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

• Published in: Acta mathematica scientia Vol. 29; no. 6; pp. 1541 - 1555
• Main Authors: Jiang, Yanqun, Xiong, Tao, Wong, S.C., Shu, Chi-Wang, Zhang, Mengping, Zhang, Peng, Lam, William H.K.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2009; Department of Mathematics,University of Science and Technology of China,Hefei 230026,China%Department of Civil Engineering,The University of Hong Kong,Hong Kong,China%Division of Applied Mathematics,Brown University,Providence,RI 02912,U.S.A%Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University,Shanghai 200072,China%Department of Civil and Structural Engineering,The Hong Kong Polytechnic University,Hong Kong,China
• Subjects: 76M12; conservation law; density-velocity relationship; Eikonal-type equation; fast marching method; finite volume method; pedestrian flows; unstructured grids; 均衡模型; 旅游设施; 有限体积法; 用户平衡模型; 耦合方程; 连续体; fast marching method; pedestrian flows; unstructured grids; conservation law; density-velocity relationship; finite volume method; Eikonal-type equation; 76M12; Elkonal-type equation
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(10)60002-1

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.