A re-examination of the role of friction in the original Social Force Model

CORNES, F.E.; I STICCO; FRANK, G.A.; C. O. DORSO

SAFETY SCIENCE

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2020 vol. 121 p. 42 - 53

0925-7535

The fundamental diagram of pedestrian dynamics gives the relation between the density and the flow within aspecific enclosure. It is characterized by two distinctive behaviors: the free-flow regime (for low densities) andthe congested regime (for high densities). In the former, the flow is an increasing function of the density, while inthe latter, the flow remains on hold or decreases. In this work, we perform numerical simulations of the pil-grimage at the entrance of the Jamaraat bridge (pedestrians walking along a straight corridor) and compareflow-density measurements with empirical measurements made by Helbing et al. (2007). We show that underhigh density conditions, the basic Social Force Model (SFM) does not completely handle the fundamental dia-gram reported in empirical measurements. We use analytical techniques and numerical simulations to prove thatwith an appropriate modification of the friction coefficient (but sustaining the SFM) it is possible to attainbehaviors which are in qualitative agreement with the empirical data. Other authors have already proposed amodification of the relaxation time in order to address this problem. In this work, we unveil the fact that ourapproach is analogous to theirs since both affect the same term of the reduced-in-units equation of motion. Weshow how the friction modification affects the pedestrian clustering structures throughout the transition fromthe free-flow regime to the congested regime. We also show that the speed profile, normalized by width andmaximum velocity yields a universal behavior regardless of the corridor dimensions.