Fractional exponential model for fractal point processes

Markov-modulated Poisson process has long been used to model arrivals at networks. Recent work has shown that such models may be inadequate because traffic on networks may exhibit self-similar (or fractal) behavior. The analysis of fractal point processes is thus of crucial importance. In this contribution, a novel analysis technique is presented, based on log-periodogram regression and fractional exponential models. A procedure, derived from the Mallows´s C/sub p/ statistics is proposed to choose the regression order. Results are presented on both simulated and real data.