3D-LD: a Graphical Wavelet-based Method for Analyzing Scaling Processes

This paper proposes a novel graphical method (3D-LD) based on wavelets for studying scaling and non-stationary signals. We show that it allows to better study the timescale-dependent qualitative properties of such signals, compared to the classical techniques. By using the 3D-LD, we study two recent network traffic traces to understand the actual nature of scaling in TCP flow arrivals. We show that the TCP flow arrivals is a complex scaling process, which is non-stationary with respect to its degree of statistical dependence as well as over timescales longer than hours. We show that the application mix in the traffic has a significant impact scaling over timescales between seconds and minutes. This scaling for timescales between seconds and minutes is created by statistical dependence within user sessions. Self-similarity (or long-range dependence) that appears over timescales larger than several minutes on the other hand seem to be an invariant of the flow arrivals and is, in all likelihood, created by the user sessions arrivals. Based on this analysis, we propose a simple model for the TCP flow arrivals process, taking into account the timescales ranging from seconds to hours, and we show that simulating realistic TCP flow arrivals conforming to this model is feasible.