We extend the classical Lighthill–Whitham–Richards (LWR) traffic model allowing different maximal speeds for different vehicles. Then we add a uniform bound on the traffic speed. The result, presented in this paper, is a new macroscopic model displaying two phases based on a nonsmooth 2×2 system of conservation laws. This model is compared with other models of the same type in the current literature, as well as with a kinetic one. Moreover, we establish a rigorous connection between a microscopic follow-the-leader model based on ordinary differential equations and this macroscopic continuum model.
Colombo, R., Marcellini, F., Rascle, M. (2010). A 2-Phase Traffic Model Based on a Speed Bound. SIAM JOURNAL ON APPLIED MATHEMATICS, 70(7), 2652-2666 [10.1137/090752468].
A 2-Phase Traffic Model Based on a Speed Bound
MARCELLINI, FRANCESCA;
2010
Abstract
We extend the classical Lighthill–Whitham–Richards (LWR) traffic model allowing different maximal speeds for different vehicles. Then we add a uniform bound on the traffic speed. The result, presented in this paper, is a new macroscopic model displaying two phases based on a nonsmooth 2×2 system of conservation laws. This model is compared with other models of the same type in the current literature, as well as with a kinetic one. Moreover, we establish a rigorous connection between a microscopic follow-the-leader model based on ordinary differential equations and this macroscopic continuum model.File | Dimensione | Formato | |
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