$Multifractal Based Network Traffic Modeling - Murali Krishna P$

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Multifractal Based Network Traffic Modeling

By: Murali Krishna P, Vikram Gadre, Uday B. Desai

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Hardcover | 31 December 2003

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Hardcover
244 Pages

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23.5 x 15.88 x 1.27

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This text provides an overview of existing broadband traffic modelling based on the Poisson process and its variants like the MM1 models. It also provides coverage of models based on self-similar processes. Throughout the book, the authors have focused on the problem of broadband traffic modelling keeping in mind long range dependencies in broadband traffic. A new model is being proposed for modeling broadband traffic based on the theory of multiplicative cascade processes. This is referred to as the Variance Gaussian Multiplier (V.V.G.M) multiplicative cascade process. The proposed model incorporates variations of the multiplier distribution used to generate the process. Information theoretic principles are used to explain increased burstiness of network traffic. Kalman filter based techniques are developed for predicting traffic burstiness. The question of complexity of broadband traffic is also examined by defining a volatility parameter.

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Non-Fiction Engineering & Technology Electronics & Communications Engineering Communications Engineering & Telecommunications Civil Engineering Highway & Traffic Engineering Energy Technology & Engineering Electrical Engineering Computing & I.T.Computer Science Business & Management Business Mathematics & Systems

