| 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 |
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