A chaos based approach for generating self-similar process

Non-Poisson bursty traffic has been detected in many real-world communication networks. It is traditionally modeled as an ON/OFF discrete-time second-order self-similar random process. It can be proved that self-similar random processes are identified by means of: a polynomially decaying trend of the auto-covariance function or a polynomially decaying trend with $k$ of the the probability of staying in either the ON or OFF states a number $k$ of time steps. In this work we concentrate on the second condition and show that we can design chaotic maps whose quantized trajectories produce ON/OFF processes with heavy tailed distribution of the sojourn times in the OFF state or both. These maps are infinite piecewise affine Markov maps and are characterized by a synthetic parameter which allows the tuning of the generator to emulate different Hurst parameter in the traffic process, independently from the traffic load. Some simulations are reported showing how, according to the theory, the map design is able to fit those specifications.