Modeling heterogeneous network traffic in wavelet domain

Abstract

Heterogeneous network traffic possesses diverse statistical properties which include complex temporal correlation and non-Gaussian distributions. A challenge to modelling heterogeneous traffic is to develop a traffic model which can accurately characterize these statistical properties, which is computationally efficient, and which is feasible for analysis. This work develops wavelet traffic models for tackling these issues. In specific, we model the wavelet coefficients rather than the original traffic. Our approach is motivated by a discovery that although heterogeneous network traffic has the complicated short- and long-range temporal dependence, the corresponding wavelet coefficients are all "short-range" dependent. Therefore, a simple wavelet 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 independent wavelet model for Gaussian traffic. We define and evaluate the (average) autocorrelation function and the buffer loss probability of the independent wavelet model for Fractional Gaussian Noise (FGN) traffic. This assesses the performance of the independent wavelet model, and the use of which for analysis. We also develop (low-order) Markov wavelet models to capture additional dependence among wavelet coefficients. We show that an independent wavelet model is sufficiently accurate, and a Markov Wavelet model only improves the performance marginally. We further extend the wavelet models to non-Gaussian traffic through developing a novel time-scale shaping algorithm. The algorithm is tested using real network traffic and shown to outperform FARIMA in both efficiency and accuracy. Specifically, the wavelet models are parsimonious, and have the computation complexity O(N) in developing a model from a training sequence of length N, and O (M) in generating a synthetic traffic trace of length M.