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Fundamental Diagram Analysis: Voronoi method

The extraction of density, velocity and specific flow from pedestrian trajectories is basis to investigate the fundamental diagram. Different methods may lead to various statistical results with different accuracy.

The Voronoi method has the advantages of higher resoulution and smaller fluctuation in trajectory analysis. With this method, profiles of density, velocity and specific flow can be calculated to study the spatiotemporal characteristics of pedestrian flow in certain geometry.

Comparison of measurement methods

Series of real crowd movement as well as well-controlled laboratory experiments ( Uni- and bidirectional pedestrian flow in straight corridor, pedestian experiments in T-junction, bottleneck, circuit corridor and so on) have been analyzed with Voronoi method. See the following video for a comparison of different measurement methods

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Density and velocity Profiles

The next figure shows profiles of density, velocity and specific flow of pedestrian movementin in a T-junction:

Density profiles

Difference between the uni- and bidirectional fundamental diagram

The following figure shows the density-flow relation of unidirectional and bidirectional movement in a straight corridor

Uni Bidirectional FD

At low densities no relevant difference is observed. However, with increasing density the discrepancies of the flow becomes obvious, which can be also seen in the following video:

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