  In this paper we propose a new modeling technique for vehicular traffic flow,
designed for capturing at a macroscopic level some effects, due to the
microscopic granularity of the flow of cars, which would be lost with a purely
continuous approach. The starting point is a multiscale method for pedestrian
modeling, recently introduced in Cristiani et al., Multiscale Model. Simul.,
2011, in which measure-theoretic tools are used to manage the microscopic and
the macroscopic scales under a unique framework. In the resulting coupled model
the two scales coexist and share information, in the sense that the same system
is simultaneously described from both a discrete (microscopic) and a continuous
(macroscopic) perspective. This way it is possible to perform numerical
simulations in which the single trajectories and the average density of the
moving agents affect each other. Such a method is here revisited in order to
deal with multi-population traffic flow on networks. For illustrative purposes,
we focus on the simple case of the intersection of two roads. By exploiting one
of the main features of the multiscale method, namely its
dimension-independence, we treat one-dimensional roads and two-dimensional
junctions in a natural way, without referring to classical network theory.
Furthermore, thanks to the coupling between the microscopic and the macroscopic
scales, we model the continuous flow of cars without losing the right amount of
granularity, which characterizes the real physical system and triggers
self-organization effects, such as, for example, the oscillatory patterns
visible at jammed uncontrolled crossroads.
