基于VMS发布诱导信息的快速路网动态最优控制
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摘要
基于可变信息标志(Variable Message Signs, VMS)的交通诱导系统是智能交通系统的组成部分,对改善路网的交通状况有重要的作用。交通诱导系统通过VMS发布诱导信息,可以有效地调节车流在路网各个道路上的分布,从而避免部分道路车流过多而产生拥堵。
由于交通诱导系统发布的信息并不是强制的要求,驾驶员对于诱导信息不一定服从,诱导结果是不确定的。这种不确定性给交通诱导信息的发布策略带来了挑战,不恰当的策略可能会使交通拥堵从一个道路转移到另一个道路,甚至加重整个路网的拥堵。因此,诱导信息的发布策略是交通诱导系统的关键。
本文应用最优控制理论的方法,研究了交通诱导系统的建模和动态信息发布策略。本文创新性地提出了在驾驶员不确定服从的情况下交通诱导系统的动态最优控制方法,以及多点控制的交通诱导系统中控制点的动态选择方法。此外,相比于大多数现有研究,本文选择VMS在有限状态之间的切换作为控制变量,使得其优化结果具有更好的可操作性。全文的主要研究内容和成果总结如下：
(1)假设驾驶员对VMS发布的诱导信息的服从率为固定值,应用宏观交通流模型将基于VMS的交通诱导问题归纳为一种最优控制问题。针对该问题中控制变量只在2个离散点取值的特殊情况,通过变量代换将最优控制问题转化为关于切换时刻的最优参数选择问题,依据离散系统的极小值原理给出了改进的最优梯度条件和相应的数值解法。仿真研究发现,交通诱导对路网的改善作用在准饱和流量需求的情况下最佳。
(2)假设驾驶员对VMS发布的诱导信息的服从率为满足正态分布的随机值,研究了含随机变量的交通诱导系统的动态优化控制问题。提出了针对该问题的双层最优控制结构,先求解下层确定的交通流分配问题,再求解上层随机的驾驶员服从问题。随后,在证明系统性能指标为服从率的凸函数的基础上,将上层的随机问题转化为系统性能指标对服从率的灵敏度最小化的确定问题并求解,解决了交通诱导系统的随机最优控制问题难以分析求解的困难。仿真结果证实该动态优化控制方法能够快速地求解出具有较好统计性能的结果,且在参数变化时仍具有稳定的优化效果。
(3)假设驾驶员在分岔路口的路径选择概率为与下游各路段旅行时间相关的时变值,以VMS是否发布实时旅行时间信息为控制变量,研究了考虑驾驶员选择行为模型的交通诱导系统的最优控制问题。其中驾驶员的路径选择行为用Logit模型描述,道路上瓶颈点的车辆排队过程用Point Queue模型描述。采用真实路网数据的仿真结果验证了最优控制方法的有效性,而持续性发布旅行时间信息并不是系统的最优策略。
(4)在上述工作的基础上,研究了包含多个VMS及入口匝道控制点的路网协调控制问题。针对控制点过多带来的负面效应,以无控制时各控制点的梯度信息作为特征值,将控制点按照对路网性能潜在影响的大小进行K平均聚类,提出了一种快速有效地动态选择控制点的方法。该方法弥补了交通诱导系统中控制点动态选取方面的研究缺失。采用真实路网数据的仿真结果表明,该方法可以根据不同的场景来动态选择最佳控制点,并显著改善路网的通行效率。
The traffic guidance system (TGS) based on variable message signs (VMS) is an important component of the intelligent transportation system. Providing traffic information via VMS potentially leads to a more efficient traffic network. By use of the TGS, the traffic is better distributed through the roads in the network, so no road is congested due to a heavy demand.
The key different aspect of the TGS comparing with the traditional signal control system is the uncertainty of the guidance effect. Unlike other control devices, VMSs are not supported by mandatory regulations. Consequently, it is uncertain whether drivers obey or disobey the guidance. This kind of uncertainty makes the design of information provision strategy challenging. Improper provision of guidance information may move the congestion from one road to another, and degrade the overall mobility of the network.
