How Can Macroscopic Models Reveal Self-Organization in Traffic Flow?

In this paper we propose a new modeling technique for ve-hicular 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 continu-ous approach. The starting point is a multiscale method for pedestrian modeling, recently introduced in [5], 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 simulta-neously described from both a discrete (microscopic) and a continuous (macroscopic) perspective. This way it is possi-ble to perform numerical simulations in which the single tra-jectories 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 illustra-tive 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 the-ory. Furthermore, thanks to the coupling between the micro-scopic and the macroscopic scales, we model the continuous flow of cars without losing the right amount of granular-ity, which characterizes the real physical system and triggers self-organization effects, such as, for example, the oscillatory patterns visible at jammed uncontrolled crossroads.