A Markov Chain based method for generating long-range dependence

TL;DR

This paper introduces a simple Markov Chain-based model for generating long-range dependent time series, particularly suited for internet traffic simulation, with known parameters and computational efficiency.

Contribution

It presents a novel Markov Modulated Process using an infinite Markov chain to generate LRD time series, offering simplicity and analytical tractability.

Findings

Successfully models internet traffic with LRD properties

Computationally efficient and analytically simple method

Can generate time series with specified long-range dependence parameters

Abstract

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 upon 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 modelling internet traffic since the time series is in terms of ones and zeros which can be interpreted as data packets and inter-packet gaps. The method is extremely simple computationally and analytically and could prove more tractable than other methods described in the literature