2015/01/28 by José A. Carrillo, S. Martin, Carrillo, José A. +3
Engineering · Social Sciences · #35F21 #35Q70 #35Q91 #91Cxx #Analysis of PDEs (math.AP) #Evacuation and Crowd Dynamics #FOS: Mathematics #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS) #Traffic control and management #Transportation Planning and Optimization
paper · pdf · doi:10.48550/arxiv.1501.07054
openalex publication_date 2015/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Roger Hughes proposed a macroscopic model for pedestrian dynamics, in which individuals seek to minimize their travel time but try to avoid regions of high density. One of the basic assumptions is that the overall density of the crowd is known to every agent. In this paper we present a modification of the Hughes model to include local effects, namely limited vision, and a conviction towards decision making. The modified velocity field enables smooth turning and temporary waiting behavior. We discuss the modeling in the micro- and macroscopic setting as well as the efficient numerical simulation of either description. Finally we illustrate the model with various numerical experiments and evaluate the behavior with respect to the evacuation time and the overall performance.