Modeling Unidirectional Pedestrian Movement: An Investigation of Diffusion Behavior in the Built Environment

Abstract

Unidirectional pedestrian movement is a special phenomenon in the evacuation process of large public buildings and urban environments at pedestrian scale. Several macroscopic models for collective behaviors have been built to predict pedestrian flow. However, current models do not explain the diffusion behavior in pedestrian crowd movement, which can be important in representing spatial-temporal crowd density differentiation in the movement process. This study builds a macroscopic model for describing crowd diffusion behavior and evaluating unidirectional pedestrian flow. The proposed model employs discretization of time and walking speed in geometric distribution to calculate downstream pedestrian crowd flow and analyze movement process based on upstream number of pedestrians and average walking speed. The simulated results are calibrated with video observation data in a baseball stadium to verify the model precision. Statistical results have verified that the proposed pedestrian diffusion model could accurately describe pedestrian macromovement behavior within the margin of error.

Adapting the Social Force Model for Low Density Crowds in Open Environments

“…For the frontal scenario, for instance, the lateral spread is slightly larger with the proposed model than with the SFM. The lowest density obtained with the proposed model is realistic because pedestrians tend to spread out in a wide and open space [4].…”

“…We believe that as the crowd density increases, pedestrians are more willing to get closer to other pedestrians. Based on empirical observations from video data and on [3,4], a second hypothesis is discussed: in sparse crowds, pedestrians are also more willing to turn rather than slow down as they approach a crowd. In brief, the base model used to build the adaptation presented in this paper is the SFM [13] including limiting acceleration plus a physical collision force to prevent overlapping [14] and an ellipse body shape.…”

“…The assumption behind this is that pedestrians slow down maintaining their trajectory rather than moving away, even if it means entering a dense area with a high risk of collision. However, our hypothesis is that in an open space, where pedestrians can spread out, they will tend to occupy the available space and seek to reduce density in order to reduce the collision risk [4]. To test this hypothesis, perception is added to pedestrians so they adapt their personal space to the crowd density and consequently modify their behaviour.…”

“…In this context, pedestrians tend to occupy the available space and seek to avoid dense areas in order to reduce the risk of collision [3,4]. In this paper a modification of the SFM is proposed.…”

A Semi-Lagrangian Scheme for a Modified Version of the Hughes’ Model for Pedestrian Flow

“…The diffusive terms allow to use standard analytical techniques from nonlinear PDE theory, see [26]. Diffusive phenomena have been observed and studied in pedestrian dynamics [47,36], giving an additional justification of the modification considered. System (2) has to be supplemented with suitable boundary and initial conditions.…”