@article{ref1,
title="A car following model-based on the lighthill-whitham theory",
journal="Transportation and traffic theory",
year="1996",
author="del Castillo, J.",
volume="13",
number="",
pages="517-538",
abstract="This work presents a car-following model. The proposed car-following model is intended to be a microscopic version of the continuity equation. First of all, a linear speed-distance curve is assumed for the Lighthill-Whitham model. The resulting model turns out to be the well-known linear car-following model proposed by Chandler et al (1958). Next, the results obtained for a linear speed-distance relationship as stationary solution, are extended for a generic nonlinear speed-distance curve. In this case, the reaction time becomes a function of the distance between vehicles. When the car-following model is written in a particular set of dimensionless variables, the resulting dimensionless car-following model does not contain any parameter. Finally, an algorithm for the nonlinear car-following model is developed. The results show that the algorithm for the nonlinear car-following model yields solutions that agree with those given by the Lighthill-Whitham model with the same speed-distance curve. (A) For the covering abstract see IRRD 886400.<p />",
language="en",
issn="",
doi="",
url="http://dx.doi.org/"
}