Lane management for mixed traffic flow on roadways considering the car-following behaviors of human-driven vehicles to follow connected and automated vehicles

The widespread adoption of emerging connected and automated vehicles (CAVs) highlights the need for identifying the roadway capacity of mixed traffic flow with CAVs and human-driven vehicles (HDVs) for future traffic management. Previous studies focus on analyzing the impacts of CAV technologies on the mixed traffic capacity. However, research on how different car-following behaviors of HDVs to follow CAVs affect the mixed traffic capacity is still lacking. This study proposes an analytical formulation of the mixed traffic capacity based on the probability distributions of HDVs and CAVs and three types of behavior willingness (i.e., believer, neutral, and skeptic) of HDV-following-CAV in a mixed traffic environment. The sufficient conditions are derived for mixed traffic capacity to increase or decrease with the behavior willingness and CAV penetration rate. Based on that, an analytical lane management (LM) model is further proposed to determine the optimal number of CAV dedicated lanes (CDLs) and CAV non-dedicated lane (CNL) strategies that maximize the mixed traffic throughput, considering the mixed traffic demand, behavior willingness, and CAV penetration rate. The results from numerical experiments show that the proposed LM strategies can significantly improve mixed traffic throughputs by deploying optimal CDLs and CNL strategies, compared to one without the LM strategy. The mixed traffic throughputs improve and reduce as the trust willingness and skeptic willingness increase and decrease, respectively. Moreover, the increment in CAV penetration rate does not certainly correspond to the high mixed traffic throughputs. The behavior willingness and heterogeneous headways could be jointly considered to guarantee the positive influences of CAV penetration rate on the mixed traffic throughputs when implementing the LM strategy for the mixed traffic flow.