Integer and Fractional Approaches of a Pair of Car-Following Models

Abstract

There exist models to represent vehicular traffic, most of them are represented by ordinary linear or nonlinear differential equations. One of such approaches is the well-known Gazis-Herman-Rothery (GHR) model, which is formed by two cars moving in a single line where the car in front acts like a disturbance to the car behind, if assuming that overtakings does not occur. In this paper we take the model already mentioned, one with a nonlinear nature which depends on positions and velocities of the involved cars, to make a comparison between the classical model and one with modifications on the degree of its derivative, changing it with to a fractional order one. A set of data was obtained directly from an experiment with vehicles and special instruments, which has been used to make simulations in order to test the level of approximation of these models to the real behaviour. Through the data obtained we can note that the fractional model does not take any advantage in contrast to the integer-degree GHR model, but this situation is different to other models.