Markov chain-based method for generating long-range dependence

This paper describes a model for generating time series which exhibit the statistical phenomenon known as long-range dependence (LRD). A Markov modulated process based on an infinite Markov chain is described. The work described is motivated by applications in telecommunications where LRD is a known property of time series measured on the Internet. The process can generate a time series exhibiting LRD with known parameters and is particularly suitable for modeling Internet traffic because the time series is in terms of ones and zeros, which can be interpreted as data packets and interpacket gaps. The method is extremely simple, both computationally and analytically, and could prove more tractable than other methods described in the literature.

Figure 1

Graph of a map that can be used to generate LRD.

Figure 2

An infinite Markov chain, which generates a time series exhibiting LRD.