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E-grāmata: Multiscale Modeling of Pedestrian Dynamics

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  • Formāts: PDF+DRM
  • Sērija : MS&A 12
  • Izdošanas datums: 12-Sep-2014
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319066202
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Multiscale Modeling of Pedestrian DynamicsPalielināt
  • Formāts: PDF+DRM
  • Sērija : MS&A 12
  • Izdošanas datums: 12-Sep-2014
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319066202
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This book presents mathematical models and numerical simulations of crowd dynamics. The core topic is the development of a new multiscale paradigm, which bridges the microscopic and macroscopic scales taking the most from each of them for capturing the relevant clues of complexity of crowds. The background idea is indeed that most of the complex trends exhibited by crowds are due to an intrinsic interplay between individual and collective behaviors. The modeling approach promoted in this book pursues actively this intuition and profits from it for designing general mathematical structures susceptible of application also in fields different from the inspiring original one. The book considers also the two most traditional points of view: The microscopic one, in which pedestrians are tracked individually and the macroscopic one, in which pedestrians are assimilated to a continuum. Selected existing models are critically analyzed. The work is addressed to researchers and graduate students.

Recenzijas

The book is very well-written and contains many excellent illustrations. It is both a valuable introduction to the modeling of pedestrian dynamics and to the methods of multiscale modeling. (Martin Gugat, zbMATH 1314.00081, 2015)

