Pareto process as a model of self-similar packet traffic

In the past few years packet traffic from various sources-Ethernet, ISDN, CCSN and VBR video-has been shown to exhibit self-similarity, and related properties of long range correlation, slowly decaying variances and fractal dimensions. This discovery has motivated research into unconventional traffic models such as fractional Brownian motion, fractional ARIMA and chaotic maps. These models explain certain queueing effects in packet networks that are difficult to explain using conventional traffic models. We argue that such exotic models may not be needed to describe self-similar traffic. We analyze the G/M/1 queue with Pareto input. Although a renewal process, and solvable by standard methods, the Pareto process generates self-similar arrivals. Its long range dependence produces qualitatively different queueing behavior from exponential models. In particular, delays can rise sharply for ρ much less than one