A REACTIVE DYNAMIC CONTINUUM USER EQUILIBRIUM MODEL FOR BI-DIRECTIONAL PEDESTRIAN FLOWS

doi:10.1016/S0252-9602(10)60002-1

数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (6): 1541-1555.doi: 10.1016/S0252-9602(10)60002-1

A REACTIVE DYNAMIC CONTINUUM USER EQUILIBRIUM MODEL FOR BI-DIRECTIONAL PEDESTRIAN FLOWS

Yanqun Jiang, Tao Xiong, S.C.Wong, Chi-Wang Shu, Mengping Zhang, Peng Zhang, William H.K. Lam

1.Department of Mathematics, University of Science and Technology of China, Hefei 230026, China
2.Department of Civil Engineering, The University of Hong Kong, Hong Kong, China
3.Division of Applied Mathematics, Brown University, Providence, RI 02912, U.S.A.
4.Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
5.Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hong Kong, China

收稿日期:2009-10-22 出版日期:2009-11-20 发布日期:2009-11-20

A REACTIVE DYNAMIC CONTINUUM USER EQUILIBRIUM MODEL FOR BI-DIRECTIONAL PEDESTRIAN FLOWS

Yanqun Jiang, Tao Xiong, S.C.Wong, Chi-Wang Shu, Mengping Zhang, Peng Zhang, William H.K. Lam

1.Department of Mathematics, University of Science and Technology of China, Hefei 230026, China
2.Department of Civil Engineering, The University of Hong Kong, Hong Kong, China
3.Division of Applied Mathematics, Brown University, Providence, RI 02912, U.S.A.
4.Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
5.Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hong Kong, China

Received:2009-10-22 Online:2009-11-20 Published:2009-11-20

摘要/Abstract

摘要：

In this paper, a reactive dynamic user equilibrium model is extended to simulate two groups of pedestrians traveling on crossing paths in a continuous walking facility. Each group makes path choices to minimize the travel cost to its destination in a reactive manner based on
instantaneous information. The model consists of a conservation law equation coupled with an Eikonal-type equation for each group. The velocity-density relationship of pedestrian movement is obtained via an experimental method. The model is solved using a finite volume method for the conservation law equation and a fast-marching method for the Eikonal-type equation on unstructured grids. The numerical results verify the rationality of the model and the validity of the numerical method. Based on this continuum model, a number of results, e.g., the formation of strips or moving clusters composed of pedestrians walking to the same destination, are also observed.

关键词: pedestrian flows, conservation law, Eikonal-type equation, density-velocity relationship, finite volume method, fast marching method, unstructured grids

中图分类号:

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Yanqun Jiang, Tao Xiong, S.C.Wong, Chi-Wang Shu, Mengping Zhang, Peng Zhang, William H.K. Lam. A REACTIVE DYNAMIC CONTINUUM USER EQUILIBRIUM MODEL FOR BI-DIRECTIONAL PEDESTRIAN FLOWS[J]. 数学物理学报(英文版), 2009, 29(6): 1541-1555.

Yanqun Jiang, Tao Xiong, S.C.Wong, Chi-Wang Shu, Mengping Zhang, Peng Zhang, William H.K. Lam. A REACTIVE DYNAMIC CONTINUUM USER EQUILIBRIUM MODEL FOR BI-DIRECTIONAL PEDESTRIAN FLOWS[J]. Acta mathematica scientia,Series B, 2009, 29(6): 1541-1555.

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A REACTIVE DYNAMIC CONTINUUM USER EQUILIBRIUM MODEL FOR BI-DIRECTIONAL PEDESTRIAN FLOWS

A REACTIVE DYNAMIC CONTINUUM USER EQUILIBRIUM MODEL FOR BI-DIRECTIONAL PEDESTRIAN FLOWS

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