双开口式逆流左转车道几何设计及信号配时优化

为解决单开口式（即仅有1个预信号开口）逆流左转车道（即通过预信号控制动态借用的出口车道）的长度与左转交通需求匹配效果不佳的问题，通过对单开口式逆流左转车道的设计进行分析，提出1种双开口式（即设置2个预信号开口）逆流左转车道的设计及控制方法。结合逆流左转车道的车辆运行规则，分析单开口式、双开口式逆流左转车道上车辆排队行为特征差异，构建逆流左转车道通行能力计算模型和延误计算模型。考虑主预信号协调控制、饱和度、交通波传递等约束条件，以车均延误最小为优化目标，采用0-1变量表示各个预信号开口是否启用，将常规设计、单开口式、双开口式信号配时整合到1个统一的混合整数非线性规划优化模型中，并给出逆流左转车道长度的设计依据。通过案例分析发现:①在逆流左转车道长度为80 m时，交叉口通行能力提升幅度最大；②当通行能力满足需求时，逆流左转车道长度越短，交叉口延误降低越明显；③若为保证通行能力而采用较长的逆流左转车道时，双开口式逆流左转车道通行效率优于单开口式；④综合考虑延误、通行能力等因素，单开口式逆流左转车道长度宜设置为40~60 m，而双开口式宜设置为80 m左右；⑤双开口式逆流左转车道可根据需要选择是否启用每个预信号开口，应用较为灵活，适用于各种流量场景。 

A Method for Optimizing Geometric Design and Signal Timing for Contraflow Left-turn Lanes with Double-exits

To solve the problem of ineffective match between the lengths of contraflow left-turn lanes(i.e., dynamic borrowed exit lines through pre-signal control)with single-exit(i.e., one pre-signal exit only)and corresponding traffic demand, a method for optimizing the geometric design and signal timing for contraflow left-turn lanes with double-exits(i.e., two pre-signal exits)is proposed after analyzing the design of contraflow left-turn lanes with single-exit. Based on the observed maneuvers of vehicles in the contraflow left-turn lanes and queuing behaviors of vehicles in left-turn lanes with single-exit and double-exits, their capacity and delay estimation models are developed, respectively. The conventional design methods for signal timing of single-exit and double-exits are integrated into a unified optimization model by introducing a dummy variable to indicate whether each pre-signal exit is enabled. Considering the constraints of coordination between main and pre-signals, saturation and traffic wave transfer, the objective of the model is to minimize the delay per vehicle. Through this model, the basis for designing the length of contraflow left-turn lanes can be obtained. Finally, a case study is carried out, the results indicate that: ①the improvement of intersection capacity is largest when the length of contraflow left-turn lanes is 80 m.②When the capacity of the roads meets traffic demand, the shorter the length of contraflow left-turn lanes, the more significant the reduction of traffic delay at the intersection.③If longer contraflow left-turn lanes are adopted to maintain road capacity, the benefit of contraflow left-turn lanes with double-exits are better than lanes with single-exit.④Considering traffic delay, capacity, and other factors, the length of contraflow left-turn lanes with single-exit is suggested to be 40 to 60 m, while lanes with double-exits should be set around 80 m. ⑤The contraflow left-turn lanes with double-exits are able to control pre-signal exits as requested, which is flexible and suitable for various traffic scenarios.