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Summary: The autocorrelation of double intermittency maps and the
simulation of computer packet traffic
M. Barenco
D.K. Arrowsmith
November 13, 2003
Abstract
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.
1 Introduction
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
CoMPLEX, University College London, United Kingdom, to whom all correspondence should be addressed.
E-mail: m.barenco@ucl.ac.uk. Tel.:++44 20 76795088. Fax.:++44 20 73835519
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