In this talk I will present a kinetic approach to the modeling of vehicular traffic. Sticking to the idea that the macroscopic characteristics of traffic flow are ultimately generated by one-to-one interactions among drivers, the approach consists in linking the changes of speed of single vehicles to binary interactions among drivers, implementing then a probabilistic description of such microscopic interactions in a Boltzmann-type collisional operator. In particular, I will discuss how this approach allows one to study the fundamental diagrams of traffic, possibly considering a heterogeneous composition of the flow of vehicles, the traffic flow on single roads as well as on road networks, up to some preliminary ideas on traffic safety issues.
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