Starting from microscopic follow-the-leader models, we develop macroscopic models of hyperbolic type where we still keep the time delay. The proposed models can be seen as an extension of the classical Lighthill-Whitham Richards-model or Aw-Rascle-Zhang model, respectively. Since standard results from the literature are not directly applicable to the delayed models, we mainly focus on numerical methods based on first principles and present simulation results inspired by real data.
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