Stability Analysis of Mixed-Autonomy Traffic with CAV Platoons using Two-class Aw-Rascle Model

This paper investigates deterministic and stochastic stability of mixed-autonomy traffic with connected and autonomous vehicle (CAV) platoons and conventional vehicles on a freeway segment. The deterministic traffic dynamics is described with a two-class Aw-Rascle (AR) traffic partial differential equations (PDEs) model. PDE states describe the evolution of densities and velocities of two-class vehicles on freeway over time and space. We consider that one class represents the human-driven vehicles while the other class represents the CAV platoon with bigger size but slower speed. We linearize the 4×4 hyperbolic PDE model around spatially uniform steady states which gives four characteristic speeds positive in the free traffic with one negative characteristic appearing in the congested traffic. The upstream propagation of velocity perturbation information potentially destroys the traffic stability. Trade-offs between stability and maximum flow rate are discussed for different ratios of CAV platoons in the mixed traffic. The uncertainty is then introduced to capture the randomness in the arrival rate of incoming CAV traffic. We focus on a simple two-mode continuous-time Markov process taking values from a set of two operation modes that represent the qualitatively distinct traffic dynamics (congestion versus free flow). Therefore, a linear hyperbolic PDEs with Markov jump model parameters and boundary conditions is considered, consisting of both the continuous PDE states and the discrete operational mode. The stochastic stability is then analyzed using the Lyapunov approach. The sufficient conditions for stochasticallyexponential stability are derived for the Markov switching system. Some implications for CAV platooning operations to limit the negative effect of the randomness are also discussed.