Cell transmission model considering queuing characteristics of channelized zone at intersections
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摘要: 为了更准确地描述城市道路交叉口交通流演化规律，以具有进口道展宽设计和合用车道功能设计的信号控制交叉口为研究对象，综合考虑排队消散过程、分流过程、可选择性换道和合用车道4个现实因素改进了元胞传输模型(CTM)；结合交叉口的几何特征，以车道组为单位提出了路段元胞划分方法；在此基础上，调整了元胞发送能力函数对排队的消散过程，并进行了建模；在分流过程建模中引入阻塞因子来描述不同车道组空间排队的相互影响，以平衡相邻车道组空间排队为目标对过渡区可选择性换道行为进行了建模，并在合用车道建模中考虑了不同流向车流的冲突效应；结合实际交叉口，选取车道组周期最大排队长度作为评价指标，验证了改进CTM的有效性。试验结果表明：改进CTM可以同时估计不同车道组的排队长度，随着直行车流比例的增大，改进CTM的估计误差逐渐减小，不同流量场景下，路段最大排队长度的平均绝对误差(MAE)、均方根误差(RMSE)和加权平均绝对百分比误差(WMAPE)的平均值分别小于16.43、21.36 m和13.51%；与基准方法相比，不同场景下改进CTM对路段最大排队长度的MAE的减小幅度为15.31%~90.03%，且在高流量场景下估计精度的提升效果更明显。由此可见，改进CTM能够更准确地刻画交叉口交通流运行特征，并提高排队长度估计精度，可作为交通管理与控制的重要依据。Abstract: In order to describe the evolution law of traffic flows at urban intersections more accurately, the signalized intersection with entrance widening areas and shared lanes was taken as the research object, and the cell transmission model (CTM) was improved by considering four practical factors: queue discharge process, divergence process, optional lane changing, and shared lanes. According to the geometric characteristics of the intersection, a method to divide cells at road sections was proposed based on lane groups. On this basis, the cell sending capacity function was adjusted to reflect and model the queue discharge process. The blocking factors were introduced in the divergence process modeling to describe the interaction of spatial queuing among different lane groups. The optional lane changing behavior in the transition zone was modeled with the goal of balancing the spatial queuing of adjacent lane groups, and the conflict effect of traffic flows with different directions was considered in the modeling of shared lanes. On the basis of an actual intersection, the maximum queue length of the lane group cycle was selected as the evaluation index to verify the effectiveness of the improved CTM. Test results show that the improved CTM can simultaneously estimate the queue lengths of different lane groups. With the increase in the proportion of through traffic flows, the estimation error of the improved CTM decreases. The mean absolute error (MAE), root mean square error (RMSE), and weighted mean absolute percentage error (WMAPE) of the maximum queue length at road sections are less than 16.43, 21.36 m, and 13.51%, respectively, under different traffic scenarios. Compared with the benchmark method, the improved CTM can reduce the MAE by 15.31%-90.03% for the maximum queue length at road sections under different scenarios, and the estimation accuracy under high-traffic scenarios improves more obviously. Thus, it can be seen that the improved CTM can more accurately describe the operational characteristics of traffic flow at intersections and improve the estimation accuracy of queue length, which can be used as an important basis for the traffic management and control.
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图 1 两个相邻交叉口间路段的几何结构
Figure 1. Geometry configuration of road section between two adjacent intersections
图 6 路段最大排队长度估计误差的分布特征
Figure 6. Distribution characteristics of estimation errors of maximum queue length at road section
图 7 场景3中不同影响因素下估计结果对比
Figure 7. Comparison of estimation results under different influencing factors in scenario 3
图 8 场景2中改进CTM与基准CTM估计结果对比
Figure 8. Comparison of estimation results obtained by improved CTM and benchmark CTM in scenario 2
图 10 实证场景周期最大排队长度估计结果
Figure 10. Cycle-based maximum queue length estimation results for empirical scenario
表 1 仿真场景设置
Table 1. Simulation scenario settings
场景 路段交通量/(veh·h-1) 左转、直行、右转流向比例 1 850 0.1:0.8:0.1 2 950 0.2:0.6:0.2 3 1 050 0.3:0.4:0.3 4 750 0.1:0.8:0.1 5 800 0.2:0.6:0.2 6 850 0.3:0.4:0.3 
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表 2 改进CTM的参数设置
Table 2. Parameter settings of improved CTM
参数 取值 自由流速度vf/(km·h-1) 54 激波速度w/(km·h-1) 15.7 饱和流量qc/(veh·h-1) 1 620 阻塞流量qjam/(veh·h-1) 500~1 500 阻塞密度kjm/(veh·km-1) 133 时间步长Δt/s 1 元胞长度l/m 15 上游混行区长度/m 420 过渡区长度/m 30 下游渠化区长度/m 60
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表 3 不同场景下估计性能的均值
Table 3. Mean values of estimation performance under different scenarios
评价指标 车道组 高流量 低流量 场景1 场景2 场景3 场景4 场景5 场景6 MAE/m 车道组1 5.94 12.48 9.03 4.35 6.45 6.93 车道组2 1.99 2.29 10.25 3.73 6.53 9.84 车道组3 1.96 1.98 5.53 3.26 6.50 9.91 路段最大排队长度 10.71 15.66 16.43 6.09 8.26 11.52 RMSE/m 车道组1 8.61 16.57 13.32 6.16 8.31 9.02 车道组2 3.06 3.66 14.36 5.67 9.17 12.74 车道组3 2.98 3.25 10.07 4.92 9.10 13.66 路段最大排队长度 13.49 19.88 21.36 7.73 10.57 14.74 WMAPE/% 车道组1 59.40 42.91 13.93 36.07 20.57 12.41 车道组2 2.39 2.77 15.47 4.98 10.58 20.09 车道组3 2.34 2.35 6.75 4.20 9.00 13.44 路段最大排队长度 5.32 8.23 12.70 6.19 10.32 13.51
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表 4 改进CTM所得路段最大排队长度的MAE减小百分比均值
Table 4. Mean percentage reductions in MAE of maximum queue length at road sections obtained by improved CTM
% 场景 车道组1 车道组2 车道组3 路段最大排队长度 1 34.65 56.82 63.50 90.03 2 19.24 57.95 64.65 83.67 3 36.93 23.88 10.98 44.45 4 25.17 45.38 56.94 71.69 5 20.15 24.29 15.72 20.92 6 31.86 44.99 2.02 15.31
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表 5 实证场景下的估计误差
Table 5. Estimation errors for empirical scenario
评价指标 车道组 改进CTM 基准CTM MAE/m 车道组1 4.44 5.70 车道组2 4.73 5.92 车道组3 5.28 6.64 路段最大排队长度 5.68 10.15 RMSE/m 车道组1 5.93 7.47 车道组2 5.61 7.95 车道组3 7.21 9.31 路段最大排队长度 7.05 14.56 WMAPE/% 车道组1 19.37 24.85 车道组2 6.36 7.97 车道组3 7.07 8.90 路段最大排队 6.62 11.83
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