A Robust Optimization Model of Delay Estimation and Signal Timing for Parallel Flow Intersection
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摘要: 为解决平行流交叉口在实际应用中因交通波动导致主预信号协调效果不佳、移位左转车道上车辆排队溢出等问题，研究了基于情景的鲁棒优化控制方法。通过解析平行流交叉口交通运行机理，确定了交通需求、饱和流率和运行车速的随机波动会影响其运行稳定性，以此关联时变交通供给与平行流交叉口控制的耦合特征。进而构建了车均延误平均值-标准差目标函数，利用权重系数直观反映决策者对通行效率和稳定性偏好程度。在此基础上，考虑主预信号协调控制、车道功能划分、车道清空等约束条件，建立了平行流交叉口鲁棒优化模型。结合移位左转车道上车辆运行规则，基于车辆到达-驶离图式推导给出延误计算模型。研究结果表明：延误模型仿真验证中，左转和直行车均延误相对误差绝对值的平均值不超过3%，且最大值不超过6%，拟合效果较好。案例分析中，鲁棒优化相对于确定性优化，在延误均值仅增加2.24%的情况下，延误标准差降低了21.23%，说明鲁棒优化在几乎不损失交叉口通行效率的前提下，提高了平行流交叉口运行稳定性，使信号控制更符合实际交通运行需要。敏感性分析中，目标函数值随移位左转车道长度、设计速度的增加呈先减后增的变化趋势，故设计阶段移位左转车道长度的取值应与交通需求相匹配，而主预信号直行相位差计算过程中设计速度的取值应比现场调查的实际运行速度平均值略大。Abstract: A robust scenario-based optimization control method is proposed to address poor coordination of the main signal and the pre-signal caused by traffic fluctuations, and the issue of vehicle queue overflows in displaced left-turn lanes at parallel flow intersections. By analyzing the mechanism of traffic operation of parallel flow inter-sections, it is found that the operational stability is affected by the stochastic fluctuations in traffic demand, saturation flow rates, and traffic speeds. Thus, the coupling characteristics between time-varying traffic supply and the control of parallel flow intersection are established. Then, an objective function is defined as the mean and standard deviation of vehicle average delay, which utilizes weighting coefficients to intuitively reflect preferences of decision-makers for traffic efficiency and stability. Moreover, a robust optimization model for parallel flow intersections is developed by considering constraints such as the coordinated control of main pre-signals, functional allocation of lanes and clearance of lanes. A delay model is derived by integrating traffic rules for displaced left-turn vehicles from the diagram of vehicle arrivals and departures. The simulation results of the delay model show that the average absolute error of delay for left-turn and through vehicles does not exceed 3%, and the maximum error does not exceed 6%, which indicates a good fit. In the case study, the proposed optimization method results in a mere 2.24% increase in the average delay while it achieves a significant 21.23% reduction in the standard deviation of delay compared to the deterministic optimization. It shows that robust optimization enhances the operational stability of parallel flow intersections without sacrificing the throughput efficiency of intersections, which enables signal control more aligned with practical requirements. In the sensitivity analysis, the objective function exhibits an initial decreasing and then an increasing trend as the length of the displaced left-turn lane and design speed increase. It means the length of the displaced left-turn lane should align with the traffic demand during the design phase. However, the design speed should be slightly higher than the average speed obtained from field surveys when calculating the phase difference of through traffic for the main and pre-signals.
