Model of vehicle interactions with autonomous cars and its properties

TL;DR

This paper develops a kinetic model for mixed traffic with autonomous and human-driven vehicles, showing that increased autonomous vehicle presence can stabilize traffic flow and reduce instabilities.

Contribution

It introduces a new hierarchy of kinetic models that do not treat autonomous cars as externally controlled, analyzing their impact on traffic stability.

Findings

Autonomous vehicles decrease traffic instabilities as their penetration rate increases.

Two indicators effectively quantify traffic instability and its reduction.

Analytical and numerical results confirm stabilization effects.

Abstract

We study a hierarchy of models based on kinetic equations for the descriptions of traffic flow in presence of autonomous and human--driven vehicles. The autonomous cars considered in this paper are thought of as vehicles endowed with some degree of autonomous driving which decreases the stochasticity of the drivers' behavior. Compared to the existing literature, we do not model autonomous cars as externally controlled vehicles. We investigate whether this feature is enough to provide a stabilization of traffic instabilities such as stop and go waves. We propose two indicators to quantify traffic instability and we find, with analytical and numerical tools, that traffic instabilities are damped as the penetration rate of the autonomous vehicles increases.