Modelling Network Data Traffic D.K. Arrowsmith1 Summary: - Modelling Network Data Traffic D.K. Arrowsmith1 , R.J. Mondrag´on2 1School of Mathematical Sciences 2 Department of Electronic Engineering Queen Mary, University of London Contents 1 Introduction 3 2 Long-Range Dependence 4 3 Packet production model 5 3.1 Equivalent packet production models . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.1.1 Closed form map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.1.2 Piece-wise linear map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.1.3 Power-law escape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.1.4 Autocorrelation of the map output . . . . . . . . . . . . . . . . . . . . . . 10 3.2 Autocorrelation for intermittency maps . . . . . . . . . . . . . . . . . . . . . . . 12 3.3 Transmission Control Protocol Dynamics . . . . . . . . . . . . . . . . . . . . . . 12 4 Topology of Networks 13 4.1 Regular-Symmetric Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Collections: Mathematics