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Mathematical Problems in Engineering
Volume 2015, Article ID 308261, 6 pages
Research Article

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

1School of Architecture, Harbin Institute of Technology, Harbin 150001, China
2Center for Green Buildings and Cities, Graduate School of Design, Harvard University, Cambridge, MA 02138, USA
3School of Transportation Science and Engineering, Harbin Institute of Technology, Harbin 150091, China

Received 3 June 2015; Revised 9 August 2015; Accepted 25 August 2015

Academic Editor: Valery Sbitnev

Copyright © 2015 Ying Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.