Abstract
We present two frameworks for the description of traffic flow. First, we consider the coupling of a micro- and a macroscopic models, the former consisting in a system of ordinary differential equations and the latter in the usual LWR conservation law, see [5, 10]. Then, inspired by this model, we consider a macroscopic model where some trajectories are known thanks to, for instance, GPS measurement devices. The result is a new traffic model able to take into account real time data, or, in other words, that encodes these data, see [4]. This work follows a long collaborationwith RinaldoM. Colombo; the author thanks him for his support.
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Marcellini, F. ODE-PDE models in traffic flow dynamics. Bull Braz Math Soc, New Series 47, 533–544 (2016). https://doi.org/10.1007/s00574-016-0167-5
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DOI: https://doi.org/10.1007/s00574-016-0167-5