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

We propose a doubly stochastic point process for modeling traffic data. The traffic intensity is modeled as a self-similar process and is generated by 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 a 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 particular attention because is often the main responsible for packet losses and thus directly affects the network performance. The model is validated by comparing the packet loss rate of a queueing buffer element driven by real and simulated traffic.