A Reliability Analysis of the Capacity of Urban Road Network Under a Mixed Human-driven and Connected Traffic Environment
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摘要: 网联自动驾驶车辆（CAVs）与人工驾驶车辆（HDVs）混行的交通发展模式会促进城市路网容量发生变化，为解析混合交通流对城市路网容量可靠性的影响，构建了智能网联环境下城市路网容量可靠性双层规划模型。为表征CAVs信息获取与自动驾驶的能力，假定CAVs遵循系统最优原则选择路径，而HDVs则根据自身经验选择路径，基于二者路径选择的差异建立描述混合交通分配的下层模型，刻画智能网联环境下的混合交通流分配特性。并且，为了快速求解大型路网交通分配，将下层混合交通分配模型转换为非线性互补下问题进行求解。考虑到实际路网的随机性，以及路网道路通行能力并非固定值，运用具有多种相关性的均匀随机分布理论，建立了的描述城市路网容量可靠性的上层模型。通过蒙特卡洛仿真分析不同CAVs渗透率下的路网容量可靠性，并进一步解析各路段对路网容量可靠性的敏感度。结果表明：当需求水平d > 0.5时，路网容量可靠性开始降低；当d > 0.7且CAVs渗透率λ＝0时，可靠性小于0.4；当d > 0.7而λ＝1时，可靠性接近1，说明CAVs可增强路网容量可靠性。研究还发现，当需求水平处于0.7~1区间时，渗透率的变化对路网容量可靠性有显著的影响，但随着需求的增大，路网处于超负荷状态，渗透率对路网容量可靠性影响较小。此外，CAVs渗透率从0增加至1的过程中，路网中存在“道路容量悖论”现象的道路从19条下降至3条，且当λ＝1时路网中仅有1条道路出现了显著的“道路容量悖论”现象，拥堵严重。表明CAVs渗透率的增大可以显著改善路网中的“道路容量悖论”现象，减少路网容量可靠性的波动，提高路网运行稳定性。Abstract: The emerging of mixed traffic involving both connected autonom ous vehicles(CAVs)and human-driven vehicles(HDVs)may change the capacity of urban road networks. A bi-level programming model is proposed to analyze the impacts of mixed traffic flow on the reliability of the capacity of urban road network in an intelligent network environment. Assuming that CAVs follow the path selected based on the system optimization principle and the drivers of the HDVs select their paths according to their own experience, a lower model is developed for the assignment of traffic flow based on the differences in the path selection between the two types of vehicles. Furthermore, the modeling of the assignment of mixed traffic at the lower level is transformed into a nonlinear complementarity problem to reduce runtime. Considering the randomness of road capacity in a network, an upper model is set up for modeling the reliability of capacity by using a uniform random distribution with multiple correlations. A Monte Carlo simulation is used to analyze the reliability of road network capacity under different market penetration rate(MPR)of CAVs. A sensitivity analysis is then carried out for studying the reliability of road capacity under such a scenario. Numerical results show that, when the level of the demand d > 0.5, the reliability of road network capacity decreases. When level of the demand d > 0.7 and the market penetration rate of CAVs λ=0, the reliability is less than 0.4. However, when d > 0.7 and λ=1, the reliability is found close to 1, indicating that CAVs can enhance the reliability of road network capacity. It is also found that when the level of the demand is between 0.7 and 1, the MPRof CAVs significantly affects the reliability of road network capacity. When the road network is overloaded, the MPR has a very minor impact on the reliability of road network capacity with the increase of traffic demand. In addition, when λ increases from 0 to 1, the number of roads showing"capacity paradox"in the road network decreases from 19 to 3. When λ=1, only one road in the entire network show the issue. Study results show that the increase of MPR can not only reduce the possibility of"road capacity paradox", but also improve the stability of the road network.
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图 3 不同相关性假设下的路网容量可靠性
Figure 3. The reliability of road network capacity under the different correlation assumption
表 1 混合交通网络均衡模型符号定义
Table 1. Symbol definition of the hybrid traffic network
符号 意义 符号 意义 A 道路集合 N 节点集合 X 混合交通流 D 目的地集合 cij 道路ij的随机道路容量，veh/h λ CAV渗透率 xa HDV在道路a上的交通流量，veh/h xa CAV在道路a上的交通流量，veh/h qik HDV i到k的出行需求，veh/h qik CAV i到k的出行需求，veh/h p HDV的路径 p CAV的路径 $f_{p, i}^k$ 从i到k路径p上的HDV的流量，veh/h $\bar{f}_{\overline{p}, i}^{k}$ 从i到k路径p上的CAV的流量，veh/h $P_i^k$ HDV从i到k的所有路径集合 $\bar{P}_i^k$ CAV从i到k的所有路径集合 $\delta_{a, p, i}^k$ 关于HDV的道路路径发生因子(如果道路a属于路径p，从i到k对HDV可用，则值为1，否则为0) $\bar{\delta}_{a, p, i}^k$ 关于CAV的道路路径发生因子(如果道路a属于路径p，从i到k对CAV可用，则值为1，否则为0) tij(X) 道路ij上关于HDV阻抗函数 tij(X) 道路ij上关于CAV阻抗函数 αij BPR函数中的路滞系数，可看作道路自由流行驶时间 βij BPR函数中的路滞系数 $\overset\frown{q}_{i}^{k}$ 从i到k的总出行需求，veh/h ξ CAV编队行驶折算系数 注：在全文中，所有术语都是非负的，除非另有说明。 
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表 2 Sioux-Falls OD需求矩阵
Table 2. Sioux-Falls OD demand matrix
单位: veh/h OD 1 2 10 13 20 1 0 700 300 500 200 2 700 0 200 400 400 10 300 200 0 600 800 13 500 400 600 0 500 20 200 400 800 500 0
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