MULTISCALE MODELING OF PEDESTRIAN DYNAMICS:
INDIVIDUALITY VS. COLLECTIVITY
Andrea Tosin
Istituto per le Applicazioni del Calcolo “M. Picone”
Consiglio Nazionale delle Ricerche
Via dei Taurini 19, 00185 Rome Italya.tosin@iac.cnr.it
http://www.iac.cnr.it/~tosin

Summary
The dynamics of human crowds are mainly ruled by mutual interactions among pedestrians.
The latter develop indeed behavioral strategies based on their perception of the state of thesurrounding environment, including especially the presence of neighboring individuals. Forinstance, when heading for a certain destination pedestrians normally deviate from theirpreferred paths in order to avoid crowded areas. Remarkably, interactions are usually noncooperative, i.e., walkers do not pursue a goal collectively, and are expressed without theapplication of any external organizing principle.
Due to the intrinsic granularity (viz. discreteness) of the system (the number N of pedestrians is possibly large, yet the approximation N → ∞ may not be always coherent), one-toone or one-to-few interactions are better described at an individual level. On the other hand,collective representations, focused on the crowd distribution as a whole, are often preferable over particle-based ones, in order to catch the spontaneously emerging self-organizedgroup behaviors, such as lane formation in counter-flows or traffic light effect at bottlenecks.
Moreover, they are often more amenable to additional mathematical analysis, numerics, andoptimization.
In this talk I will present a measure-theoretic approach, which offers useful conceptual
tools for tackling such an “individuality vs. collectivity” dualism. Indeed, it allows for amultiscale representation of the crowd in which single individuals, described as point masses,
are embedded into a continuous pedestrian flow. This way it is possible to study the effects
of a balanced interplay between small and large scales on the overall dynamics.

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