Application of multifractals in the characterization of WWW traffic

We explore the viability of multifractal analysis in modeling the traffic generation process at a WWW server. In principle, a WWW traffic model can be used for generating representative WWW traces and in designing prefetching and cache replacement policies. Multifractal processes constitute a superset of monofractal (selfsimilar) processes. They are characterized by a time-dependent scaling law, which provides flexibility in describing irregularities that are localized in time. R. Riedi et al. (see IEEE Trans. on Inf. Theory, vol.45, no.3, p.992-1018, 1999) presented a multifractal process that can be fitted to empirical time series with an arbitrary autocorrelation function (ACF) and with an approximately lognormal marginal distribution. We use this model to capture simultaneously the temporal and spatial localities of WWW traffic. Furthermore, the popularity profile is captured by a construction using the LRU (least recently used) stack and the popularity profiles of each file in the real trace. We classify files into several classes according to their popularity profile and model the stack distance of each class separately. Trace-driven simulations are used to study the performance of our model and contrast it with a previously proposed model.