Multiscale analysis of fractal point processes and queues

Using a powerful, recently-developed multiscale representation for fractal point processes, we characterize these processes under fundamental transformations which arise in a variety of important applications such as data network traffic modeling. Distribution results are obtained, including the inter-arrival density for a fractal point process subject to random erasure, the counting process distribution for the superposition of fractal point processes, and the steady-state customer distribution in queues with self-similar customer arrivals. Interpretations and implications of these results for applications are also discussed