Linear scale-invariant system models for self-similar wireless traffic characterization

It is now empirically documented that data traffic over networks of various types exhibit fractal or self-similar behavior in many instances. Accurate analysis of traffic density and estimation of buffer size must take into account this self-similar nature. Researchers have investigated procedures for generating self-similar signals to model the traffic. Approaches based on the discrete wavelet transform (DWT) are among those that have been proposed. The basis for using the DWT is that it possesses certain scale-invariance properties and scale-invariance provides the foundation for characterizing self-similarity. However, self-similar processes generated with the DWT demonstrate self-invariance to dyadic scaling factors. Zhao and Rao have proposed novel models for purely discrete-time self-similar processes and linear scale-invariant (LSI) systems based on a new interpretation of the discrete-time scaling (equivalently dilation or contraction) operation which is defined through a mapping between discrete and continuous time. They show that it is possible to have continuous scaling factors through this operation although the signal itself is discrete-time. In this paper, we demonstrate application of these LSI systems to the synthesis of data whose self-similarity parameters match those observed in network traffic. Both theoretical development and experimental results are provided.