The Inflection Point of the Speed-Density Relation and the Social Force Model

TL;DR

This paper investigates the inflection point in the speed-density relation of pedestrian movement, showing that common Social Force Model variants lack this feature and proposing a modified model that captures it.

Contribution

The paper demonstrates that standard Social Force Models do not produce the inflection point and introduces a modified model that successfully reproduces it.

Findings

Common SFM variants lack the inflection point in the speed-density diagram.

A modified SFM can produce the inflection point.

Empirical data supports the existence of the inflection point.

Abstract

It has been argued that the speed-density digram of pedestrian movement has an inflection point. This inflection point was found empirically in investigations of closed-loop single-file pedestrian movement. The reduced complexity of single-file movement does not only allow a higher precision for the evaluation of empirical data, but it occasionally also allows analytical considerations for micosimulation models. In this way it will be shown that certain (common) variants of the Social Force Model (SFM) do not produce an inflection point in the speed-density diagram if infinitely many pedestrians contribute to the force computed for one pedestrian. We propose a modified Social Force Model that produces the inflection point.