Scaling Analysis of Conservative Cascades, with Applications to Network Traac

Recent studies have demonstrated that measured wide-area network traac such as Internet traac 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 traac at a particular layer in the well-deened protocol hierarchy that characterizes modern data networks, namely the transport or TCP layer. To investigate this new scaling phenomenon associated with the dynamics of measured network traac 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 traac traces.