Pedestrian Walking Behavior Revealed through a Random Walk Model

Hui Xiong,Wuhong Wang,Huachun Tan,Liya Yao

doi:10.1155/2012/405907

Hui Xiong, Wuhong Wang + Show 2 more

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https://doi.org/10.1155/2012/405907

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Abstract

This paper applies method of continuous‐time random walks for pedestrian flow simulation. In the model, pedestrians can walk forward or backward and turn left or right if there is no block. Velocities of pedestrian flow moving forward or diffusing are dominated by coefficients. The waiting time preceding each jump is assumed to follow an exponential distribution. To solve the model, a second‐order two‐dimensional partial differential equation, a high‐order compact scheme with the alternating direction implicit method, is employed. In the numerical experiments, the walking domain of the first one is two‐dimensional with two entrances and one exit, and that of the second one is two‐dimensional with one entrance and one exit. The flows in both scenarios are one way. Numerical results show that the model can be used for pedestrian flow simulation.

Highlights

In recent years, modeling pedestrian flow has attracted considerable attention, partly because the model serves as basis for efficient crowd evacuation management and pedestrian facility operations
Cellular automata models are widely used for capturing pedestrian walking behaviors, such as bi-direction movement 1, 3, 4, pedestrian counter flow with different walk velocities
Instead of describing individual pedestrian’s behavior, this type of models treats the crowd as a whole and applies the conservation laws to capture the relationship among speed, flow, and density of pedestrian flow 17–21

Summary

Introduction

In recent years, modeling pedestrian flow has attracted considerable attention, partly because the model serves as basis for efficient crowd evacuation management and pedestrian facility operations. Most of the existing models for pedestrian flow are of microscopic nature, describing in detail the interactions among pedestrians, and between pedestrians and obstacles Those models include, among others, cellular automata models 1–7 , lattice gas models 8–12 , the social force models , the centrifugal force models , and the floor field models 15, 16. Instead of describing individual pedestrian’s behavior, this type of models treats the crowd as a whole and applies the conservation laws to capture the relationship among speed, flow, and density of pedestrian flow 17–21. Motivated by the work by Barkai et al 22 , this paper attempts to apply the approach of continuous-time random walks CTRW to derive a partial differential equation model to describe the motion of pedestrians.

Numerical Algorithm

Numerical Example

Conclusion