A Method for Optimizing Geometric Design and Signal Timing for Contraflow Left-turn Lanes with Double-exits
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摘要: 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。Abstract: 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.
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图 6 中国重庆市南滨路-烟雨路交叉口
Figure 6. intersection of Nanbin Road and Yanyu Road in Chongqing，China
图 8 综合功能区总长度影响分析
Figure 8. Influence analysis for total length of comprehensive functional area
表 1 逆流左转车道长度设置梳理
Table 1. Contraflow left-turn lane length setting
文献 推荐或使用长度/m 设置依据 [6] 70 通行能力 [7] 50 [8] 43, 50, 53 实地调查数据 [9] 60 通行能力、延误 [11] 40, 50 实地调查数据 [12] 40 排队长度、几何特征 [13] 50, 0 实地调查数据 [14] 50 [17] 43, 0, 3 实地调查数据 [18] 50 排队长度、几何特征 [20] 61~91 通行能力 [23] 40, 0 排队长度、几何特征 [24] 40, 45, 50, 55, 60 实地调查数据 [25] 40, 0 排队长度、几何特征 [26] 60 通行能力、延误 [27] 50, 0 实地调查数据 [28] 55 排队长度 [29] 50 排队长度、几何特征 [30] 40~60 [31] 60 [32] 50 排队长度、几何特征 [33] 55 实地调查数据 
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表 2 对比方案
Table 2. Schemes for comparison
方案编号 δ1 δ2 类型 Lilp/m Lilp1/m Lilp2/m 1 0 0 常规交叉口 2 1 0 单开口式 13 40 30 3 0 1 单开口式 4 1 1 双开口式 5 0 0 常规交叉口 6 1 0 单开口式 13 50 40 7 0 1 单开口式 8 1 1 双开口式
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表 3 信号配时结果
Table 3. Signal timing result
单位: s 方案编号 流量场景 东西 南北 周期时长 左转相位
时长直行相位
时长预信号1
启亮/关闭预信号2
启亮/关闭左转相位
时长直行相位
时长预信号1
启亮/关闭预信号2
启亮/关闭低流量 29 19 29 19 96 1 中流量 过饱和 高流量 过饱和 低流量 19 19 66/6 19 19 28/44 76 2 中流量 19 19 66/6 19 19 28/44 76 高流量 过饱和 低流量 20 19 73/1 20 19 34/40 78 3 中流量 24 21 84/6 24 21 39/51 90 高流量 29 29 102/11 29 29 44/69 116 低流量 20 19 68/78 73/1 20 19 29/39 34/40 78 4 中流量 24 21 79/89 84/6 24 21 34/44 39/51 90 高流量 29 29 97/107 102/11 29 29 39/49 44/69 116 低流量 29 19 29 19 96 5 中流量 过饱和 高流量 过饱和 低流量 19 19 67/4 19 19 29/42 76 6 中流量 19 19 67/4 19 19 29/42 76 高流量 过饱和 低流量 23 19 81/2 23 19 39/44 84 7 中流量 28 23 96/7 28 23 45/58 102 高流量 过饱和 低流量 23 19 75/4 81/2 23 19 33/46 39/44 84 8 中流量 28 23 89/102 96/7 28 23 38/51 45/58 102 高流量 过饱和
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表 4 仿真结果对比
Table 4. Comparison of simulation results
方案编号 流量场景 交叉口输入
流量（/ pcu/h）交叉口通过车辆数/(pcu/h) 车均延误/s 左转 直行 交叉口 左转 直行 交叉口 低流量 3 200 1 624 1 581 3 205 34.76 37.55 36.14 1 中流量 过饱和 高流量 过饱和 低流量 3 200 1 627 1 583 3 210 29.46 26.64 28.07 2 中流量 4 400 2 228 2 171 4 399 33.86 28.34 31.14 高流量 过饱和 低流量 3 200 1 617 1 583 3 201 39.16 27.82 33.56 3 中流量 4 400 2 225 2 171 4 396 46.63 34.34 40.58 高流量 5 280 2 661 2 605 5 266 56.54 42.84 49.78 低流量 3 200 1 618 1 583 3 201 31.97 27.82 29.92 4 中流量 4 400 2 224 2 171 4 395 39.74 34.33 37.08 高流量 5 280 2 662 2 605 5 267 53.39 42.83 48.18 低流量 3 200 1 624 1 581 3 205 34.76 37.55 36.14 5 中流量 过饱和 高流量 过饱和 低流量 3 200 1 627 1 583 3 210 30.24 26.64 28.47 6 中流量 4 400 2 227 2 171 4 398 36.95 28.34 32.71 高流量 过饱和 低流量 3 200 1 626 1 582 3 209 37.28 31.01 34.19 7 中流量 4 400 2 227 2 175 4 401 49.37 39.34 44.43 高流量 过饱和 低流量 3 200 1 628 1 582 3 210 31.53 31.01 31.27 8 中流量 4 400 2 219 2 175 4 394 39.32 39.34 39.33 高流量 过饱和
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