Mathematical models and methods for crowd dynamics control

TL;DR

This survey reviews mathematical models and control strategies for crowd management, focusing on using leaders and environmental modifications to guide pedestrians naturally without overt intervention.

Contribution

It provides a comprehensive overview of recent models and methods for crowd control, emphasizing strategies that minimize external influence and preserve natural behavior.

Findings

Control via leaders leverages social influence and herding effects.

Environmental modifications with obstacles can naturally guide crowd movement.

Models span microscopic to macroscopic scales, showing their interrelations.

Abstract

In this survey we consider mathematical models and methods recently developed to control crowd dynamics, with particular emphasis on egressing pedestrians. We focus on two control strategies: The first one consists in using special agents, called leaders, to steer the crowd towards the desired direction. Leaders can be either hidden in the crowd or recognizable as such. This strategy heavily relies on the power of the social influence (herding effect), namely the natural tendency of people to follow group mates in situations of emergency or doubt. The second one consists in modify the surrounding environment by adding in the walking area multiple obstacles optimally placed and shaped. The aim of the obstacles is to naturally force people to behave as desired. Both control strategies discussed in this paper aim at reducing as much as possible the intervention on the crowd. Ideally the natural behavior of people is kept, and people do not even realize they are being led by an external intelligence. Mathematical models are discussed at different scales of observation, showing how macroscopic (fluid-dynamic) models can be derived by mesoscopic (kinetic) models which, in turn, can be derived by microscopic (agent-based) models.