Analysis and modelling of macroscopic and microscopic dynamics of a pedestrian cross-flow

Abstract

In this work we investigate the behaviour of a human crowd in a cross-flow. In the first part of our work we analyse the results of a set of controlled experiments in which subjects were divided into two groups, organised in such a way to explore different density settings, and asked to walk through the crossing area. We study the results of the experiment by defining and analysing a few macroscopic and microscopic observables. Along with analysing traditional indicators such as density and velocity, whose dynamics was, to the extent of our knowledge, poorly understood for this setting, we pay particular attention to walking and body orientation, studying how these microscopic observables are influenced by density. Furthermore, we report a preliminary but quantitative analysis on the emergence of self-organising patterns (stripes) in the crossing area, a phenomenon that had been previously qualitatively reported for human crowds, and reproduced in models, but whose quantitative analysis (in particular with respect to density conditions) is, again according to our knowledge, a novel contribution.In the second part of our work, we try to reproduce the empirical results using a hierarchy of models, which differ in the details of the body shape (using a disk-shaped body vs a more realistic elliptical shape) and in how collision avoiding is performed (using only information regarding "centre of mass" distance and velocity, or actually introducing body shape information). We verified that the most detailed model (i.e., using body shape information and an elliptical body) outperforms in a significant way the simplest one (using only centre of mass distance and velocity, and disk-shaped bodies). Furthermore, we observed that if elliptical bodies are introduced without introducing such information in collision avoidance, the performance of the model is relatively poor. Nevertheless, the difference between the different models is relevant only in describing the "tails" of the observable distributions, suggesting that the more complex models could be of practical use only in the description of high density settings. Although we did not calibrate our model in order to reproduce the "stripe formation" self-organising pattern, we verified that it naturally emerges in all models.

Crowd Evacuation through Crossing Configurations: Effect of Crossing Angles and Walking Speeds on Speed Variation and Evacuation Time

“…Nevertheless, the other patterns, e.g., diagonal stripes, were not observed in intersecting streams of ants. Recently, a quantitative analysis of the stripe formation in the intersection area concerning density conditions was provided by Zanlungo et al [32]. Mullick et al [33] introduced computational methods to analyze the striped patterns, in addition to analyzing the geometric properties of the stripes.…”