Modeling heterogeneous network traffic in wavelet domain

Heterogeneous network traffic possesses diverse statistical properties whic h include complex temporal correlation and non-Gaussian distributions. A ch allenge to modeling heterogeneous traffic is to develop a traffic model whi ch can accurately characterize these statistical properties, which is compu tationally efficient and which is feasible for analysis. This work develops wavelet traffic models for tackling these issues. In specific, we model th e wavelet coefficients rather than the original traffic. Our approach is mo tivated by a discovery that although heterogeneous network traffic has the complicated short- and long-range temporal dependence, the corresponding wa velet coefficients are all "short-range" dependent. Therefore, a simple wav elet model may be able to accurately characterize complex network traffic. We first investigate what short-range dependence is important among wavelet coefficients. We then develop the simplest wavelet model, i.e., the indepe ndent wavelet model for Gaussian traffic. We define and evaluate the (avera ge) autocorrelation function and the buffer loss probability of the indepen dent wavelet model for Fractional Gaussian Noise (FGN) traffic. This assess es the performance of the independent wavelet model, and the use of which f or analysis. We also develop (low-order) Markov wavelet models to capture a dditional dependence among wavelet coefficients. We show that an independen t wavelet model is sufficiently accurate, and a Markov wavelet model only i mproves the performance marginally. We further extend the wavelet models to non-Gaussian traffic through developing a novel time-scale shaping algorit hm. The algorithm is tested using real network traffic and shown to outperf orm FARIMA in both efficiency and accuracy. Specifically, the wavelet model s are parsimonious, and have the computation complexity O(N) in developing a model from a training sequence of length N. and O (AI) in generating a sy nthetic traffic trace of length M.