estimator does not consider the possibility of changes to the fractal parameters over time. We propose using the Schwarz information criterion (SIC) to detect changes in the variance structure of the wavelet decomposition and then segmenting the trace into pieces with homogeneous characteristics for the Hurst parameter. The procedure can be extended to the stationary wavelet transform (SWT), a non-orthogonal transform that provides higher accuracy in the estimation of the change points. The SIC analysis can be performed progressively. The DWT-SIC and SWT-SIC algorithms were tested against synthetic and well-known real traffic traces, with promising results.

This work was supported in part by the Spanish Government under grant CICYT TIC2001-0956-C04-02, and the EuroNGI European Network of Excellence (IST-FP6).