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表 1 延误计算模型检验误差
Table 1. Test error of delay calculation model
交通需求/（pcu/h） 运行速度/（km/h） 相对误差绝对值/% 平均值 最大值 左转 直行 左转 直行 4 000 25 2.87 0.64 5.01 1.23 30 2.65 0.97 4.52 2.4 35 1.95 2.68 3.84 3.51 5 000 25 2.9 1.22 5.24 2.36 30 2.94 2.1 5.89 3.89 35 1.69 2.43 2.82 4.02 金桥路-张杨路交叉口调查数据 25 2.97 1.74 5.45 2.68 30 2.89 2.36 5.93 4.31 35 2.12 2.53 3.48 4.57 
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表 2 现场调查数据
Table 2. Field survey data
转向 交通需求/（pcu/h） 饱和流率/（pcu/h） 车道数 平均值 标准差 最小值 最大值 平均值 标准差 最小值 最大值 W-左转 210 20 181 248 1 500 126 1 250 1 750 2 W-直行 502 56 390 619 1 550 140 1 310 1 830 2 W-右转 700 130 420 980 1 500 126 1 250 1 750 1 S-左转 387 52 282 496 1 490 124 1 240 1 740 2 S-直行 500 66 370 637 1 500 128 1 250 1 750 2 S-右转 302 28 230 360 1 490 128 1 240 1 740 1 E-左转 432 35 360 505 1 540 123 1 300 1 780 2 E-直行 1 002 90 820 1 180 1 600 138 1 320 1 880 4 E-右转 443 60 322 560 1 540 123 1 300 1 780 1 N-左转 369 55 249 485 1 580 110 1 360 1 800 1 N-直行 601 90 410 798 1 620 120 1 380 1 860 3 N-右转 240 30 180 300 1 600 100 1 370 1 800 1
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表 3 基础参数
Table 3. Basic parameters
参数 取值 参数 取值 参数 取值 Cmin 60 s gmin 20 s gmink 20 s Cmax 120 s gmax 60 s gmaxk 60 s υ'i2 7.5 m/s △tij 1.2 s I 4 s σij 6 m/pcu Ymax 0.9
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表 4 2种方法结果对比
Table 4. Result comparison of two methods
控制方法 指标 延误均值 延误标准差 延误最小值 延误最大值 确定性优化 延误/s 20.12 1.56 17.78 26.89 鲁棒优化 20.57 1.23 18.54 25.55 二者对比 变化率/% 2.24 -21.23 4.24 -4.96
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[1] 杨晓芳, 王影. 动态出口左转车道控制优化研究[J]。交通信息与安全, 2021, 39(5): 85-92. doi: 10.3963/j.jssn.1674-4861.2021.05.011YANG X F, WANG Y. Optimization control of dynamic use of exit-lanes for left-turn traffic[J]. Journal of Transport Information and Safety, 2021, 39(5): 85-92. (in Chinese) doi: 10.3963/j.jssn.1674-4861.2021.05.011 [2] ZHAO J, YAN J, WANG J. Analysis of alternative treatments for left turn bicycles at tandem intersections[J]. Transportation Research Part A: Policy and Practice, 2019, 126: 314-328. doi: 10.1016/j.tra.2019.06.020 [3] ALZOUBAIDI M, ZLATKOVIC M. Operational assessment of continuous flow intersections in a connected vehicle environment[J]. Transportation Planning and Technology, 2022, 45(6): 524-543. doi: 10.1080/03081060.2022.2136177 [4] MOLAN A M, HUMMER J E, KSAIBATI K. Modeling safety performance of the new super DDI design in terms of vehicular traffic and pedestrian[J]. Accident Analysis & Prevention, 2019, 127: 198-209. [5] 陈松, 李显生, 任园园. 公交车钩形转弯交叉口自适应信号控制方法[J]. 吉林大学学报(工学版), 2018, 48(2): 423-429.CHEN S, LI X S, REN Y Y. Adaptive signal control method for intersection with hook-turn buses[J]. Journal of Jilin University(Engineering and Technology Edition), 2018, 48(2): 423-429. (in Chinese) [6] PARSONS G F. The parallel flow intersection: a new two-phase signal alternative[J]. ITE Journal, 2007, 77(10): 28-32, 37. [7] PARSONS G F. The parallel flow intersection: a new high capacity urban intersection[C]. The Fifth Advanced Forum on Transportation of China, Beijing, China: IET, 2009. [8] 安实, 宋浪, 王健, 等. 平行流交叉口信号控制策略及效益分析[J]. 