Crowd Dynamics, Volume 1 (eBook)

Preface 6
Contents 8
Contributors 9
Behavioral Human Crowds 11
1 Plan of the Chapter 11
2 On the Modeling of Crowd Dynamics 12
3 On the Contents of the Edited Book 18
4 Critical Analysis and Perspectives 20
References 22
Crowd Dynamics in Virtual Reality 25
1 Introduction 26
1.1 When to (Not) Use VR 27
2 VR Studies of Crowd Behavior 29
2.1 Comparing Virtual and Real Behavior 29
2.1.1 Walking in VR 30
2.1.2 Social Interactions in VR 30
2.1.3 Comparing Crowd Dynamics in Real and Virtual Environments 31
2.2 Crowd Dynamics in VR 34
2.2.1 Behavioral Dynamics in VR 36
2.3 VR Studies of Crowd Evacuation Behavior 38
3 The Road Ahead 42
References 43
Pedestrian Movement in Smoke: Theory, Data and Modelling Approaches 47
1 Introduction 47
2 Theory and Data 49
2.1 Fire Factors 49
2.1.1 Visibility 50
2.1.2 Irritancy 52
2.1.3 Cognitive and Emotional Influences 53
2.1.4 Tenability 53
2.2 Pedestrian Factors 54
2.2.1 Unimpeded Movement Speed 54
2.2.2 Visual Acuity 54
2.2.3 Physical Exertion 55
2.3 Environmental Factors 55
2.3.1 Geometric Complexity 55
2.3.2 Way-Finding Systems 56
2.3.3 Inclination, Stairs and Surface Material 56
3 Modelling Pedestrian Movement in Smoke 57
3.1 Modelling the Impact of Reduced Visibility Conditions 59
3.2 Modelling Way-Finding in Smoke 63
4 Discussion 65
5 Conclusion 67
References 67
Pedestrian Dynamics: From Empirical Results to Modeling 73
1 Introduction 73
2 Empirical Results 74
2.1 Observables: Flow, Density, and Velocity 75
2.1.1 Flow 75
2.1.2 Density 77
2.1.3 Mean Speed 78
2.2 Collective Phenomena 79
2.2.1 Jamming and Clogging 79
2.2.2 Density Waves, Stop-and-Go Waves 80
2.2.3 Lane Formation 81
2.2.4 Other Collective Effects 82
2.2.5 Emergency Situations, ``Panic'' 83
2.3 Fundamental Diagram 83
2.3.1 Single-File Movement in Circuit 83
2.3.2 Pedestrian Movement in Straight Corridor 84
2.3.3 Pedestrian Movement Through Bottlenecks 85
2.3.4 Pedestrian Movement on Stairs 86
2.3.5 Other Geometries 87
3 Classification of Models 87
3.1 Acceleration-Based Models 91
3.2 Velocity-Based Models 93
3.3 Decision-Based Models 95
3.3.1 Cellular Automata 96
3.3.2 Floor Field Model 97
3.3.3 Other CA Models and Related Approaches 99
4 Performance of Models: Quantitative and Qualitative ``Benchmarking'' 100
4.1 Stability Analysis 100
4.2 Verification and Validation 101
5 Summary 102
References 103
One-Dimensional Conservation Laws with Nonlocal Point Constraints on the Flux 113
1 Introduction 113
2 Nonlocally Constrained LWR 116
2.1 Existence and Uniqueness Results 117
2.2 Finite Volume Approximation 120
2.3 Examples 122
3 Locally Constrained ARZ 127
3.1 Existence and Uniqueness Results 129
3.2 Example 132
4 Locally Constrained PT 137
4.1 Existence Result 138
4.2 Example 141
References 143
Measure-Theoretic Models for Crowd Dynamics 146
1 Introduction 146
2 Microscopic and Multi-scale Models 148
2.1 Microscopic: The Social Force Models 148
2.1.1 Panic 150
2.2 Microscopic: Models for Animal Groups 150
2.3 Microscopic: Cucker-Smale Model 151
2.4 Multi-scale Models 152
2.4.1 The Wasserstein Distance 153
2.4.2 Existence and Uniqueness of Solutions to (6) 155
2.4.3 Regularity of Interaction Kernels 156
2.5 Wasserstein Distance and Total Variation Norm 158
