The book contains self-contained descriptions of existing models, accompanied by critical analyses of their properties both from a theoretical and practical standpoint. It aims to develop 'modeling skills' within the readers, giving them the ability to develop their own models and improve existing ones. Written in connection with a full, open source Python Library (cromosim), this project also enables readers to run the simulations discussed within the text.
Author(s): Bertrand Maury ; Sylvain Faure
Series: Advanced Textbooks in Mathematics
Publisher: World Scientific
Year: 2019
Language: English
Pages: 201
Contents......Page 8
Foreword......Page 6
1.1. From Passive to Active Entities......Page 12
1.2. Basics on Crowd Motion Modeling......Page 14
1.3. The Mathematical Standpoint......Page 16
1.4. How to Use this Book?......Page 23
2. One-Dimensional Microscopic Models......Page 24
2.1. Follow-the-Leader Model......Page 25
2.2. Accounting for Inertia/Delays......Page 41
3.1. Inertial Social Force Model......Page 48
3.2. Overdamped Social Force Model......Page 60
3.3. Alternative Approaches......Page 67
4.1. One-Dimensional Model......Page 70
4.2. Two-Dimensional Model......Page 72
4.3. Numerical Scheme......Page 75
4.4. Numerical Experiments......Page 77
4.5. Mathematical Issues......Page 79
4.6. Critical Discussion......Page 87
5. Cellular Automata......Page 94
5.1. Cellular Automata: General Principles......Page 95
5.2. Algorithms......Page 96
5.3. Variations, Extensions......Page 103
5.4. Cellular Automata, Mathematical Issues......Page 104
6.1. Compartment Models: Toy Versions and General Setting......Page 108
6.2. Numerical Solution......Page 112
6.3. Extensions......Page 113
6.5. Mathematical Framework: A Cascade of Gradient Flows......Page 115
7. Toward Macroscopic Models......Page 122
7.1. One-Dimensional Macroscopic Traffic Model......Page 123
7.2. Two-Dimensional Models......Page 126
7.3. Granular Models: Hard Congestion......Page 128
7.4. Micro–Macro Issues......Page 134
7.5. Alternative Macroscopic Models......Page 136
8. Computing Distances and Desired Velocities......Page 138
8.1. Shortest Path Problem on a Graph......Page 141
8.2. Shortest Path on a Domain: The Eikonal Equation......Page 143
8.3. Non-homogenous Domains, Various Extensions......Page 146
8.4. Shortest Paths in a Dynamic Environment......Page 150
8.5. Alternative Way to Compute Desired Velocities......Page 153
8.6. Illustrations......Page 154
9.1. Diameters......Page 156
9.2.1. Proxemics and confort densities, experimental evidence......Page 157
9.2.2. Proxemics, modeling aspects......Page 158
9.4. Pedestrian Speed, Fundamental Diagram......Page 159
9.6.1. Capacity Drop phenomenon, experimental evidence......Page 162
9.7.1. Faster-is-Slower effect, experimental evidence......Page 163
9.7.2. Faster-is-Slower effect, modeling aspects......Page 164
9.8. Influence of an Obstacle......Page 165
9.8.1. Influence of an obstacle, experimental evidence......Page 166
9.8.2. Influence of an obstacle, modeling aspects......Page 167
9.9. Stop-and-Go Waves......Page 168
9.10. Further Considerations on Human Behavior......Page 169
10.1. Faster-is-Slower Effect......Page 172
10.2. Fluidizing Effect of an Obstacle......Page 179
10.3. Damping, Propagation, and Stop-and-Go Waves......Page 181
A.1. Ordinary Differential Equations......Page 188
A.2. Constrained Optimization......Page 191
Bibliography......Page 194
Index......Page 200
