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From the modelling of driver’s behavior to hydrodynamic models and problems of traffic flow. (English) Zbl 1005.90016
From the introduction: The optimization and control of traffic flow along a road or networks of raods, either highways or urban streets, is an intereting and challenging field of interactions between mathematics and engineering sciences. Dealing with such a problem may take advantage of suitable models which describe the evolution in time and space of the flow conditions: car density and velocity.
The content is organized into nine sections. The first part of the paper refer to the state-of-the-art. The second part indicates several research perspectives.
Section 1 is a general introduction which provides a description of the aims of this paper and of its contents.
Section 2 defines the general hydrodynamics framework, mass and momentum conservation equations, that generates specific traffic flow models. This section already contains a preliminary discussion on the validity of hydrodynamic models.
Section 3 deals with the modelling of the interaction between driver and vehicle, that is with the driver model which is the fundamental background for the design of hydrodynamic models.

MSC:
90B20 Traffic problems in operations research
35Q35 PDEs in connection with fluid mechanics
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