Complex Dynamics in Communication Networks (Understanding Complex Systems)

Front-matter......Page 1
Preface......Page 6
Contents......Page 10
1 Introduction......Page 12
2 TCP Congestion Control......Page 13
3 The Basic Lab Model and TCP Dynamics......Page 14
4 System Trajectories......Page 16
5 Sensitivity......Page 19
6 Controllability......Page 24
7 Tra.c Burstiness at Di.erent Timescales......Page 27
8 Conclusions......Page 29
Reference......Page 30
1 Introduction......Page 32
2.1 Description......Page 34
Invariant Con.gurations......Page 35
2.3 Two Sources, a Special Case......Page 41
3.1 Simulation Setup......Page 45
3.2 Packet Arrival Rate and Queue Occupancy......Page 47
3.3 Assumption #1: Immediate Response to Congestion......Page 50
3.5 When Does Aggregate Periodic Behavior not Occur?......Page 52
4 Conclusion......Page 56
References......Page 57
1 Introduction......Page 59
2.1 Unfairness......Page 60
2.2 The TCP Butter.y E.ect......Page 61
3 Characterizing Chaos......Page 62
3.1 Poincar´e Sections......Page 63
3.2 Symbolic Description......Page 64
4 The Statistical Tool-box of Chaos......Page 65
5 Cellular Chaos......Page 68
6 Exploring Periodic Orbits......Page 70
7 E.ects of Parameter Rescaling......Page 73
References......Page 77
1 Introduction......Page 79
2.1 Simpli.ed TCP Model......Page 81
2.2 State-Space Characterization of TCP......Page 84
2.3 Dynamic Regimes of TCP......Page 86
3 Simulations of TCP competing with UDP......Page 93
4 Message Delay Measurements......Page 95
5 Analysis of Internet TCP Traces......Page 96
5.1 Time-Dependent Exponent Curves......Page 99
5.2 Anomalous Di.usions......Page 103
5.3 Random Losses and TCP Dynamics......Page 104
6 Conclusions......Page 107
References......Page 109
1 Introduction......Page 112
1.1 A Short Review of the TCP-Reno Algorithm......Page 113
1.2 Method of Investigation and Topology Descriptio......Page 114
2 The Case of a Single Driven TCP Connection......Page 115
3 The Case of Multiple Driven TCP Connections......Page 120
4 The Impact of Active Probing Measuerements on TCP Tra.c......Page 122
4.1 The Dilemma......Page 123
4.2 Measuring a Single Persistent TCP......Page 124
4.3 Correlation Analysis......Page 125
4.4 Measuring Time-dependent Aggregate TCP Tra.c......Page 126
4.5 The Impact on the Statistical Properties......Page 128
4.6 Implications for Spectral Measurements and Hurst-parameter Estimation......Page 130
5 Summary......Page 132
References......Page 133
1 Introduction......Page 135
2 Long-Range Dependence......Page 136
3 Packet Production Models......Page 138
3.1 Closed Form Map......Page 140
3.3 Autocorrelation of the Map Output......Page 141
4 Topology and Models of Networks......Page 143
4.1 Regular-Symmetric Networks......Page 145
4.2 Random Networks......Page 146
4.3 Scale-free Networks......Page 147
4.4 Model of Networked Data Tra.c......Page 149
5 Congestion......Page 150
5.1 Mean Field Approximation......Page 151
5.2 LRD at Criticality......Page 156
5.3 Congestion and LRD Tra.c......Page 157
6 Control of Queue Sizes......Page 158
6.1 Control in Scale-free Networks Using TCP......Page 159
References......Page 163
1 Introduction......Page 166
2 Chaotic Piecewise A.ne Markov Maps and Higher Order Correlations of Quantized Trajectories......Page 169
3 A More General Model of Quantized Chaotic Trajectories......Page 178
4 Piecewise-A.ne Pseudo-Markov Systems......Page 181
5 Statistical Characterization of PWAPM Systems......Page 182
