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Are We Predictable Pedestrians?

To answer that question, Dr. Chung-min Lee (Mathematics and Statistics) researched pedestrian movement with colleagues in the Netherlands at the Eindhoven University of Technology during her sabbatical.

CSULB and the Eindhoven University of Technology

With her collaborators, Dr. Lee applied particle flow mathematical models to pedestrian movement since particle size is relative: they can be as small as gas molecules or as large as humans. Using Microsoft Kinect depth sensors, the group recorded pedestrians moving down a university corridor and walking through a crowded train station. From these real life recordings, Dr. Lee is developing mathematical models for pedestrian dynamics. The research applies to building safety, city planning, and emergency preparation for crowded events.

Many existing mathematical models come from short-time experiments with artificial setup; Dr. Lee and her colleagues felt that real life, long-term data in large quantities are necessary to bring the mathematical models closer to reality. With tens of thousands of recorded trajectories in the corridor setting and millions of trajectories from the train station, Dr. Lee and her collaborators built and validated mathematical pedestrian models at the statistical level.

Recordings of 3D depth map of pedestrians in one morning rush hour at the Eindhoven train station (the Netherlands) with Voronoi diagram superimposed. Numbers in the video indicate topology change of the crowd. [NO AUDIO]

They modeled pedestrians as active particles using kinetic theory. Pedestrian movements are influenced by their destination, by environmental geometry, by other pedestrians and by random events such as phone calls or bumping into acquaintances. Beginning with the simplest scenario where a pedestrian walks alone in a corridor, the collaborators considered dynamics of pedestrian movement. The pedestrian could walk toward either exit depending on his/her destination and whether he/she changes his/her mind. The dynamics of the pedestrian were written into Langevin equations, which are commonly used for modeling many stochastic processes. Their study found that this model generated data quantitatively consistent with measurements not only on average quantities but also at statistical levels.

Next, they modeled interactions among pedestrians. They asked how pedestrians avoid walking into each other, and what type of forces result from this avoidance. From the asymmetry of their measured pedestrian data, they learned that having a clear view ahead on the path is an important factor for pedestrians when considering modifying their original velocity and desired trajectory. This multi-pedestrian model, extended from the single pedestrian model, was able to reproduce the measured statistics.

Their work has been accepted by The Conference on Traffic and Granular Flow that will be held this month in the Netherlands.

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