Lagrangian Models for Controlling Large-Scale Heterogeneous Traffic

Heterogeneous traffic with a mixture of human-driven and connected automated vehicles is discussed to study how the penetration rate and the control design of connected automated vehicles affect the traffic flow on a large scale. Continuum traffic models are constructed by incorporating time delays to take into account the reaction time of human drivers and the delays in the control loops of connected automated vehicles. It is shown that Lagrangian delayed continuum models are suitable for studying heterogeneity, introducing delay, and taking into account the on-board traffic data used by the controllers of connected automated vehicles. We show that these models possess realistic stability properties and are capable of capturing the large-scale dynamics of vehicle automation-induced and connectivity-induced heterogeneity.