3 Mean-Field Limits of Microscopic Models 160
3.1 Definition of the Mean-Field Limit 160
3.2 The Mean-Field Limit of the Helbing-Molnár Model 163
4 Microscopic Models with Varying Mass 165
5 Measure Dynamics for Mass-Varying Models 168
5.1 The Generalized Wasserstein Distance 168
5.2 The Mean-Field Limit for Mass-Varying Models 169
References 172
Numerical Methods for Mean-Field and Moment Modelsfor Pedestrian Flow 175
1 Introduction 175
2 Pedestrian Flow Models 178
2.1 A Microscopic Social Force Model with Optimal Path Computation 178
2.2 Mean Field and Macroscopic Limits 180
2.3 Scalar Macroscopic Models 184
3 Numerical Methods 186
3.1 Macroscopic Flow Simulation Using Finite-Volume Methods 186
3.2 Particle Methods for Macroscopic Equations 187
3.3 A Multi-scale Particle Method Based on the Mean-Field Approximation 189
4 Numerical Results 189
4.1 Numerical Transition from Microscopic to Macroscopic Description 189
4.2 Numerical Comparison of Macroscopic Equations 192
5 Multigroup Traffic 199
5.1 The Microscopic Multigroup Model 199
5.2 The Multigroup Hydrodynamic Model 201
5.3 The Multigroup Scalar Model 202
5.4 Numerical Results 203
5.4.1 Comparison Between Single and Multigroup Pedestrian Flow Models with Weak and Strong Reciprocal Interaction 204
5.4.2 Comparison Between Models with Weak and Strong Centre of Mass Attraction 204
5.5 Discussion of Experimental Data 205
6 Coupling Pedestrian to Traffic Flow 207
6.1 The Traffic and Pedestrian Flow Model 207
6.2 The Coupling 208
6.3 Numerical Methods and Results 209
7 Conclusions and Outlook 213
References 214
Modelling Interactions Between Active and Passive AgentsMoving Through Heterogeneous Environments 218
1 Introduction 218
2 Related Contributions 220
3 Agent-Based Dynamics (Model 1) 221
3.1 Active Agents 221
3.2 Passive Agents 224
3.3 Smoke Effects 226
4 Results Model 1: Agent-Based Dynamics 227
5 Lattice Gas Dynamics (Model 2) 231
6 Results Model 2: Lattice Gas Dynamics 234
7 Mathematical Aspects of Social Dynamics in Mixed Populations 235
7.1 Technical Preliminaries, Notation, and Assumptions 236
7.1.1 Geometry 236
7.1.2 Function Spaces 236
7.1.3 Hypotheses 238
7.1.4 First-Order Social Agents Dynamics 238
7.2 Well-Posedness 240
7.3 Background Results 249
7.3.1 A Regularized Eikonal Equation 249
7.3.2 Higher Regularity Estimates for the Smoke Concentration 250
8 Discussion 261
References 262
Pedestrian Models Based on Rational Behaviour 265
1 Introduction 265
2 A Model with Rational Behaviour 267
2.1 Perception Stage 268
2.1.1 Pairwise Encounters 268
2.1.2 Assumptions on the Heuristics 269
2.1.3 Global Encounters 270
2.2 Decision Stage 271
2.2.1 The Decision Potential 271
2.2.2 A Choice of Potential 272
2.3 A Gradient-Based Formulation 272
2.3.1 Optimality Versus Efficiency 273
2.4 Summary of the General Model 273
3 Towards a High-Density Model 274
3.1 A Frontal Collision 274
3.2 Grading by Collision Severity 276
3.3 Modelling Variable Speeds 277
3.4 Environmental Coercion 280
3.4.1 Repulsion as Anticipation 283
3.4.2 Friction and the Fundamental Diagram 284
3.5 Summary of the Modified Gradient Model 288
4 Conclusion and Outlook 293
Supplementary Material 295
Data Statement 295
References 295