Scaling analysis of conservative cascades, with applications to network traffic

Previous studies have demonstrated that measured wide-area network traffic such as Internet traffic exhibits locally complex irregularities, consistent with multifractal behavior. It has also been shown that the observed multifractal structure becomes most apparent when analyzing measured network traffic at a particular layer in the well-defined protocol hierarchy that characterizes modern data networks, namely the transport or transmission control protocol (TCP) layer. To investigate this new scaling phenomenon associated with the dynamics of measured network traffic over small time scales, we consider a class of multiplicative processes, the so-called conservative cascades, that serves as a cascade paradigm for and is motivated by the networking application. We present a wavelet-based time/scale analysis of these cascades to determine rigorously their global and local-scaling behavior. In particular, we prove that for the class of multifractals generated by these conservative cascades the multifractal formalism applies and is valid, and we illustrate some of the wavelet-based techniques for inferring multifractal scaling behavior by applying them to a set of wide-area traffic traces.