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Relating Car-Following and Continuum Models of Road Traffic

In: Traffic and Granular Flow ’99

Author

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  • P. Berg

    (University of Bristol, School of Mathematics)

  • A. Woods

    (University of Bristol, School of Mathematics)

Abstract

We derive a transformation that relates car-following models to their analogous continuum counterpart by using an integral representation of the density. A Taylor expansion of the latter yields an ordinary differential equation in terms of the density and the headway, hence a relation between the two characteristic variables in the corresponding models. This formal approach is supported by similar numerical solutions of the optimal-velocity (OV) model [1] and its continuum analogue. Moreover, the same stability criterion holds in both models. It can be seen that dispersive and anticipation terms of continuum models are a result of applying our transformation to car-following models.

Suggested Citation

  • P. Berg & A. Woods, 2000. "Relating Car-Following and Continuum Models of Road Traffic," Springer Books, in: Dirk Helbing & Hans J. Herrmann & Michael Schreckenberg & Dietrich E. Wolf (ed.), Traffic and Granular Flow ’99, pages 389-394, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-59751-0_39
    DOI: 10.1007/978-3-642-59751-0_39
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