Freezing transition in a four-directional traffic model for facing and crossing pedestrian flow

Takashi Nagatani and Kazuhito Komada

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 8, 1729-1738

Abstract: We study the traffic behavior in the facing and crossing traffic of pedestrians numerically and analytically. There are four kinds of walkers, those moving to east, to west, to north, and to south. We present the mean-field approximation (MFA) model for the four-directional traffic. The model is described in terms of four nonlinear difference equations. The excluded-volume effect and directionality are taken into account. The fundamental diagrams (current–density diagrams) are derived. When pedestrian density is higher than a critical value, the dynamical phase transition occurs from the free flow to the frozen (stopping) state. The critical density is derived by using the linear stability analysis. The velocity and current (flow) at the steady state are derived analytically. The analytical result is consistent with that obtained by the numerical simulation.

Keywords: Pedestrian flow; Traffic flow; Mean-field approximation; Freezing transition; Instability (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:8:p:1729-1738

DOI: 10.1016/j.physa.2009.12.038

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