Point process approaches to the modeling and analysis of self-similar traffic .I. Model construction

We propose four fractal point processes (FPPs) as novel approaches to modeling and analyzing various types of self-similar traffic: the fractal renewal process (FRP), the superposition of several fractal renewal processes (Sup-FRP), the fractal-shot-noise-driven Poisson process (FSNDP), and the fractal-binomial-noise-driven Poisson process (FBNDP). These models fall into two classes depending on their construction. A study of these models provides a thorough understanding of how self-similarity arises in computer network traffic. We find that (i) all these models are (second-order) self-similar in nature; (ii) the Hurst parameter alone does not fully capture the burstiness of a typical self-similar process; (iii) the heavy-tailed property is not a necessary condition to yield self-similarity; and (iv) these models permit parsimonious modeling (using only 2-5 parameters) and fast simulation. Simulation verifies that these models exhibit a fractal behavior over a wide range of time scales