An application of deterministic chaotic maps to model packet traffic

The authors 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. They describe one approach whereby traffic sources can be modeled by chaotic maps, and illustrate the traffic characteristics than can be generated by analyzing several classes of maps. The authors outline a potential performance analysis approach based on chaotic maps that can be used to assess the traffic significance of fractal properties. They show that low order nonlinear maps can capture several of the fractal properties observed in actual data, and show that the source characteristics observed in actual traffic can lead to heavy-tailed queue length distributions. It is the present 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.