Point Process Models for Self - Similar 1

Self-similar processes based on fractal point processes (FPPs) provide natural and attractive network traac models. We show that the point process formulation yields a wide range of FPPs which in turn yield a diversity of parsimonious, computationally eecient, and highly practical asymptotic second-order self-similar processes. Using this framework, we show that the relevant second-order fractal characteristics such as long-range dependence (LRD), slowly-decaying variance, and 1=f noise are completely characterized by three fundamental quantities: mean arrival rate, Hurst parameter, and fractal onset time. Four models are proposed, and the relationship between their model parameters and the three fundamental quantities are analyzed. By successfully applying the proposed models to Bellcore's Ethernet traces, we show that the FPP models prove useful in evaluating and predicting the queueing performance of various types of fractal traac sources. 1 Throughout this paper, self-similarity refers to asymptotic second-order self-similarity 4], 13] unless otherwise deened.