There are two different approaches to model traffic flow phenomena: microscopic models describe the motion of each single vehicle, predicting the evolution of its position and speed by means of a system of ODEs, the macroscopic models instead focus on the evolution of the macroscopic quantities by means of PDEs.
In this talk we will describe a new microscopic second order model specifically conceived to reproduce stop and go waves, a typical feature of congested traffic. We will analyze the connections with the macroscopic scale and we will couple this microscopic second order model with a first order macroscopic model avoiding any interface or boundary conditions between them. In this way we obtain a new multi-scale model able to reproduce real traffic phenomena, easy to use thanks to the advantages inherited from the two approaches mixed together.
This is a joint work with Emiliano Cristiani.
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