Modeling network traffic data by doubly stochastic point processes with self-similar intensity process and fractal renewal point process

In this paper we propose a doubly stochastic point process for modeling traffic data. The traffic intensity is modeled as a self-similar process and is generated applying an inverse orthogonal wavelet transform to a sequence of independent random sequences, having different variances at different scales. The underlying point process is characterized by a fractal renewal point process of dimension less than one. The proposed model is intrinsically able to synthesize a point process characterized by arrivals packed into sparsely located clusters separated by occasionally very long interarrival times. This behavior is often encountered on real traffic data and it deserves a particular attention because is often the main responsible for packet losses and thus directly affects the network performance. The model is validated comparing the packet loss rate of a queueing buffer element driven by real and simulated traffic.