交通运输系统工程与信息, 2020, 20(3): 75-82.AN S, SONG L, WANG J, et al. Signal control strategy and benefit analysis of parallel flow intersection[J]. Journal of Transportation Systems Engineering and Information Technology, 2020, 20(3): 75-82. (in Chinese) [9] 安实, 宋浪, 王健, 等. 平行流交叉口行人过街控制策略研究[J]. 交通运输系统工程与信息, 2020, 20(5): 64-71.AN S, SONG L, WANG J, et al. Research on pedestrian crossing control strategy of parallel flow intersection[J]. Journal of Transportation Systems Engineering and Information Technology, 2020, 20(5): 64-71. (in Chinese) [10] SALMA A B, MOHAMED E E, AHMED O. Operational and safety performance evaluation of parallel flow intersection[J]. Transportation Research Record, 2022, 2676(6): 61-74. doi: 10.1177/03611981211070283 [11] ZHAO J, MA W J, HEAD K L, et al. Optimal operation of displaced left-turn intersections: a lane-based approach[J]. Transportation Research Part C: Emerging Technologies, 2015, 61: 29-48. doi: 10.1016/j.trc.2015.10.012 [12] 陈思妤, 李洁, 胡演诚, 等. 面向常发性拥堵的城市局部路网韧性评价与分析[J]. 交通信息与安全, 2022, 40(4): 138-147. doi: 10.3963/j.jssn.1674-4861.2022.04.015CHEN S Y, LI J, HU Y C, et al. An evaluation and analysis on the resilience of the urban local road network for recurrent congestions[J]. Journal of Transport Information and Safety, 2022, 40(4): 138-147. (in Chinese) doi: 10.3963/j.jssn.1674-4861.2022.04.015 [13] LI J Q. Discretization modeling, integer programming formulations and dynamic programming algorithms for robust traffic signal timing[J]. Transportation Research Part C: Emerging Technologies, 2011, 19(4): 708-719. [14] HAO W, MA C, MOGHIMI B, et al. Robust optimization of signal control parameters for unsaturated intersection based on tabu search-artificial bee colony algorithm[J]. IEEE Access, 2018(6): 32015-32022. [15] 陈娟, 余雨轩, 荆昊. 相邻交叉口混合交通流鲁棒多目标信号优化控制[J]. 上海大学学报(自然科学版), 2018, 24 (4): 665-674.CHEN J, YU Y X, JING H. Robust multi-objective signal optimization control for mixed traffic at adjacent intersection[J]. Journal of Shanghai University(Natural Science Edition), 2018, 24(4): 665-674. (in Chinese) [16] 赵靖, 陈凯佳, 周溪召. 出口道左转交叉口信号控制鲁棒优化方法[J]. 中国公路学报, 2020, 33(7): 145-155.ZHAO J, CHEN K J, ZHOU X Z. Robust optimization of exit-lanes for left-turn intersections[J]. China Journal of Highway and Transport, 2020, 33(7): 145-155. (in Chinese) [17] 赵靖, 陈凯佳, 周溪召. 排阵式交叉口几何设计与信号控制协同鲁棒优化[J]. 中国公路学报, 2021, 34(11): 296-305.ZHAO J, CHEN K J, ZHOU X Z. Joint robust optimization of layout design and signal control for tandem intersections[J]. China Journal of Highway and Transport, 2021, 34 (11): 296-305. (in Chinese) [18] MULVEY J M, VANDERBEI R J, ZENIOS S A. Robust optimization of large-scale systems[J]. Operations Research, 1995, 43(2): 264-281。 [19] 牟海维, 戚先锋, 刘彦昌, 等. 单交叉口多目标联合优化的信号配时研究[J]. 电子测量与仪器学报, 2020, 34(9): 62-68.MU H W, QI X F, LIU Y C, et al. Research on signal timing of multi-objective joint optimization at single intersection[J]. Journal of Electronic Measurement and Instrumentation, 2020, 34(9): 62-68. (in Chinese) [20] 姚荣涵, 刘美妮, 徐洪峰。信号控制交叉口车均延误模型适用性分析[J]. 吉林大学学报(工学版), 2016, 46(2): 390-398.YAO R H, LIU M N, XU H F. Applicability analysis of vehicle delay models for isolated signalized intersection[J]. Journal of Jilin University(Engineering and Technology Edition), 2016, 46(2): 390-398. (in Chinese) -
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