Scalable traffic stability analysis in mixed-autonomy using continuum models

This paper presents scalable traffic stability analysis for both pure connected and autonomous vehicle (CAV) traffic and mixed traffic based on continuum traffic flow models. Human-drive vehicles (HDVs) are modeled by a non-equilibrium traffic flow model, i.e., Aw-Rascle-Zhang (ARZ) to capture HDV traffic's unstable nature. CAVs are modeled by a mean field game describing their non-cooperative behaviors as rational utility-optimizing agents. Working with continuum models helps avoiding scalabillty issues in microscopic multi-class traffic models. We demonstrate from linear stability analysis that the mean field game traffic flow model behaves differently from traditional traffic flow models and stability can only be proved when the total density is in a certain regime. We also show from numerical experiments that CAVs help stabilize mixed traffic. Further, we quantify the impact of CAV's penetration rate and controller design on traffic stability. The results may provide qualitative insights on traffic stability in mixed-autonomy for human drivers and city planners. The results also provide suggestions on CAV controller design for CAV manufacturers.