Modeling of flows with the power-law spectral densities and power-law distributions of flow's intensities

Abstract

We present analytical and numerical results of modeling of flows represented as the correlated non-Poissonian point process and as the Poissonian sequence of pulses of the different size. Both models may generate signals with the power-law distributions of the intensity of the flow and the power-law spectral density. Furthermore, different distributions of the interevent time of the point process and different statistics of the size of pulses may result in $1/f^{\beta}$ noise (one-over-f noise, 1-f noise) with $0.5\lesssim\beta\lesssim2$. Combination of the models is applied for modeling of the Internet traffic.