Asymptotic limits of a discrete kinetic theory model of vehicular traffic. (English) Zbl 1210.90047
Summary: The paper proposes a rigorous method to construct the hyperbolic asymptotic limit of the discrete kinetic theory model of vehicular traffic proposed in [D. Helbing, “Derivation of non-local macroscopic traffic equations and consistent traffic pressures from microscopic car-following models”, Eur. Phys. J. B 69, 539–548 (2009)]. A second-order macroscopic model of the Payne-Whitham type is derived and the coefficients of the equations are obtained from the detailed description of the microscopic interactions developed in the kinetic model.
MSC:
| 90B20 | Traffic problems in operations research |
References:
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