Designing the information provision strategy is important for the TGS, and is studied in the dissertation. The optimal control method is adopted to get the optimal information provision strategy via VMS. We innovatively propose a dynamical optimal control method for the TGS considering the uncertain behavior of driver, and a clustering method for the control location selecting problem in network with multi-VMS and on-ramps. Moreover, the switches between several countable states of VMS are used as the control variables in the dissertation. It makes the derived optimal strategy easier to understand and more manipulatable in compare with most current works. The main contributions of the dissertation are summarized as follows:
First, assuming that drivers have a constant compliance rate with respect to the messages via VMS, a second-order macroscopic traffic flow model is adopted to formulate the basic optimal control problem for the TGS. The control variables in the problem are the on-off states of VMS, i.e. binary variables, so the optimal control problem is transformed to an easy-to-solve optimal parameter selecting problem. The problem is then solved by use of revised gradient based on the maximum principle. It is shown by simulation that the proposed method performs best in scenarios with critically saturated flow demand.
Second, assuming that drivers' compliance rate to VMS follows a given stochastic distribution, the optimal control for the TGS with stochastic parameters is studied. The problem is formulated in the format of a bi-level optimal control problem, which consists of a deterministic lower level problem about the traffic network and a stochastic upper level problem about drivers' stochastic compliance. Then, the sensitivity of cost function with respect to drivers' compliance is utilized to convert the upper level problem to a deterministic one, and the convexity of cost function with respect to drivers' compliance is proved. The proposed conversion method makes it able to avoid the complexity and difficulty of solving a stochastic optimal control problem. Simulation shows that the expectation of the cost criterion is improved, and the improvement is rather robust while parameters change.
Third, drivers are assumed to choose a route that maximizes their individual utility according to their perception of travel time, and drivers' diversion rate turns out a time-varying parameter. A discrete choice model named the logit model, together with a vehicle queuing model named the point queue model are adopted to formulate the new optimal control problem, in which whether or not providing real-time travel time information via VMS is used as the control variable. The proposed method is tested via numerical examples that use real-world traffic demand levels in a commuting network in Minneapolis, MN. It is found that always giving information may not be the optimal strategy, while the proposed on-off control method always performs best. The sensitivity of the solution to varying demand patterns is also analyzed.
Finally, the problem of designing optimal strategy for coordinated control of route guidance via VMS and ramp metering is considered. To conquer the side effect arising from the big number of control variables, the gradients of control variables are utilized and a K-means cluster algorithm is applied to select the best control locations. Simulation of a real-world traffic network shows that the proposed method can dynamically select control locations and efficiently reduce the total time spent of drivers. In some specific scenario, the selective control method performs even better than the one employing all control variables.
由于交通诱导系统发布的信息并不是强制的要求,驾驶员对于诱导信息不一定服从,诱导结果是不确定的。这种不确定性给交通诱导信息的发布策略带来了挑战,不恰当的策略可能会使交通拥堵从一个道路转移到另一个道路,甚至加重整个路网的拥堵。因此,诱导信息的发布策略是交通诱导系统的关键。
本文应用最优控制理论的方法,研究了交通诱导系统的建模和动态信息发布策略。本文创新性地提出了在驾驶员不确定服从的情况下交通诱导系统的动态最优控制方法,以及多点控制的交通诱导系统中控制点的动态选择方法。此外,相比于大多数现有研究,本文选择VMS在有限状态之间的切换作为控制变量,使得其优化结果具有更好的可操作性。全文的主要研究内容和成果总结如下：
(1)假设驾驶员对VMS发布的诱导信息的服从率为固定值,应用宏观交通流模型将基于VMS的交通诱导问题归纳为一种最优控制问题。针对该问题中控制变量只在2个离散点取值的特殊情况,通过变量代换将最优控制问题转化为关于切换时刻的最优参数选择问题,依据离散系统的极小值原理给出了改进的最优梯度条件和相应的数值解法。仿真研究发现,交通诱导对路网的改善作用在准饱和流量需求的情况下最佳。
(2)假设驾驶员对VMS发布的诱导信息的服从率为满足正态分布的随机值,研究了含随机变量的交通诱导系统的动态优化控制问题。提出了针对该问题的双层最优控制结构,先求解下层确定的交通流分配问题,再求解上层随机的驾驶员服从问题。随后,在证明系统性能指标为服从率的凸函数的基础上,将上层的随机问题转化为系统性能指标对服从率的灵敏度最小化的确定问题并求解,解决了交通诱导系统的随机最优控制问题难以分析求解的困难。仿真结果证实该动态优化控制方法能够快速地求解出具有较好统计性能的结果,且在参数变化时仍具有稳定的优化效果。
(3)假设驾驶员在分岔路口的路径选择概率为与下游各路段旅行时间相关的时变值,以VMS是否发布实时旅行时间信息为控制变量,研究了考虑驾驶员选择行为模型的交通诱导系统的最优控制问题。其中驾驶员的路径选择行为用Logit模型描述,道路上瓶颈点的车辆排队过程用Point Queue模型描述。采用真实路网数据的仿真结果验证了最优控制方法的有效性,而持续性发布旅行时间信息并不是系统的最优策略。
(4)在上述工作的基础上,研究了包含多个VMS及入口匝道控制点的路网协调控制问题。针对控制点过多带来的负面效应,以无控制时各控制点的梯度信息作为特征值,将控制点按照对路网性能潜在影响的大小进行K平均聚类,提出了一种快速有效地动态选择控制点的方法。该方法弥补了交通诱导系统中控制点动态选取方面的研究缺失。采用真实路网数据的仿真结果表明,该方法可以根据不同的场景来动态选择最佳控制点,并显著改善路网的通行效率。
The traffic guidance system (TGS) based on variable message signs (VMS) is an important component of the intelligent transportation system. Providing traffic information via VMS potentially leads to a more efficient traffic network. By use of the TGS, the traffic is better distributed through the roads in the network, so no road is congested due to a heavy demand.
