An analytical solution of the Social Force Model for uni-directional flow

Abstract

A function for the dependence of flow on pedestrian density is derived analytically from the Social Force Model (SFM) for the case of a homogeneous population walking in the same direction and being in steady state. Assuming that only nearest Voronoi neighbors effectuate forces the resulting function matches a variety of very different fundamental diagrams that were found empirically.

Submitted for publication in proceedings of Traffic and Granular Flow (TGF) 19