In order to get the optimal road congestion charging scheme in mixed driving environment of connected autonomous vehicles (CAV) and human-driven vehicles (HDV), this paper conducts a quantitative analysis of the impact of CAV on road networks (especially on road capacity), and analyzes the functional relationship between the road capacity and HDV flows as well as CAV flows. Secondly, the traditional Bureau of Public Road (BPR) Function is improved, and the system optimal allocation model is established based on the new BPR function. The system optimum (SO) assignment is performed on the traffic flow under the conditions of different CAV proportions and different HDV-CAV headways. Then, Frank-Wolfe algorithm is used to solve the SO model, by considering the extra traffic cost of HDV in the differences of SO results under different conditions. The corresponding road networks are formulated using the optimal toll theory charge plan. Finally, the model and the algorithm are applied to the Nguyen-Dupuis transportation network. The results show that under the coexisting condition of HDV and CAV, the marginal cost under the optimal allocation result of the system is the optimal congestion charging which can be the basis for the road toll scheme design under the coexistence of HDV and CAV.

connected autonomous vehicles, road network, Bureau of Public Road (BPR) function, system optimum assignment, Frank-Wolfe algorithm, congestion charging

为了得到自动驾驶汽车(CAV)与人工驾驶汽车(HDV)并存条件下最优道路收费方案, 针对CAV在道路上的通行能力, 特别是对道路容量产生的影响进行量化分析, 获得道路容量与HDV流量和CAV流量之间的非线性关系。然后, 对传统的美国公路局路阻函数进行改进, 并基于改进后的路阻函数, 建立系统最优(system optimal, SO)流量分配模型, 对不同CAV占比条件下和不同HDV与CAV安全车距比值条件下的交通流进行系统最优分配。采用Frank-Wolfe算法, 对SO模型进行求解, 并考虑因HDV而产生的额外道路出行成本对不同条件下系统最优分配结果的差异性进行比较。基于最优收费理论, 针对不同规模道路网制定相应的收费方案。最后, 将模型与算法应用到Nguyen-Dupuis交通网络中。结果表明, 在HDV与CAV并存条件下, 以系统最优分配结果下的边际成本进行收费是道路交通系统最优拥堵收费方案, 可作为HDV与CAV并存条件下道路收费方案设计的依据。