The key different aspect of the TGS comparing with the traditional signal control system is the uncertainty of the guidance effect. Unlike other control devices, VMSs are not supported by mandatory regulations. Consequently, it is uncertain whether drivers obey or disobey the guidance. This kind of uncertainty makes the design of information provision strategy challenging. Improper provision of guidance information may move the congestion from one road to another, and degrade the overall mobility of the network.
Designing the information provision strategy is important for the TGS, and is studied in the dissertation. The optimal control method is adopted to get the optimal information provision strategy via VMS. We innovatively propose a dynamical optimal control method for the TGS considering the uncertain behavior of driver, and a clustering method for the control location selecting problem in network with multi-VMS and on-ramps. Moreover, the switches between several countable states of VMS are used as the control variables in the dissertation. It makes the derived optimal strategy easier to understand and more manipulatable in compare with most current works. The main contributions of the dissertation are summarized as follows:
First, assuming that drivers have a constant compliance rate with respect to the messages via VMS, a second-order macroscopic traffic flow model is adopted to formulate the basic optimal control problem for the TGS. The control variables in the problem are the on-off states of VMS, i.e. binary variables, so the optimal control problem is transformed to an easy-to-solve optimal parameter selecting problem. The problem is then solved by use of revised gradient based on the maximum principle. It is shown by simulation that the proposed method performs best in scenarios with critically saturated flow demand.
Second, assuming that drivers' compliance rate to VMS follows a given stochastic distribution, the optimal control for the TGS with stochastic parameters is studied. The problem is formulated in the format of a bi-level optimal control problem, which consists of a deterministic lower level problem about the traffic network and a stochastic upper level problem about drivers' stochastic compliance. Then, the sensitivity of cost function with respect to drivers' compliance is utilized to convert the upper level problem to a deterministic one, and the convexity of cost function with respect to drivers' compliance is proved. The proposed conversion method makes it able to avoid the complexity and difficulty of solving a stochastic optimal control problem. Simulation shows that the expectation of the cost criterion is improved, and the improvement is rather robust while parameters change.
Third, drivers are assumed to choose a route that maximizes their individual utility according to their perception of travel time, and drivers' diversion rate turns out a time-varying parameter. A discrete choice model named the logit model, together with a vehicle queuing model named the point queue model are adopted to formulate the new optimal control problem, in which whether or not providing real-time travel time information via VMS is used as the control variable. The proposed method is tested via numerical examples that use real-world traffic demand levels in a commuting network in Minneapolis, MN. It is found that always giving information may not be the optimal strategy, while the proposed on-off control method always performs best. The sensitivity of the solution to varying demand patterns is also analyzed.
Finally, the problem of designing optimal strategy for coordinated control of route guidance via VMS and ramp metering is considered. To conquer the side effect arising from the big number of control variables, the gradients of control variables are utilized and a K-means cluster algorithm is applied to select the best control locations. Simulation of a real-world traffic network shows that the proposed method can dynamically select control locations and efficiently reduce the total time spent of drivers. In some specific scenario, the selective control method performs even better than the one employing all control variables.
引文
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