We present microscopic-macroscopic models in the description of traffic flow dynamics. The first model consists in ODEs for the trajectories of (microscopic)
slower vehicles and a scalar conservation law for the (macroscopic) car density. In our formulation, the presence of the slower and larger vehicles influences the whole traffic in terms of a non negligible capacity dropping of the vehicular flow, thus giving rise to a moving bottleneck effect. We study existence of the solution of that model and then we present numerical simulations, also in the case of a bus route in a urban network of roads. In the second model, we couple the (macroscopic) fluid dynamic Aw-Rascle model and the (microscopic) Follow the Leader model in two sections of a one dimensional road. The coupling is obtained by means of appropriate transmission conditions at the interface of the two regime, and, more precisely, by merging two initial boundary value problems for the aforementioned systems in the two quadrant t>0, x>0 and x<0.
We prove the existence of solutions of these models, and, based on the proposed conditions at the interface, we present possible numerical approximations.
The results are in collaboration with G. Bretti (IAC-CNR Rome), E. Cristiani (Sapienza, Univ., Rome), I. Gasser, A. Maurizi (Hamburg Univ.) and B. Piccoli (Rugters Univ., Camden).
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