586 RWTH Publication No: 960324        2021       
TITLE Model of vehicle interactions with autonomous cars and its properties
AUTHORS Michael Herty, G. Puppo, Giuseppe Visconti
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.
KEYWORDS vehicular traffic, autonomous cars, kinetic equations, BGK models, Chapman-Enskog expansion
DOI 10.3934/dcdsb.2022100
PUBLICATION Centered around dynamics, Discrete and Continuous Dynamical Systems - Series B
2023, Volume 28, Issue 2: 833-853