Jamming transitions in force-based models for pedestrian dynamics

TL;DR

This paper analyzes force-based pedestrian models, revealing intrinsic issues like unrealistic backward movement and overlaps, and proposes a new model that avoids these problems while accurately capturing jam dynamics.

Contribution

It identifies fundamental flaws in existing force-based models and introduces a new model that produces realistic pedestrian jam behavior without unrealistic negative speeds.

Findings

Unstable regimes lead to unrealistic backward movement and overlaps.

Existing models do not exhibit stop-and-go waves due to intrinsic flaws.

A new model is proposed that avoids negative speeds and captures realistic jam dynamics.

Abstract

Force-based models describe pedestrian dynamics in analogy to classical mechanics by a system of second order ordinary differential equations. By investigating the linear stability of two main classes of forces, parameter regions with unstable homogeneous states are identified. In this unstable regime it is then checked whether phase transitions or stop-and-go waves occur. Results based on numerical simulations show, however, that the investigated models lead to unrealistic behavior in form of backwards moving pedestrians and overlapping. This is one reason why stop-and-go waves have not been observed in these models. The unrealistic behavior is not related to the numerical treatment of the dynamic equations but rather indicates an intrinsic problem of this model class. Identifying the underlying generic problems gives indications how to define models that do not show such unrealistic behavior. As an example we introduce a new force-based model which produces realistic jam dynamics without the appearance of unrealistic negative speeds for empirical desired walking speeds.