Complex dynamics in communication networks

✍ Scribed by Ljupco Kocarev, Gabor Vattay

• Publisher: Springer
• Year: 2005
• Tongue: English
• Leaves: 368
• Series: Springer complexity, Understanding complex systems
• Edition: 1
• Category: Library

✦ Synopsis

Computer and communication networks are among society's most important infrastructures. The internet, in particular, is a giant global network of networks with central control or administration. It is a paradigm of a complex system, where complexity may arise from different sources: topological structure, network evolution, connection and node diversity, and /or dynamical evolution. This is the first book entirely devoted to the new and emerging field of nonlinear dynamics of TCP/IP networks. It addresses both scientists and engineers working in the general field of communication networks.

✦ Table of Contents

cover.jpg......Page 1
front-matter.pdf......Page 2
1 Introduction......Page 13
2 TCP Congestion Control......Page 14
3 The Basic Lab Model and TCP Dynamics......Page 15
4 System Trajectories......Page 17
5 Sensitivity......Page 20
6 Controllability......Page 25
7 Tra.c Burstiness at Di.erent Timescales......Page 28
8 Conclusions......Page 30
Reference......Page 31
1 Introduction......Page 33
2.1 Description......Page 35
Invariant Con.gurations......Page 36
2.3 Two Sources, a Special Case......Page 42
3.1 Simulation Setup......Page 46
3.2 Packet Arrival Rate and Queue Occupancy......Page 48
3.3 Assumption #1: Immediate Response to Congestion......Page 51
3.5 When Does Aggregate Periodic Behavior not Occur?......Page 53
4 Conclusion......Page 57
References......Page 58
1 Introduction......Page 60
2.1 Unfairness......Page 61
2.2 The TCP Butter.y E.ect......Page 62
3 Characterizing Chaos......Page 63
3.1 Poincar´e Sections......Page 64
3.2 Symbolic Description......Page 65
4 The Statistical Tool-box of Chaos......Page 66
5 Cellular Chaos......Page 69
6 Exploring Periodic Orbits......Page 71
7 E.ects of Parameter Rescaling......Page 74
References......Page 78
1 Introduction......Page 80
2.1 Simpli.ed TCP Model......Page 82
2.2 State-Space Characterization of TCP......Page 85
2.3 Dynamic Regimes of TCP......Page 87
3 Simulations of TCP competing with UDP......Page 94
4 Message Delay Measurements......Page 96
5 Analysis of Internet TCP Traces......Page 97
5.1 Time-Dependent Exponent Curves......Page 100
5.2 Anomalous Di.usions......Page 104
5.3 Random Losses and TCP Dynamics......Page 105
6 Conclusions......Page 108
References......Page 110
1 Introduction......Page 113
1.1 A Short Review of the TCP-Reno Algorithm......Page 114
1.2 Method of Investigation and Topology Descriptio......Page 115
2 The Case of a Single Driven TCP Connection......Page 116
3 The Case of Multiple Driven TCP Connections......Page 121
4 The Impact of Active Probing Measuerements on TCP Tra.c......Page 123
4.1 The Dilemma......Page 124
4.2 Measuring a Single Persistent TCP......Page 125
4.3 Correlation Analysis......Page 126
4.4 Measuring Time-dependent Aggregate TCP Tra.c......Page 127
4.5 The Impact on the Statistical Properties......Page 129
4.6 Implications for Spectral Measurements and Hurst-parameter Estimation......Page 131
5 Summary......Page 133
References......Page 134
1 Introduction......Page 136
2 Long-Range Dependence......Page 137
3 Packet Production Models......Page 139
3.1 Closed Form Map......Page 141
3.3 Autocorrelation of the Map Output......Page 142
4 Topology and Models of Networks......Page 144
4.1 Regular-Symmetric Networks......Page 146
4.2 Random Networks......Page 147
4.3 Scale-free Networks......Page 148
4.4 Model of Networked Data Tra.c......Page 150
5 Congestion......Page 151
5.1 Mean Field Approximation......Page 152
5.2 LRD at Criticality......Page 157
5.3 Congestion and LRD Tra.c......Page 158
6 Control of Queue Sizes......Page 159
6.1 Control in Scale-free Networks Using TCP......Page 160
