A CLASS OF NONLOCAL MODELS FOR PEDESTRIAN TRAFFIC

被引：141

作者：

Colombo, Rinaldo M. ^{[1
]}

Garavello, Mauro ^{[2
]}

Lecureux-Mercier, Magali ^{[3
]}

机构：

[1] Univ Brescia, Dipartimento Matemat, I-25123 Brescia, Italy

[2] Univ Piemonte Orientale, Di STA, I-15121 Alessandria, Italy

[3] Univ Orleans, Lab MAPMO, UFR Sci, F-45067 Orleans, France

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2012年 / 22卷 / 04期

关键词：

Crowd dynamics; macroscopic pedestrian model; nonlocal conservation laws; CROWD DYNAMICS; MACROSCOPIC MODEL; FLOW; OPTIMIZATION;

D O I：

10.1142/S0218202511500230

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a new class of macroscopic models for pedestrian flows. Each individual is assumed to move towards a fixed target, deviating from the best path according to the instantaneous crowd distribution. The resulting equation is a conservation law with a nonlocal flux. Each equation in this class generates a Lipschitz semigroup of solutions and is stable with respect to the functions and parameters defining it. Moreover, key qualitative properties such as the boundedness of the crowd density are proved. Specific models are presented and their qualitative properties are shown through numerical integrations. In particular, the present model accounts for the possibility of reducing the exit time from a room by carefully positioning obstacles that direct the crowd flow.

引用

页数：34

共 30 条

[1]

[Anonymous], 2009, Encyclopedia of Complexity and Systems Science, DOI DOI 10.1007/978-0-387-30440-3_382

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