Sample set | a | b | c | |
0.944 | ||||
0.972 | ||||
0.982 |
Understanding and predicting the collective behaviour of crowds is essential to improve the efficiency of pedestrian flows in urban areas and minimize the risks of accidents at mass events. We advocate for the development of crowd traffic management systems, whereby observations of crowds can be coupled to fast and reliable models to produce rapid predictions of the crowd movement and eventually help crowd managers choose between tailored optimization strategies. Here, we propose a Bi-directional Macroscopic (BM) model as the core of such a system. Its key input is the fundamental diagram for bi-directional flows, i.e. the relation between the pedestrian fluxes and densities. We design and run a laboratory experiments involving a total of 119 participants walking in opposite directions in a circular corridor and show that the model is able to accurately capture the experimental data in a typical crowd forecasting situation. Finally, we propose a simple segregation strategy for enhancing the traffic efficiency, and use the BM model to determine the conditions under which this strategy would be beneficial. The BM model, therefore, could serve as a building block to develop on the fly prediction of crowd movements and help deploying real-time crowd optimization strategies.
Citation: |
Figure 1.
Experiments and data acquisition. (a) A typical experiment where bi-directional circulation is analyzed. (b) Participants equipped with reflexive markers were tracked by means of an optoelectronic motion capture system (VICON MX-40, Oxford Metrics, UK). (c) The area-weighting assignment procedure: The particle
Figure 2.
Characteristic speeds in the BM model. (a) Perspective view of the BFD
Figure 3.
Bi-directional Fundamental Diagram (BFD). (a) Estimated BFD expressing the flux
Figure 4.
Model results and comparisons with experimental data. (a) Setting for the model: the density at the entry of the corridor (
Figure 6.
Pedestrian and cluster velocities. Comparison between the pedestrian velocity
Figure 7.
Efficiency segregation strategy. Estimation of the relative gain using the segregation strategy (in %) as a function of the densities
Figure 8.
Cluster and cluster velocity. (a) Illustration of a cluster defined from a density distribution
Figure 9.
Level curves of the density. Level curves
Table 1.
Parametric estimation of the bi-directional fundamental diagram. The coefficients
Sample set | a | b | c | |
0.944 | ||||
0.972 | ||||
0.982 |
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