Time-Evolving Measures and Macroscopic Modeling of Pedestrian Flow

被引：110

作者：

Piccoli, Benedetto ^{[1
]}

Tosin, Andrea ^{[2
]}

机构：

[1] Rutgers State Univ, Dept Math Sci, Camden, NJ 08102 USA

[2] CNR, Ist Applicaz Calcolo Mauro Picone, I-00185 Rome, Italy

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2011年 / 199卷 / 03期

关键词：

TRAFFIC FLOW; DYNAMICS; WAVES;

D O I：

10.1007/s00205-010-0366-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper introduces a new model of pedestrian flow, formulated within a measure-theoretic framework. It consists of a macroscopic representation of the system via a family of measures which, pushed forward by some flow maps, provide an estimate of the space occupancy by pedestrians at successive times. From the modeling point of view, this setting is particularly suitable for treating nonlocal interactions among pedestrians, obstacles, and wall boundary conditions. In addition, the analysis and numerical approximation of the resulting mathematical structures, which are the principal objectives of this work, follow more easily than for models based on standard hyperbolic conservation laws.

引用

页码：707 / 738

页数：32

共 17 条

[1]

[Anonymous], P 17 IFAC WORLD C

[2] On the modelling crowd dynamics from scaling to hyperbolic macroscopic models [J].

Bellomo, Nicola ;

Dogbe, Christian .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2008, 18 (1317-1345) :1317-1345

[3] Crowd-structure interaction in footbridges: Modelling, application to a real case-study and sensitivity analyses [J].

Bruno, Luca ;

Venuti, Fiammetta .

JOURNAL OF SOUND AND VIBRATION, 2009, 323 (1-2) :475-493

[4] AN OPTIMIZATION PROBLEM FOR MASS TRANSPORTATION WITH CONGESTED DYNAMICS [J].

Buttazzo, G. ;

Jimenez, C. ;

Oudet, E. .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (03) :1961-1976

[5] Existence of nonclassical solutions in a Pedestrian flow model [J].

Colombo, Rinaldo M. ;

Rosini, Massimiliano D. .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2009, 10 (05) :2716-2728

[6] Pedestrian flows and non-classical shocks [J].

Colombo, RM ;

Rosini, MD .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2005, 28 (13) :1553-1567

[7] SOCIAL FORCE MODEL FOR PEDESTRIAN DYNAMICS [J].

HELBING, D ;

MOLNAR, P .

PHYSICAL REVIEW E, 1995, 51 (05) :4282-4286

[8] Self-organizing pedestrian movement [J].

Helbing, D ;

Molnár, P ;

Farkas, IJ ;

Bolay, K .

ENVIRONMENT AND PLANNING B-PLANNING & DESIGN, 2001, 28 (03) :361-383

[9]

Helbing D., 2007, P 4 C EUR SOC SIM AS, P623

[10] Dynamics of crowd disasters: An empirical study [J].

Helbing, Dirk ;

Johansson, Anders ;

Al-Abideen, Habib Zein .

PHYSICAL REVIEW E, 2007, 75 (04)

← 1 2 →