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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