Computer Hardware Network Hardware

List of Symbols	p. xi
List of Acronyms	p. xiii
List of Figures	p. xv
List of Tables	p. xix
Acknowledgments	p. xxi
Preface	p. xxiii
Introduction	p. 1
Complexity of Broadband Network Traffic	p. 1
Geographical Complexity	p. 2
Behavior Generated Complexity	p. 3
Temporal Complexity	p. 3
Teletraffic Modeling: Historical Perspective	p. 4
Motivation for the Problem	p. 7
Contributions of the Monograph	p. 9
Organization of the Monograph	p. 12
Mathematical Preliminaries	p. 15
Random Processes	p. 16
Stationary and Non Stationary Random Process	p. 16
Bernoulli (Counting) Process	p. 18
Poisson Process	p. 20
Applications to Queuing Theory	p. 22
Markov Process	p. 24
Independent Increment Processes	p. 25
Self Similar Processes	p. 28
Structure of Variance	p. 28
Structure of Covariance	p. 29
Long Range Dependence Property	p. 30
Fractional Brownian Motion	p. 31
fBm from Linear System Theory	p. 32
Correlation of fBm	p. 35
Multifractal Brownian Motion	p. 37
Fractional ARIMA	p. 37
Wavelet Based Models for Self Similar Process	p. 39
Heavy Tailed Processes	p. 41
Analysis and Estimation Techniques for Self Similar Processes	p. 42
R/S Statistic	p. 43
Variance Aggregation plot	p. 43
Spectral Estimator	p. 44
Wavelet Based Analysis of Self Similar Process	p. 45
Statistical Properties of Wavelet Coefficients of Self Similar Processes	p. 47
Abry-Veitch Estimator	p. 47
The Need for Multifractal Processes	p. 48
Characterizing the Distribution of [alpha]	p. 50
Local Singularity Analysis Using Wavelets	p. 51
Holder Exponents from Taylor Series	p. 51
Wavelet Vanishing Moments and Local Regularity	p. 52
Salient points from the chapter	p. 53
Broadband Network Traffic Modeling	p. 55
Broadband Network Traffic Characteristics	p. 55
Network Traffic Modeling Methodology	p. 57
State-of-the-Art in Teletraffic Modeling	p. 58
ON-OFF Model	p. 58
CIPP Process	p. 60
Multiple Scaling in Network Data	p. 61
From Self similarity to Multifractals	p. 62
Multifractal Wavelet Model	p. 63
Video Traffic Modeling	p. 67
MPEG Video Source Encoding	p. 67
Models for VBR Video Traffic	p. 69
Summary of Broadband Traffic Models	p. 70
Multiplicative Cascades	p. 71
Binomial Multiplicative Cascade	p. 72
Characterizing Multifractals through Multifractal Spectrum	p. 75
Methods to Estimate Multifractal Spectrum	p. 81
Histogram Method	p. 81
Method Of Moments	p. 82
Interpreting the Multifractal Spectrum	p. 84
Multifractal Spectrum as Fractal Dimension	p. 84
Multifractal Spectrum from Large Deviation theory	p. 84
Generalized Dimensions	p. 87
Summary of the Chapter	p. 90
V.V.G.M Multifractal Model	p. 93
Development of V.V.G.M Multifractal Model	p. 94
Estimation of Multiplier Distributions	p. 96
Synthesis Algorithm	p. 97
Statistical Comparison Tests	p. 98
Autocorrelation Function	p. 98
Higher Order Moments of Aggregated Data	p. 99
Multifractal Spectrum Curve	p. 101
Test for Robustness of the Parametric Model	p. 104
Performance and Queuing Tests	p. 107
Queue length Distribution	p. 107
Comparison of Packet Loss	p. 108
Comparison of Delay	p. 110
Inter Departure Process	p. 111
V.V.G.M and MWM : A Comparison	p. 112
Salient Points of the V.V.G.M Model	p. 114
Analysis of the Multiplexing of Traffic	p. 115
Analysis of Multiplexing using V.V.G.M Model	p. 116
Analysis of Multiplexing using Multifractal Spectrum	p. 118
Analysis of the Multiplexing using Entropy	p. 120
Proof of Entropy Scaling	p. 123
Relation with Generalized Dimensions	p. 124
How Complex is Inter Arrival Data?	p. 125
Salient points from the chapter	p. 127
Modeling of VBR Video Traces	p. 129
VBR Video Modeling Using Multifractals	p. 130
Statistical Tests for Model Evaluation	p. 132
Higher Order Moments of Aggregated Data	p. 132
Index Of Dispersion of Counts	p. 134
Multifractal Spectrum	p. 135
Results of Queuing Simulations	p. 137
Behavior of Queue Lengths	p. 137
Variance of Cell Delay	p. 137
Comparison of Cell Loss	p. 139
Complexity of VBR Video Traces	p. 140
Salient points from the Chapter	p. 142
QoS Issues and Control of Broadband Traffic	p. 143
Statistics of Multiplicative Cascade Processes	p. 144
Global Scaling Parameter	p. 146
Heavy Tailed Distribution of V.V.G.M	p. 149
Queuing Theory for Cascade Processes	p. 150
Effective Bandwidth Estimation for QoS	p. 152
Effective Bandwidth for V.V.G.M Process	p. 153
Estimation and Prediction of Burstiness	p. 156
Results of Estimation of Traffic Burstiness	p. 157
Burstiness Prediction Using Kalman Filter	p. 159
Salient points from the chapter	p. 161
Conclusions	p. 165
V.V.G.M Cascade Process for Broadband Network Traffic	p. 165
Future Work	p. 166
System theoretic Modeling of Computer Networks	p. 166
Development of Network Processors	p. 167
Signal Processing and Networking	p. 167
Study of Complex Systems	p. 167
Appendices	p. 169
Wavelet Transform	p. 169
Legendre Transform	p. 171
Large Deviation Theory	p. 175
Norros's Queuing Model	p. 179
Parameterizing QoS Requirements	p. 180
Parameterizing Buffer Length	p. 182
Parameterizing Service Rate	p. 182
Parameterizing Queue Length Distribution	p. 182
Effective Bandwidth	p. 185
Properties	p. 185
Application in Queuing Systems	p. 186
Kalman Filter	p. 189
Some Websites of Interest	p. 195
References	p. 197
Index	p. 209
Table of Contents provided by Ingram. All Rights Reserved.

Multifractal Based Network Traffic Modeling

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