Part I Pedestrian Behavior: Phenomenology and Simulations
1 An Introduction to the Modeling of Crowd Dynamics
3(26)
1.1 Modeling-Oriented Phenomenological Issues
3(6)
1.1.1 Behavioral Rules
3(3)
1.1.2 Self-Organization
6(3)
1.2 Preliminary Reasonings on Mathematical Modeling
9(6)
1.2.1 Crowds as a Living Complex System
9(2)
1.2.2 Scaling and Representation
11(3)
1.2.3 Critical Analysis
14(1)
1.3 The Interplay Between Modeling and Experimenting
15(2)
1.3.1 Fundamental Diagrams
16(1)
1.3.2 Data on Emerging Collective Behaviors
16(1)
1.3.3 Data on Individual Behaviors and on Interactions
16(1)
1.4 Book Contribution
17(9)
1.4.1 A Multiscale Approach
17(3)
1.4.2 Generalizations and Applications to Other Fields
20(2)
1.4.3 Purpose and Structure of the Book
22(4)
1.5 Bibliographical Notes
26(3)
2 Problems and Simulations
29(24)
2.1 An Informal Introduction to the Multiscale Model
29(2)
2.2 Effects of Repulsion
31(4)
2.3 Metric vs. Topological Attraction
35(1)
2.4 Flow Through a Bottleneck
36(4)
2.5 Crossing Flows
40(7)
2.5.1 Lane Formation
40(4)
2.5.2 Intermittent Flow
44(3)
2.6 Social Groups and One-Many Interactions
47(4)
2.7 Bibliographical Notes
51(2)
3 Psychological Insights
53(20)
3.1 Wide Literatures
53(1)
3.2 Specific Characteristics of Pedestrians
54(6)
3.2.1 Cognitive Maps
55(1)
3.2.2 Geographical and Social Features
56(1)
3.2.3 Self-Organization and Re-organization
57(3)
3.3 Models for the Single Pedestrian
60(2)
3.3.1 The 2/3 Power Law and Other Empirical Laws
60(1)
3.3.2 Models of Path Choice
61(1)
3.4 Experimental Settings and Measurements
62(6)
3.4.1 Experimental Setting
63(2)
3.4.2 Measurements
65(1)
3.4.3 Comparison of Different Experimental Settings
66(2)
3.5 Bibliographical Notes
68(5)
Part II Modeling and Mathematical Problems
4 An Overview of the Modeling of Crowd Dynamics
73(36)
4.1 Microscopic Models
73(7)
4.1.1 Force Models
73(4)
4.1.2 Maury and Venel's Model
77(1)
4.1.3 Cellular Automata Models
78(2)
4.1.4 Discrete Choice Models
80(1)
4.2 Macroscopic Models
80(9)
4.2.1 Fundamental Diagram
82(1)
4.2.2 Coscia and Canavesio's Model
83(1)
4.2.3 Colombo and Rosini's Model
84(2)
4.2.4 Maury et al.'s Model
86(1)
4.2.5 Nonlocal Models
86(2)
4.2.6 Bellomo and Dogbe's Model
88(1)
4.3 Mesoscopic Models
89(5)
4.3.1 Dogbe's Model
91(1)
4.3.2 Bellomo and Bellouquid's Model
92(2)
4.4 Models for Rational Pedestrians
94(9)
4.4.1 The Arechavaleta et al.'s Model
95(1)
4.4.2 Hoogendoorn and Bovy's Microscopic Model
95(2)
4.4.3 Eikonal Equation and Minimum Time Problems
97(2)
4.4.4 Hughes' Model
99(1)
4.4.5 Hoogendoorn and Bovy's Macroscopic Model
100(1)
4.4.6 Mean Field Game Models
101(2)
4.4.7 Playing with Rationality
103(1)
4.5 Bibliographical Notes
103(6)
5 Multiscale Modeling by Time-Evolving Measures
109(28)
5.1 Conservation Laws by Time-Evolving Measures
109(2)
5.2 Velocity from Planning and Interactions
111(6)
5.2.1 Desired Velocity
112(1)
5.2.2 Interaction Velocity
113(4)
5.2.3 Metric and Topological Interactions
117(1)
5.3 Recovering Single-Scale Models
117(3)
5.3.1 Microscopic Models
118(1)
5.3.2 Macroscopic Models
119(1)
5.4 Multiscale Model
120(5)
5.5 Multiscale Numerical Scheme
125(8)
5.5.1 Discrete-in-Time Model
125(2)
5.5.2 Spatial Approximation
127(3)
5.5.3 The Algorithm
130(3)
5.6 Two-Population Models
133(2)
5.7 Bibliographical Notes
135(2)
6 Basic Theory of Measure-Based Models
137(32)
6.1 Phenomenological Model with Perception
137(3)
6.2 From the Phenomenological to a Mathematical-Physical Model
140(1)
6.3 Probabilistic Interpretation
141(1)
6.4 Uniqueness and Continuous Dependence of the Solution
142(4)
6.5 Existence of the Solution
146(4)
6.6 Approximation of the Solution
150(7)
6.7 Spatial Structure of the Solution
157(3)
6.8 Study of Pedestrian Velocity Models
160(7)
6.9 Bibliographical Notes
167(2)
7 Evolution in Measure Spaces with Wasserstein Distance
169(26)
7.1 The Homogeneous Nonlinear Evolution Equation
169(6)
7.2 Transport Equation, Optimal Transportation, and the Wasserstein Distance
175(5)
7.2.1 Wasserstein Distance Under the Action of Flows
178(1)
7.2.2 Existence and Uniqueness of Solutions
179(1)
7.3 Lagrangian and Eulerian Numerical Schemes
180(5)
7.3.1 Discrete Lagrangian Scheme with Velocity of Centers
181(2)
7.3.2 Eulerian Scheme
183(2)
7.4 Interaction Velocities for Pedestrians
185(3)
7.5 Transport Equation with Source
188(1)
7.6 Generalized Wasserstein Distance
189(3)
7.7 Existence and Uniqueness of Solutions for the Transport Equation with Source
192(2)
7.8 Bibliographical Notes
194(1)
8 Generalizations of the Multiscale Approach
195(26)
8.1 Second Order Time-Evolving Measures
195(9)
8.1.1 Phenomenological Microscopic Model
195(2)
8.1.2 Mathematical-Physical Model
197(2)
8.1.3 Mass and Momentum Equations
199(4)
8.1.4 Monokinetic Solutions
203(1)
8.2 Multidimensional Multiscale Coupling
204(3)
8.3 Space-Time-Dependent Multiscale Coupling
207(4)
8.4 More General ODE-PDE Coupling
211(8)
8.4.1 Coupling the Heat Equation and the Brownian Motion
211(2)
8.4.2 Numerical Approximation of the Coupled Equation
213(6)
8.5 Conclusions
219(1)
8.6 Bibliographical Notes
219(2)
A Basics of Measure and Probability Theory
221(26)
A.1 Measurable Spaces, Measures, and Measurable Functions
221(6)
A.1.1 Sets and Operations with Sets
221(1)
A.1.2 σ-Algebras and Measurable Spaces
222(2)
A.1.3 Measures
224(2)
A.1.4 Measurable Functions
226(1)
A.2 Integration with Respect to an Abstract Measure
227(5)
A.3 Decomposition of a Measure
232(2)
A.4 Probabilities
234(3)
A.4.1 Events, Operations with Events, and σ-Algebras
234(1)
A.4.2 Probability Measures
235(1)
A.4.3 Random Variables
235(1)
A.4.4 Integrals of Random Variables
236(1)
A.5 Product Spaces, Marginals, and Disintegration of a Measure
237(4)
A.6 Wasserstein Distance in Probability Spaces
241(2)
A.7 Measures as Distributions
243(2)
A.8 Bibliographical Notes
245(2)
B Pseudo-code for the Multiscale Algorithm
247(4)
B.1 Preliminaries
247(1)
B.2 The Pseudo-code
248(3)
References 251(8)
Index 259
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