A mesoscopic model for the effect of density on pedestrian group dynamics

Abstract

We introduce a mesoscopic model of pedestrian group behaviour, in which the internal group dynamics is modelled using a microscopic potential, while the effect of the environment is modelled using a harmonic term whose intensity depends on a macroscopic quantity, crowd density. We show that, in order to properly describe the behaviour of 2-person groups, the harmonic term is directed orthogonally to the walking direction, and its intensity grows linearly with density. We also show that, once calibrated on 2-person groups, the model correctly predicts the velocity and spatial extension of 3-person groups in the walking direction, while in order to describe properly also the abreast extension of 3-person groups a modification in the microscopic group dynamics has to be introduced. The model also correctly predicts the presence of a bifurcation phenomenon, namely the emergence of a stable 3-person Λ configuration at high densities, while only the V formation is stable at low densities.

Intrinsic group behaviour: Dependence of pedestrian dyad dynamics on principal social and personal features

“…After a revision of the coding procedure, we could analyse if, according to gender, age or height differences, roles such as "leader" or "follower" emerge. Finally, a mathematical modelling following [1] and [25] could be performed.…”

“…The model proposed in [1] introduced a non Newtonian [26] potential for group interaction on the basis of few and intuitive ideas about social interaction in pedestrian groups, and its predictions for group size, structure and velocity are in agreement with the observed natural behaviour of pedestrians. In [2] we studied a large data set of pedestrian trajectories to see how an extrinsic, i.e., environmental, property such as crowd density influences the dynamics of groups, and in [25] we introduced a mathematical model to explain such a crowd density effect on groups 1 .…”

People’s V-Formation and Side-by-Side Model Adapted to Accompany Groups of People by Social Robots

“…8, while second neighbors interact through a weaker and simplified potential depending only on the radial potential of Eq. 9, [26].…”

“…In this model, a pedestrian's neighborhood is decided based on its position on the axis orthogonal to the direction of the goal, see [26] for details. The model, in agreement with observational data, predicts that 3 people group:…”

Social group behaviour of triads. Dependence on purpose and gender

“…Researchers in the fields of pedestrian behaviour and crowd modelling have become recently more and more aware of the necessity of studying and modelling the behaviour of social groups. Groups represent an important, if not predominant, portion of urban pedestrian crowds [1,2], and they exhibit groupspecific behaviour [3,4,5,6] and thus understanding and modelling them is necessary to reproduce crowd behaviour in normal and emergency conditions [7]. As a result, a few statistical studies, mathematical and numerical models of group behaviours have been developed [3,8,9,10,11,12,13,14].…”