Self - Similarity and Heavy Tails : Structural Modeling of Network

High-resolution traac measurements from modern communications networks provide unique opportunities for developing and validating mathematical models for aggregate traac. To exploit these opportunities, we emphasize the need for structural models that take into account spe-ciic physical features of the underlying communication network structure. This approach is in sharp contrast to the traditional black box modeling methodology from time series analysis that ignores, in general, speciic physical structures. We demonstrate, in particular, how the proposed structural modeling approach provides a direct link between the observed self-similarity characteristic of measured aggregate network traac, and the strong empirical evidence in favor of heavy-tailed, innnite variance phenomena at the level of individual network connections.