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Advances in Mathematical Physics
Volume 2016, Article ID 6902086, 17 pages
Research Article

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

1Department of Structural and Geotechnical Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
2Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
3Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185 Roma, Italy

Received 27 October 2015; Accepted 11 February 2016

Academic Editor: Prabir Daripa

Copyright © 2016 Alessandro Corbetta and Andrea Tosin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A comparison between first-order microscopic and macroscopic differential models of crowd dynamics is established for an increasing number of pedestrians. The novelty is the fact of considering massive agents, namely, particles whose individual mass does not become infinitesimal when grows. This implies that the total mass of the system is not constant but grows with . The main result is that the two types of models approach one another in the limit , provided the strength and/or the domain of pedestrian interactions are properly modulated by at either scale. This is consistent with the idea that pedestrians may adapt their interpersonal attitudes according to the overall level of congestion.