On the Generation of Self-similar with Long-range Dependent Traffic Using Piecewise Affine Chaotic One-dimensional Maps (Extended Version)

TL;DR

This paper introduces a novel chaotic model using piecewise affine one-dimensional maps to generate self-similar traffic with long-range dependence, providing insights into controlling the Hurst exponent through model parameters.

Contribution

It extends existing chaotic models by incorporating piecewise affine maps and offers a method to explain and control the Hurst exponent in generated traffic.

Findings

The model effectively generates self-similar traffic with LRD.

The Hurst exponent behavior can be explained and controlled via model parameters.

The approach offers a new way to model and analyze network traffic patterns.

Abstract

A qualitative and quantitative extension of the chaotic models used to generate self-similar traffic with long-range dependence (LRD) is presented by means of the formulation of a model that considers the use of piecewise affine one-dimensional maps. Based on the disaggregation of the temporal series generated, a valid explanation of the behavior of the values of Hurst exponent is proposed and the feasibility of their control from the parameters of the proposed model is shown.