Analyzing the impact of automated vehicles on uncertainty and stability of the mixed traffic flow

This paper proposes a stochastic model for mixed traffic flow with human-driven vehicles (HVs) and automated vehicles (AVs). The model is formulated in Lagrangian coordinates considering the heterogeneous behavior of human drivers. We further derive a first and second order approximation of the stochastic model describing the mean and the covariance dynamics, respectively, under different combinations of HVs and AVs in the traffic stream (e.g., randomly distributed in the stream, at the front of the stream, in the middle of the stream and in the rear of the stream). The proposed model allows us to explicitly investigate the interaction between AVs and HVs considering the uncertainty of human driving behavior. Six performance metrics are proposed to measure the impact of AVs on the uncertainty of HVs' behavior, as well as on the stability of the system. The numerical experiment results show that AVs have significant impact on the uncertainty and stability of the mixed traffic flow system. Larger AV penetration rates can reduce the uncertainty inherent in HV behavior and improve the stability of the mixed flow substantially. Whereas AVs' reaction time only has subtle impact on the uncertainty of the mixed stream; as well as the position of AVs in the traffic stream has marginal influence in terms of reducing uncertainty and improving stability.