On the existence and uniqueness properties of the Hoogendoorn–Bovy pedestrian flow model

IF 3.3 2区工程技术 Q2 TRANSPORTATION

Transportmetrica B-Transport Dynamics Pub Date : 2022-11-16 DOI:10.1080/21680566.2022.2146022

Liangze Yang, Chi-Wang Shu, S. C. Wong, Mengping Zhang, Jie Du

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引用次数: 1

Abstract

This study addresses the existence and uniqueness of solutions to the Hoogendoorn–Bovy (HB) pedestrian flow model, which describes the dynamic user-optimal pedestrian flow assignment problem in continuous space and time. The HB model consists of a forward conservation law (CL) equation that governs density and a backward Hamilton–Jacobi–Bellman (HJB) equation that contains a maximum admissible speed constraint (MASC), in which the flow direction is determined by the path-choice strategy. The existence and uniqueness of solutions are significantly more difficult to determine when the HJB equation contains an MASC; however, we prove that the HB model can be formulated as a forward CL equation and backward Hamilton–Jacobi (HJ) equation in which the MASC is non-binding if suitable model parameters are selected. This model is formulated as a fixed-point problem upon the simultaneous satisfaction of both equations. To verify the existence and uniqueness results, we first demonstrate the existence and uniqueness of the solutions to the CL and HJ equations, and then show that the coupled HB model is well-posed and has a unique solution. A numerical example is presented to illustrate the properties of the HB model.

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Hoogendoorn–Bovy行人流动模型的存在性和唯一性

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来源期刊

Transportmetrica B-Transport Dynamics TRANSPORTATION SCIENCE & TECHNOLOGY-

CiteScore

5.00

自引率

21.40%

发文量

期刊介绍： Transportmetrica B is an international journal that aims to bring together contributions of advanced research in understanding and practical experience in handling the dynamic aspects of transport systems and behavior, and hence the sub-title is set as “Transport Dynamics”. Transport dynamics can be considered from various scales and scopes ranging from dynamics in traffic flow, travel behavior (e.g. learning process), logistics, transport policy, to traffic control. Thus, the journal welcomes research papers that address transport dynamics from a broad perspective, ranging from theoretical studies to empirical analysis of transport systems or behavior based on actual data. The scope of Transportmetrica B includes, but is not limited to, the following: dynamic traffic assignment, dynamic transit assignment, dynamic activity-based modeling, applications of system dynamics in transport planning, logistics planning and optimization, traffic flow analysis, dynamic programming in transport modeling and optimization, traffic control, land-use and transport dynamics, day-to-day learning process (model and behavioral studies), time-series analysis of transport data and demand, traffic emission modeling, time-dependent transport policy analysis, transportation network reliability and vulnerability, simulation of traffic system and travel behavior, longitudinal analysis of traveler behavior, etc.