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Specified homogenization of a discrete traffic model leading to an effective junction condition

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  • In this paper, we focus on deriving traffic flow macroscopic models from microscopic models containing a local perturbation such as a traffic light. At the microscopic scale, we consider a first order model of the form "follow the leader" i.e. the velocity of each vehicle depends on the distance to the vehicle in front of it. We consider a local perturbation located at the origin that slows down the vehicles. At the macroscopic scale, we obtain an explicit Hamilton-Jacobi equation left and right of the origin and a junction condition at the origin (in the sense of [25]) which keeps the memory of the local perturbation. As it turns out, the macroscopic model is equivalent to a LWR model, with a flux limiting condition at the junction. Finally, we also present qualitative properties concerning the flux limiter at the junction.

    Mathematics Subject Classification: 35D40, 90B20, 35B27, 35F20, 45K05.

    Citation:

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  • Figure 1.  Schematic representation of the microscopic model

    Figure 2.  Schematic representation of the macroscopic model

    Figure 3.  Schematic representation of the optimal velocity function $V$

    Figure 4.  Schematic representation of $\bar{H}$

    Figure 5.  Schematic representation of the function $\rho$

    Figure 6.  Schematic representation of the function $\rho$

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