Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models

  title={Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models},
  author={A. Aw and Axel Klar and Michel Rascle and Thorsten Materne},
  journal={SIAM Journal of Applied Mathematics},
In this paper we establish a connection between a microscopic follow-the-leader model based on ordinary differential equations and a semidiscretization of a macroscopic continuum model based on a conservation law. Naturally, it also turns out that the natural discretization of the conservation law in Lagrangian coordinates is equivalent to a straightforward time discretization of the microscopic model. We also show rigorously that, at least in the homogeneous case, the macroscopic model can be… CONTINUE READING
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