From the modelling of driver’s behavior to hydrodynamic models and problems of traffic flow.

*(English)*Zbl 1005.90016From 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.

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.

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\textit{N. Bellomo} et al., Nonlinear Anal., Real World Appl. 3, No. 3, 339--363 (2002; Zbl 1005.90016)

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