# American Institute of Mathematical Sciences

September  2014, 19(7): 1869-1888. doi: 10.3934/dcdsb.2014.19.1869

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

 1 King Abdulaziz University, Jeddah, Saudi Arabia, and Politecnico of Torino, Italy 2 Cadi Ayyad University, Ecole Nationale des Sciences Appliquées, Marrakech, Morocco 3 Departamento de Matemática Aplicada, Universidad de Granada

Received  April 2013 Revised  May 2013 Published  August 2014

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.
Citation: Nicola Bellomo, Abdelghani Bellouquid, Juanjo Nieto, Juan Soler. On the multiscale modeling of vehicular traffic: From kinetic to hydrodynamics. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 1869-1888. doi: 10.3934/dcdsb.2014.19.1869
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