Approximation capability of independent wavelet models to heterogeneous network traffic

In our previous work, we showed empirically that independent wavelet models were parsimonious, computationally efficient, and accurate in modeling heterogeneous network traffic measured by both auto-covariance functions and buffer loss rate. In this work, we focus on auto-covariance functions, to establish a theory of independent wavelet models as unified models for heterogeneous network traffic. We have developed the theory on the approximation capability of independent wavelet models for heterogeneous traffic in terms of the decay rate of auto-covariance functions at large lags. Average auto-covariance functions of independent wavelet models have been derived and shown to be linear combinations of basis functions. Through a simple analytical expression, we have shown that the decay rate of the auto-covariance functions of independent wavelet models is determined explicitly through a single quantity called the rate function of variances of wavelet coefficients. By specifying analytical forms of the rate function, independent wavelet models have been shown as unified models of heterogeneous traffic in terms of auto-covariance functions. The simplicity of the theory thereby provides both quantitative and qualitative explanations why independent wavelet models are unified models of heterogeneous traffic