期刊
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
卷 35, 期 4, 页码 949-973出版社
SIAM PUBLICATIONS
DOI: 10.1137/S0036141002411490
关键词
hyperbolic systems of conservation laws; traffic flow; multiclass models; homogenization; discontinuous flux; uniqueness; hydrodynamic limit
We introduce a new homogenized hyperbolic (multiclass) traffic flow model, which allows us to take into account the behaviors of different type of vehicles (cars, trucks, buses, etc.) and drivers. We discretize the starting Lagrangian system introduced below with a Godunov scheme, and we let the mesh size h in (x, t) go to 0: the typical length (of a vehicle) and time vanish. Therefore, the variables - here (w, a) - which describe the heterogeneity of the reactions of the different car-driver pairs in the traffic, develop large oscillations when h --> 0. These (known) oscillations in (w, a) persist in time, and we describe the homogenized relations between velocity and density. We show that the velocity is the unique solution `a la Kruzkov of a scalar conservation law, with variable coefficients, discontinuous in x. Finally, we prove that the same macroscopic homogenized model is also the hydrodynamic limit of the corresponding multiclass Follow-the-Leader model.
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