Statistical Models of Internet Traffic - Long Range Dependence and
Multifractal

Bowei Xi

One well known property of Internet traffic is the traffic being long
range dependent (LRD). In the early papers on LRD, there was much
discussion on self-similar processes such as fractional
Brownian motion (fBm). But as Leland et al. themselves pointed out,
the traffic is not exactly self similar. Instead,
it was noted that with increasing time aggregation of the traffic,
it approaches fBm and thus becomes asymptotically self-similar.

A next wave of models involve multifractal models. The concept is
that at different time scales, the LRD is
changing. Therefore different time scales need different statistical
descriptions. Very creative work was done in the development of
Multifractal Wavelet Models. Meanwhile there has been intensive study
of scaling effects.