Relating Car-Following and Continuum Models of Road Traffic

P. Berg and A. Woods
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P. Berg: University of Bristol, School of Mathematics
A. Woods: University of Bristol, School of Mathematics

A chapter in Traffic and Granular Flow ’99, 2000, pp 389-394 from Springer

Abstract: 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.

Date: 2000
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DOI: 10.1007/978-3-642-59751-0_39

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