Kinetic Traffic Flow Models

TL;DRAbstract

This survey contains a description of different types of mathematical models used for the simulation of vehicular traffic. It concentrates on traffic flow models based on a kinetic or Boltzmann type description. However, microscopic models modelling the behaviour of single vehicles and macroscopic models based on fluid dynamic equations are discussed as well. For an example, it is shown in detail how kinetic models can be derived from microscopic ones and how macroscopic models can be derived from the underlying kinetic models. Connections between the different types of models are presented and numerical methods and simulations are shown for all types of models.

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