A Mathematical Model for the Behavior of Pedestrians

TL;DR

This paper introduces a mathematical model simulating pedestrian movement based on individual decision-making, attraction, repulsion, and fluctuations, enabling realistic computer simulations of behaviors like group formation and collision avoidance.

Contribution

It presents a novel explicit mathematical framework for pedestrian behavior, incorporating decision processes and effects, applicable to various real-world scenarios.

Findings

Model accurately simulates pedestrian group formation

Effectively predicts behavior in queues and collision avoidance

Provides a basis for realistic pedestrian behavior simulations

Abstract

The movement of pedestrians is supposed to show certain regularities which can be best described by an ``algorithm'' for the individual behavior and is easily simulated on computers. This behavior is assumed to be determined by an intended velocity, by several attractive and repulsive effects and by fluctuations. The movement of pedestrians is dependent on decisions, which have the purpose of optimizing their behavior and can be explicitly modelled. Some interesting applications of the model to real situations are given, especially to formation of groups, behavior in queues, avoidance of collisions and selection processes between behavioral alternatives.