Comparing First-Order Microscopic and Macroscopic Crowd Models for an Increasing Number of Massive Agents

Abstract EN

A comparison between first-order microscopic and macroscopic differential models of crowd dynamics is established for an increasing number N of pedestrians.

The novelty is the fact of considering massive agents, namely, particles whose individual mass does not become infinitesimal when N grows.

This implies that the total mass of the system is not constant but grows with N .

The main result is that the two types of models approach one another in the limit N → ∞ , provided the strength and/or the domain of pedestrian interactions are properly modulated by N at either scale.

This is consistent with the idea that pedestrians may adapt their interpersonal attitudes according to the overall level of congestion.