A study of the emergence of kinematic waves in targeted state car-following models of traffic

Abstract

We propose to study the emergence of kinematic waves in microscopic models of traffic flow. The vehicles motion is given by car-following differential systems that incorporate a targeted state function and a strictly positive reaction time. Through simulations, we observe two types of stationary state for a line of vehicle evolving on a ring: a homogeneous state in which vehicle speed and gap are constant and equal and a heterogeneous state in which kinematic waves spread out. The reaction time and the form of the targeted state function seem to be the determining microscopic factors of the macroscopic stationary state stability. A stability linear analysis of the homogeneous state is done with a basic car-following model. The results indicate an explicit condition between the reaction time, the form of the targeted state function and the stationary state nature of the vehicle line.