Point Process Approaches to the Modelingand Analysis of Self - Similar Tra c { Part I : Model

We propose four fractal point processes (FPPs) as novel approaches to modeling and analyzing various types of self-similar traac: 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. Study of these models provides a thorough understanding of how self-similarity arises in computer network traac. We nd 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 veriies that these models exhibit fractal behavior over a wide range of time scales.