References......Page 164
1 Introduction......Page 167
2 Chaotic Piecewise A.ne Markov Maps and Higher Order Correlations of Quantized Trajectories......Page 170
3 A More General Model of Quantized Chaotic Trajectories......Page 179
4 Piecewise-A.ne Pseudo-Markov Systems......Page 182
5 Statistical Characterization of PWAPM Systems......Page 183
6 Self-Similarity & Network tra.c......Page 190
7 Conclusion......Page 195
References......Page 196
1 Introduction......Page 199
2.2 Tra.c Sources......Page 203
3.1 Representing Network Flow Data......Page 205
3.2 Cross-Correlation Analysis......Page 206
4 Capturing Shifting Spatial-temporal Patterns......Page 207
4.1 Timescale of Interest......Page 208
4.3 Spatial-Temporal Pattern......Page 209
5 Monitoring DDoS Flooding Attacks......Page 212
5.1 Modeling DDoS Attacks......Page 213
5.2 Constant Rate Attack......Page 214
5.3 Subgroup Attack......Page 215
6 Concluding Remarks......Page 216
References......Page 218
1.1 Historical Background......Page 220
1.2 A Local-World Model......Page 223
2.1 Di.erent Internet Topologies......Page 224
3 MODELLING THE INTERNET......Page 228
3.1 The MLW Model for the Internet......Page 231
3.2 Degree Distribution of the MLW Model......Page 232
3.3 Some Special Cases of the MLW Model......Page 236
4 Conclusions......Page 239
References......Page 240
1 Introduction......Page 242
2 Internet Evolution as a Multiplicative Stochastic Process......Page 244
3 Growth Dynamics of the Internet......Page 245
4 Degree Correlation and Modular Structure......Page 248
5 Adaptation Model......Page 251
6 Load Distribution of the Internet......Page 252
7 Summary......Page 255
References......Page 257
1 Introduction......Page 258
2.1 TCP Congestion Control Algorithms......Page 259
2.2 TCP Implementations......Page 260
2.3 RED Algorithm......Page 261
3 Modeling Methodologies......Page 262
3.1 Survey of Related TCP/RED Models......Page 263
4 Discrete-time Dynamical Model of TCP/RED......Page 265
4.1 TCP/RED Model......Page 266
4.2 Case 1: No Loss......Page 267
4.4 Case 3: At Least Two Packet Losses......Page 268
4.5 Properties of the S-model......Page 269
5 S-Model Validation and Comparison......Page 270
5.1 Default RED Parameters......Page 271
5.3 Drop Probability p max......Page 277
5.4 Thresholds qmin and q max......Page 278
5.5 Validation Summary......Page 279
6 Conclusions......Page 280
References......Page 281
1 Introduction......Page 286
2.2 Random Early Detection......Page 288
3 Discrete-Time Feedback Model for TCP-RED......Page 289
3.1 Plant Function......Page 292
4 Fixed Point and Its Bifurcation......Page 294
4.2 Bifurcation analysis......Page 295
5 Border Collision Bifurcation (BCB)......Page 298
6 Numerical Examples......Page 299
6.1 E.ect of Exponential Averaging Weigh......Page 300
7 Chaotic Behavior......Page 303
8.1 Washout Filter Based Control......Page 306
8.2 Application to TCP-RED......Page 307
8.3 Stability Analysis with Washout Filter......Page 308
8.5 Nonlinear Control......Page 311
8.6 Numerical Example......Page 313
References......Page 314
1 Introduction......Page 316
1.1 Synchronization in TCP/IP Networks......Page 318
1.2 Synchronization in Networks......Page 321
2.1 Preliminaries......Page 322
2.2 Synchronization in Classical Random Networks......Page 323
2.3 Synchronization in Power-Law Networks......Page 324
3 Synchronization in Hybrid Networks......Page 328
4 Conclusion......Page 332
References......Page 333
1 Introduction......Page 336
2 Statistical Model of Simple Queue......Page 339
3 Observation of the Internet Flow......Page 341
4 Ping Experiment and Visualization of the Internet Tra.cs......Page 348
5 Numerical Simulation Results of the Internet Tra.cs......Page 355
6 An Attempt to Revise TCP : Introduction of LEAP......Page 359
7 Discussions......Page 363
References......Page 364
back-matter.pdf......Page 366