Pedestrian Flow Models With Slowdown Interactions

Abstract

In this paper, we introduce and study one-dimensional models for the behavior of pedestrians in a narrow street or corridor. We begin at the microscopic level by formulating a stochastic cellular automata model with explicit rules for pedestrians moving in two opposite directions. Coarse-grained mesoscopic and macroscopic analogs are derived leading to the coupled system of PDEs for the density of the pedestrian traffic. The obtained PDE system is of a mixed hyperbolic-elliptic type and therefore, we rigorously derive higher-order nonlinear diffusive corrections for the macroscopic PDE model. We perform numerical experiments, which compare and contrast the behavior of the microscopic stochastic model and the resulting coarse-grained PDEs for various parameter settings and initial conditions. We also demonstrate that the nonlinear diffusion is essential for reproducing the behavior of the stochastic system in the nonhyperbolic regime.

A kinetic theory approach to the dynamics of crowd evacuation from bounded domains

“…In this sense, we refer to some important contributions related to flux limiters, 22,40 while dependence of pedestrians' speed on the local density is an important way to control overcrowding. 12,13,24,39 We assume that the maximal reachable dimensionless velocity modulus v m = v m (α) depends linearly on the quality of the environment, in such a way that v m (0) = 0 -any movement is hindered -and v m (1) = 1 -the maximal speed can be reached. The dependence of the velocity modulus on the local density proposed in this paper is motivated by the fundamental diagrams for crowd flow, critically analyzed in Ref.…”

Derivation and analysis of continuum models for crossing pedestrian traffic

“…Hence we study a 1D reduction, which has a similar structure and behavior as the models analyzed in Ref. [11] and in Ref. [1], and obtain linear stability and local L 2 stability in certain density regimes (namely where the overall density is not too high).…”

Reducing Bidirectional Pedestrian Conflict Based on Lane Formation Phenomenon in Subway Corridors

“…With the theoretical and methodical analysis of pedestrian flow, the bidirectional flow, which is a typical pedestrian flow organization, has attracted substantial attention [8][9][10][11][12][13]. The interactions of bidirectional pedestrian streams would induce a serious conflicting effect [14][15].…”