Fluctuations around mean walking behaviours in diluted pedestrian flows

Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasing the safety of civil facilities. A key feature of crowds is its intrinsic stochasticity, appearing even under very diluted conditions, due to the variability in individual behaviours. Individual stochasticity becomes even more important under densely crowded conditions, since it can be nonlinearly magnified and may lead to potentially dangerous collective behaviours. To understand quantitatively crowd stochasticity, we study the real-life dynamics of a large ensemble of pedestrians walking undisturbed, and we perform a statistical analysis of the fully-resolved pedestrian trajectories obtained by a year-long high-resolution measurement campaign. Our measurements have been carried out in a corridor of the Eindhoven University of Technology via a combination of Microsoft Kinect 3D-range sensor and automatic head-tracking algorithms. The temporal homogeneity of our large database of trajectories allows us to robustly define and separate average walking behaviours from fluctuations parallel and orthogonal with respect to the average walking path. Fluctuations include rare events when individuals suddenly change their minds and invert their walking direction. Such tendency to invert direction has been poorly studied so far even if it may have important implications on the functioning and safety of facilities. We propose a novel model for the dynamics of undisturbed pedestrians, based on stochastic differential equations, that provides a good agreement with our experimental observations, including the occurrence of rare events.