Traffic signal control optimization model of over-saturated intersection based on dynamic programming
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摘要: 为满足过饱和交叉口信号控制的需求, 应用动态规划理论, 建立了过饱和交叉口信号控制优化模型, 界定了模型的阶段、状态变量和决策变量, 推导了平均排队长度状态转移方程和控制器状态转移方程, 确定了基于交叉口不同饱和状态的目标函数与约束条件, 提出了模型优化框架。非饱和状态以最小化延误为控制目标, 饱和状态和过饱和状态以最大化通行能力为控制目标。通过迭代运算判断保持或者切换当前相位, 并将控制效果实时反馈以调节下一阶段信号配时方案。以秦皇岛市某交叉口为例, 基于实际采集数据得到了非饱和、饱和与过饱和3种状态的交通流量, 应用动态规划模型获得配时方案, 并与TRANSYT方法给出的配时方案进行了对比分析。分析结果表明: 在非饱和状态下, 采用动态规划模型计算的平均延误、饱和度、平均排队长度分别为49.3s、0.76、13.7veh, 采用TRANSYT方法计算的对应值分别为52.0s、0.78、14.4veh; 在过饱和状态下, 采用动态规划模型计算的饱和度与平均延误分别为0.85、78.5s, 采用TRANSYT方法计算的对应值分别为0.86、82.5s, 但对应的平均排队长度为27.3veh, 略优于动态规划模型的27.6veh; 饱和状态控制效果与过饱和状态控制效果类似。可见, 采用动态规划模型可以有效降低交叉口饱和度, 减少各相位不同进口道车辆的平均延误。Abstract: In order to satisfy the signal control demand of over-saturated intersection, an optimization model was established by using dynamic programming theory.The stages, state variables, and decision variables were redefined.The state transition equations of average queue length and controller were built.The objective functions and constraints based on different intersection saturated states were determined.The optimization framework of the model was proposed.The control objective of unsaturated states was designed as the minimum delay, and the control objectives of saturated and over-saturated states were designed as the maximum capacity.Through iteration operations, retaining or changing the current phase was decided, and the signal timing program of next stage was adjusted by the real-time feedback of control effects.Taking an intersection of Qinhuangdao City as an example, the traffic flows of unsaturated, saturated and over-saturated states were obtained based on the actual collected data.The signal timing program was obtained by using the dynamic programming model, and compared with the signal timing program obtained by using TRANSYT method.Analysis result indicates that for the unsaturated state, the average delay, saturation, and average queue length obtained by the proposed model are 49.3s, 0.76, 13.7veh respectively, and the corresponding values obtained by TRANSYT method are 52.0s, 0.78, 14.4veh, respectively.For over-saturated state, the saturation and average delay obtained by the proposed model are 0.85 and 78.5 srespectively, and the corresponding values obtained by TRANSYT method are 0.86 and 82.5 srespectively, however, the corresponding average queue length is 27.3 veh that is slight better than the optimization value 27.6veh.The control effect of saturated state is similar to over-saturated state.Obviously, the proposed model based on dynamic programming can effectively reduce the intersection saturation and the average delay of vehicle for each import of each phase.
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图 9 过饱和状态的信号配时方案比较
Figure 9. Comparison of signal timing plans of over-saturated state
表 1 交通流量与饱和度
Table 1. Traffic flows and saturations
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