Small and Large Time Scale Analysis of a Network Traffic Model

Recent empirical studies of the internet and WAN traffic data have observed multifractal behavior at time scales below a few hundred milliseconds. There have been some attempts to model this phenomenon, but there is no model to connect the small time scale behavior with behavior observed at large time scales of bigger than a few hundred milliseconds. There have been separate analyses of models for high speed data transmissions, which show that appropriate approximations to large time scale behavior of cumulative traffic are either fractional Brownian motion or stable Lévy motion, depending on the input rates assumed. This paper tries to bridge this gap and develops and analyzes a model offering an explanation of both the small and large time scale behavior of a network traffic model based on the infinite source Poisson model. Previous studies of this model have usually assumed that transmission rates are constant and deterministic. We consider a non-constant, multifractal, random transmission rate at the user level which results in cumulative traffic exhibiting multifractal behavior on small time scales and self-similar behavior on large time scales. Also, we model the file size and the transmission rate, which are more natural objects than the usually modeled transmission time and rate.