Fundamental Diagram Modeling of Mixed Traffic Flow Considering Dedicated Lanes for Human-Driven Vehicles

To mitigate the impact of human-driven vehicles (HDVs) on connected and automated vehicles (CAVs) in mixed traffic environments, the implementation of dedicated lanes has been proposed to achieve partial separation between CAVs and HDVs, thereby improving the operational efficiency of both CAVs and the road segment. The lane management policy, where dedicated lanes for HDV (HDLs) and general lanes (GLs) coexist on a road segment, is referred to as the (G, H) policy. This paper proposes a multi-lane fundamental diagram model for mixed traffic flow and aims to investigate the effects of HDL configuration on the efficiency of road segments under the (G, H) policy. Firstly, different car-following modes in mixed traffic flow are analyzed, and various car-following models are employed to characterize the mixed traffic flow. Secondly, two lane selection principles are introduced to describe the lane choice behavior of HDVs under the (G, H) policy. Based on these principles, five equilibrium states that may exist on the road segment under the (G, H) policy are analyzed. Subsequently, a multi-lane fundamental diagram model incorporating HDL is derived based on the lane selection principles of HDV. Finally, numerical analysis is conducted to investigate the influence of lane configuration schemes under the (G, H) policy on the distribution of equilibrium states, fundamental diagram, and capacity. The results indicate that: (1) Based on the lane choice behavior of vehicles, the equilibrium states of road segment can be classified into five types. The distribution of each equilibrium state under different traffic conditions only depends on the proportion of HDL to the total number of lanes on road segment. A higher number of HDL leads to a reduced applicability of the (G, H) policy under different traffic conditions. (2) Under different penetration rates, as density increases, the overall traffic volume of road segment initially increases and then decreases until reaching the critical jammed density. (3) In a three-lane scenario, compared to the absence of HDL, the optimal HDL configuration scheme can increase the traffic volume of road segment by approximately 11%. (4) With HDL deployment, the capacity of road segment initially increases and then decreases with an increase in CAVs penetration rate.