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

TL;DR

This paper derives an analytical function linking pedestrian flow to density from the Social Force Model for uni-directional steady flow, matching various empirical fundamental diagrams.

Contribution

It provides the first analytical solution of the Social Force Model for steady, uni-directional pedestrian flow, assuming only nearest neighbor interactions.

Findings

Derived a flow-density function from the Social Force Model

Function matches a variety of empirical fundamental diagrams

Applicable to homogeneous, steady-state pedestrian 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.