Modelling and Optimisation of Flows on Networks by Luigi Ambrosio Alberto Bressan Dirk Helbing Axel Klar & Enrique Zuazua

Author:Luigi Ambrosio, Alberto Bressan, Dirk Helbing, Axel Klar & Enrique Zuazua
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

(85)

where T is the safe time headway and the maximum vehicle density. This formula makes also sense in the low-density limit , where χ → 1 and p → 1.

A linear stability analysis of the non-local traffic model can be done via a gradient expansion. It results in equations of the kind (77) and further viscosity and diffusion terms [8].

Acknowledgements

The author would like to thank for the inspiring discussions with the participants of the Workshop on “Multiscale Problems and Models in Traffic Flow” organized by Michel Rascle and Christian Schmeiser at the Wolfgang Pauli Institute in Vienna from May 5–9, 2008, with partial support by the CNRS.

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