The effect of social roles on group behaviour

- In a recent series of papers, we proposed a mathematical model for the dynamics of a group of interacting pedestrians. The model is based on a non-Newtonian potential, that accounts for the need of pedestrians to keep both their interacting partner and their walking goal in their vision field, and to keep a comfortable distance between them. These two behaviours account respectively for the angular and radial part of the potential from which the force providing the pedestrian acceleration is derived. The angular term is asymmetric, i.e. does not follow the third law of dynamics, with observable effects of group formation and velocity. We first assumed the group to move in a scarcely dense environment, whose effect could be modelled through a “white noise thermic bath”, and successfully compared the predictions of the model with observations of real world pedestrian behaviour. We then studied, both from an empirical and a theoretical standpoint, the effect of crowd density on group dynamics. We verified that the average effect of crowd density may be modelled by adding a harmonic term to the group potential. The model predictions, which include “phase transitions” in the group configuration (e.g. in 3 people groups transition from a “V” formation to a “Λ” one, and eventually to pedestrians walking in a line), are again confirmed, at least in the observed density range, by a comparison with real world data. Until now we had averaged all pedestrian data collected in a given environmental setting (i.e. in corridors of similar width and at similar crowd densities) without differentiating on group composition and social roles. In this work, we present preliminary results on these features, namely we study how the group configuration and velocity is affected by inter-pedestrian relation (family, couples, colleagues, friends), purpose (work, leisure) and gender. We also show results related to the effect of asymmetric interactions, that confirm further the non-Newtonian nature of gaze-based angular interaction in our model.