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On the multiscale modeling of vehicular traffic: From kinetic to hydrodynamics

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  • This paper deals with the multiscale modeling of vehicular traffic according to a kinetic theory approach, where the microscopic state of vehicles is described by position, velocity and activity, namely a variable suitable to model the quality of the driver-vehicle micro-system. Interactions at the microscopic scale are modeled by methods of game theory, thus leading to the derivation of mathematical models within the framework of the kinetic theory. Macroscopic equations are derived by asymptotic limits from the underlying description at the lower scale. This approach shows the hypothesis under which macroscopic models known in the literature can be derived and how new models can be developed.
    Mathematics Subject Classification: 35Q91, 35L65, 35Q70.


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