Summary: The autocorrelation of double intermittency maps and the
simulation of computer packet traffic
November 13, 2003
Since the discovery in the early 1990's that packet traffic exhibits long-range-dependence
there has been considerable interest in finding 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.
In the beginning of the 1990's, Leland and co-workers showed that packet traffic in computer
networks exihibited long-range dependence [10, 9, 11], when it was previously thought that
data traffic, like voice traffic, would be memoryless. This has major consequences as long-range
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