| Introduction to IP Traffic | p. 1 |
| TCP/IP Architecture Model | p. 1 |
| Physical Layer | p. 3 |
| Data Link Layer | p. 4 |
| Network Layer | p. 5 |
| Transport Layer | p. 5 |
| Application Layer | p. 8 |
| Aspects of IP Modeling | p. 9 |
| Levels of Modeling | p. 10 |
| Traffic Relations | p. 13 |
| Asymmetry in IP Traffic | p. 17 |
| Temporal Behavior | p. 17 |
| Network Topology | p. 18 |
| Quality of Service | p. 19 |
| Best Effort Traffic | p. 19 |
| Time Sensitive Data Traffic | p. 20 |
| Overprovisioning | p. 20 |
| Prioritization | p. 21 |
| Why Traditional Models Fail | p. 22 |
| Classical Traffic Theory | p. 29 |
| Introduction to Traffic Theory | p. 29 |
| Basic Examples | p. 29 |
| Basic Processes and Kendall Notation | p. 32 |
| Basic Properties of Exponential Distributions | p. 33 |
| Kolmogorov Equation | p. 34 |
| State Probability | p. 36 |
| Stationary State Equation | p. 37 |
| Transition Processes | p. 38 |
| Pure Markov Systems M/M/n | p. 40 |
| Loss Systems M/M/n | p. 40 |
| Queueing Systems M/M/n | p. 44 |
| Application to Teletraffic | p. 52 |
| Special Traffic Models | p. 58 |
| Loss Systems M/M/[infinity] | p. 58 |
| Queueing Systems of Engset | p. 58 |
| Queueing Loss Systems | p. 59 |
| Renewal Processes | p. 60 |
| Definitions and Concepts | p. 60 |
| Bounds for the Renewal Function | p. 65 |
| Recurrence Time | p. 67 |
| Asymptotic Behavior | p. 68 |
| Stationary Renewal Processes | p. 71 |
| Random Sum Processes | p. 71 |
| General Poisson Arrival and Serving Systems M/G/n | p. 73 |
| Markov Chains and Embedded Systems | p. 73 |
| General Loss Systems M/G/n | p. 74 |
| Queueing Systems M/G/n | p. 74 |
| Heavy-Tail Serving Time Distribution | p. 81 |
| Application of M/G/1 Models to IP Traffic | p. 95 |
| Markov Serving Times Models GI/M/1 | p. 102 |
| General Serving Systems GI/G/n | p. 107 |
| Loss Systems | p. 107 |
| The Time-Discrete Queueing System GI/G/1 | p. 109 |
| GI/G/1 Time Discrete Queueing System with Limitation | p. 117 |
| Network Models | p. 122 |
| Jackson's Network | p. 122 |
| Systems with Priorities | p. 130 |
| Systems with Impatient Demands | p. 131 |
| Conservation Laws Model | p. 133 |
| Packet Loss and Velocity Functions on Transmission Lines | p. 134 |
| Riemann Solvers | p. 141 |
| Stochastic Velocities and Density Functions | p. 146 |
| Matrix-Analytical Methods | p. 148 |
| Phase Distribution | p. 148 |
| Examples for Different Phase Distributions | p. 153 |
| Markovian Arrival Processes | p. 156 |
| Queueing Systems MAP/G/1 | p. 161 |
| Application to IP Traffic | p. 173 |
| Mathematical Modeling of IP-based Traffic | p. 181 |
| Scalefree Traffic Observation | p. 181 |
| Motivation and Concept | p. 181 |
| Self-Similarity | p. 183 |
| Self-Similar Processes | p. 184 |
| Definition and Basic Properties | p. 184 |
| Fractional Brownian Motion | p. 190 |
| [alpha]-stable Processes | p. 194 |
| Long-Range Dependence | p. 202 |
| Definition and Concepts | p. 203 |
| Fractional Brownian Motion and Fractional Brownian Noise | p. 207 |
| Farima Time Series | p. 211 |
| Fractional Brownian Motion and IP Traffic - the Norros Approach | p. 218 |
| Influence of Heavy-Tail Distributions on Long-Range Dependence | p. 226 |
| General Central Limit Theorem | p. 226 |
| Heavy-Tail Distributions in M/G/[infinity] Models | p. 233 |
| Heavy-Tail Distributions in On-Off Models | p. 235 |
| Aggregated Traffic | p. 240 |
| Models for Time Sensitive Traffic | p. 245 |
| Multiscale Fractional Brownian Motion | p. 245 |
| Norros Models for Differentiating Traffic | p. 249 |
| Fractional Levy Motion in IP-based Network Traffic | p. 259 |
| Description of the Model | p. 259 |
| Calibration of a Fractional Levy Motion Model | p. 260 |
| Fractional Ornstein-Uhlenbeck Processes and Telecom Processes | p. 261 |
| Description of the Model | p. 261 |
| Fractional Ornstein-Uhlenbeck Gaussian Processes | p. 262 |
| Telecom Processes | p. 263 |
| Representations of Telecom Processes | p. 263 |
| Application of Telecom Processes | p. 265 |
| Multifractal Models and the Influence of Small Scales | p. 267 |
| Multifractal Brownian Motion | p. 267 |
| Wavelet-Based Multifractal Models | p. 270 |
| Characteristics of Multifractal Models | p. 280 |
| Multifractal Formalism | p. 292 |
| Construction of Cascades | p. 296 |
| Multifractals, Self-Similarity and Long-Range Dependence | p. 308 |
| Summary of Models for IP Traffic | p. 316 |
| Statistical Estimators | p. 321 |
| Parameter Estimation | p. 321 |
| Unbiased Estimators | p. 322 |
| Linear Regression | p. 329 |
| Estimation of the Heavy-Tail Exponent [alpha] | p. 335 |
| Maximum Likelihood Method | p. 344 |
| Estimators of Hurst Exponent in IP Traffic | p. 349 |
| Absolute Value Method (AVM) | p. 349 |
| Variance Method | p. 352 |
| Variance of Residuals | p. 354 |
| R/S Method | p. 356 |
| Log Periodogram - Local and Global | p. 359 |
| Maximum Likelihood and Whittle Estimator | p. 363 |
| Wavelet Analysis | p. 368 |
| Quadratic Variation | p. 379 |
| Remarks on Estimators | p. 380 |
| Performance of IP: Waiting Queues and Optimization | p. 383 |
| Queueing of IP Traffic for Perturbation with Long-Range Dependence Processes | p. 383 |
| Waiting Queues for Models with Fractional Brownian Motion | p. 384 |
| Queueing in Multiscaling FBM | p. 392 |
| Fractional Levy Motion and Queueing in IP Traffic Modeling | p. 395 |
| Queueing Theory and Performance for Multifractal Brownian Motion | p. 405 |
| Queueing in Multifractal Traffic | p. 411 |
| Queueing in Multifractal Tree Models | p. 411 |
| Queueing Formula | p. 417 |
| Traffic Optimization | p. 423 |
| Mixed Traffic | p. 423 |
| Optimization of Network Flows | p. 424 |
| Rate Control: Shadow Prices and Proportional Fairness | p. 436 |
| Optimization for Stochastic Perturbation | p. 442 |
| Optimization of Network Flows Using an Utility Approach | p. 449 |
| References | p. 465 |
| Index | p. 479 |
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