6 Self-Similarity & Network tra.c......Page 189
7 Conclusion......Page 194
References......Page 195
1 Introduction......Page 198
2.2 Tra.c Sources......Page 202
3.1 Representing Network Flow Data......Page 204
3.2 Cross-Correlation Analysis......Page 205
4 Capturing Shifting Spatial-temporal Patterns......Page 206
4.1 Timescale of Interest......Page 207
4.3 Spatial-Temporal Pattern......Page 208
5 Monitoring DDoS Flooding Attacks......Page 211
5.1 Modeling DDoS Attacks......Page 212
5.2 Constant Rate Attack......Page 213
5.3 Subgroup Attack......Page 214
6 Concluding Remarks......Page 215
References......Page 217
1.1 Historical Background......Page 219
1.2 A Local-World Model......Page 222
2.1 Di.erent Internet Topologies......Page 223
3 MODELLING THE INTERNET......Page 227
3.1 The MLW Model for the Internet......Page 230
3.2 Degree Distribution of the MLW Model......Page 231
3.3 Some Special Cases of the MLW Model......Page 235
4 Conclusions......Page 238
References......Page 239
1 Introduction......Page 241
2 Internet Evolution as a Multiplicative Stochastic Process......Page 243
3 Growth Dynamics of the Internet......Page 244
4 Degree Correlation and Modular Structure......Page 247
5 Adaptation Model......Page 250
6 Load Distribution of the Internet......Page 251
7 Summary......Page 254
References......Page 256
1 Introduction......Page 257
2.1 TCP Congestion Control Algorithms......Page 258
2.2 TCP Implementations......Page 259
2.3 RED Algorithm......Page 260
3 Modeling Methodologies......Page 261
3.1 Survey of Related TCP/RED Models......Page 262
4 Discrete-time Dynamical Model of TCP/RED......Page 264
4.1 TCP/RED Model......Page 265
4.2 Case 1: No Loss......Page 266
4.4 Case 3: At Least Two Packet Losses......Page 267
4.5 Properties of the S-model......Page 268
5 S-Model Validation and Comparison......Page 269
5.1 Default RED Parameters......Page 270
5.3 Drop Probability p max......Page 276
5.4 Thresholds qmin and q max......Page 277
5.5 Validation Summary......Page 278
6 Conclusions......Page 279
References......Page 280
1 Introduction......Page 285
2.2 Random Early Detection......Page 287
3 Discrete-Time Feedback Model for TCP-RED......Page 288
3.1 Plant Function......Page 291
4 Fixed Point and Its Bifurcation......Page 293
4.2 Bifurcation analysis......Page 294
5 Border Collision Bifurcation (BCB)......Page 297
6 Numerical Examples......Page 298
6.1 E.ect of Exponential Averaging Weigh......Page 299
7 Chaotic Behavior......Page 302
8.1 Washout Filter Based Control......Page 305
8.2 Application to TCP-RED......Page 306
8.3 Stability Analysis with Washout Filter......Page 307
8.5 Nonlinear Control......Page 310
8.6 Numerical Example......Page 312
References......Page 313
1 Introduction......Page 315
1.1 Synchronization in TCP/IP Networks......Page 317
1.2 Synchronization in Networks......Page 320
2.1 Preliminaries......Page 321
2.2 Synchronization in Classical Random Networks......Page 322
2.3 Synchronization in Power-Law Networks......Page 323
3 Synchronization in Hybrid Networks......Page 327
4 Conclusion......Page 331
References......Page 332
1 Introduction......Page 335
2 Statistical Model of Simple Queue......Page 338
3 Observation of the Internet Flow......Page 340
4 Ping Experiment and Visualization of the Internet Tra.cs......Page 347
5 Numerical Simulation Results of the Internet Tra.cs......Page 354
6 An Attempt to Revise TCP : Introduction of LEAP......Page 358
7 Discussions......Page 362
References......Page 363
Index......Page 365