Modeling Packet Traffic with Chaotic Maps

We investigate the application of deterministic chaotic maps to model traffic sources in packet based networks, motivated in part by recent measurement studies which indicate the presence of significant statistical features in packet traffic more characteristic of fractal processes than conventional stochastic processes. We outline one approach whereby traffic sources can be modeled by chaotic maps, and illustrate the traffic characteristics that can be generated by analyzing three maps. We show that low order nonlinear maps can capture several of the fractal properties observed in actual data. Finally, we outline a potential performance analysis approach based on chaotic maps that can be used to assess the traffic significance of fractal properties. It is our conclusion that while there are considerable analytical difficulties, chaotic maps may allow accurate, yet concise, models of packet traffic, with some potential for transient and steady state analysis.