The autocorrelation of double intermittency maps and the simulation of computer packet traffic

Since the discovery in the early 1990s that packet traffic exhibits long-range dependence, there has been considerable interest in finding a system that could generate reliable pseudo-traffic traces. One such system is a one-dimensional chaotic map. We examine a particular instance of such maps. It is non-smooth, but its nature is such that analytical results are easier to obtain. In particular we derive a theorem about the asymptotics of the autocorrelation. In the subsequent discussion, it is argued that to get a relevant description of packet traffic, one needs to venture beyond first- and second-order statistics.

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