Eulerian vs. Lagrangian analyses of pedestrian dynamics asymmetries in a staircase landing

TL;DR

This study compares Eulerian and Lagrangian methods for analyzing pedestrian flow asymmetries on a staircase landing, emphasizing the importance of selecting homogeneous data for accurate statistical analysis.

Contribution

The paper introduces and compares two approaches for querying pedestrian data—Eulerian and Lagrangian—to improve analysis of flow asymmetries in real-life crowd movements.

Findings

Eulerian and Lagrangian approaches yield different insights into pedestrian dynamics.

Flow condition homogeneity significantly affects statistical analysis accuracy.

Cross-comparisons reveal distinct patterns in pedestrian velocities and accelerations.

Abstract

Real-life, out-of-laboratory, measurements of pedestrian movements allow extensive and fully-resolved statistical analyses. However, data acquisition in real-life is subjected to the wide heterogeneity that characterizes crowd flows over time. Disparate flow conditions, such as co-flows and counter-flows at low and at high pedestrian densities, typically follow randomly one another. When analysing the data in order to study the dynamics and behaviour of pedestrians it is crucial to be able disentangle and to properly select (query) data from statistically homogeneous flow conditions in order to avoid spurious statistics and to enable qualitative comparisons. In this paper we extend our previous analysis on the asymmetric pedestrian dynamics on a staircase landing, where we collected a large statistical database of measurements from ad hoc continuous recordings. This contribution has a two-fold aim: first, method-wise, we discuss two possible approaches to query experimental datasets for homogeneous flow conditions. For given flow conditions, we can either agglomerate measurements on a time-frame basis (Eulerian queries) or on a trajectory basis (Lagrangian queries). Second, we employ these two different perspectives to further explore asymmetries in the pedestrian dynamics in our measurement site. We report cross-comparisons of statistics of pedestrian positions, velocities and accelerations vs. flow conditions as well as vs. Eulerian or Lagrangian approach.