Existing fixed-time traffic signal optimization methods mainly use traffic volumes collected by infrastructure-based detectors (e.g., loop detectors). These infrastructure-based detectors generally have high maintenance costs and low coverage. With the deployment of probe vehicles, vehicle trajectory data provide more information about traffic states and can be utilized for signal timing. However, most related studies assume high penetration rates of probe vehicles or short sampling intervals. This paper develops a hierarchical multi-objective optimization framework to optimize fixed-time traffic signals based on sampled vehicle trajectories at isolated signalized intersections, which is applicable to low-resolution trajectory data. Cycle length and green splits are optimized under both under- and slightly over-saturated traffic conditions. The number of over-saturated phases and average vehicle delays are adopted as the primary and the secondary objectives, respectively. Note that the queues of over-saturated phases cannot be discharged. The queue length and traffic delay of over-saturated phases will go infinite as time goes. The consideration of the over-saturated phase number helps increase vehicle throughput and reduce queue length and traffic delay. The aggregation of sampled trajectory data during the same period across multiple cycles and Same-ratio Principles (SRPs) are proposed to compensate for the limitations of low penetration rates of probe vehicles. The evolution of sampled trajectories with varying signal timings are formulated explicitly. A sampled-trajectory-density method is proposed to identify over-saturated phases. Then a mixed integer non-linear programming (MINLP) model is formulated and transformed to a series of mixed integer linear programming (MILP) models by linearization and enumerating cycle lengths. Simulation studies validate the advantages of the proposed model over the one in Synchro Studio. Sensitivity analysis shows that: (1) the proposed model is applicable to Poisson vehicle arrivals; (2) the proposed model can handle sampling intervals as long as 15 s when sufficient sampled vehicle trajectories are collected; (3) the number of sampled trajectories has impacts on the performance of the proposed model instead of probe vehicle penetration rates, especially with under-saturated traffic; (4) cycle lengths of initial signal timing plans have no noticeable impacts on the required number of sampled trajectories when a short sampling interval is applied; and (5) the proposed model is insensitive to the quality of initial signal timing plans with under- and slightly over-saturated traffic. The proposed model is also implemented with field data to demonstrate its applicability in the real world.

现有的固定时间交通信号优化方法主要使用由基于基础设施的检测器（例如，环路检测器）收集的交通量。这些基于基础设施的探测器通常维护成本高且覆盖率低。随着探测车辆的部署，车辆轨迹数据可提供有关交通状态的更多信息，并可用于信号计时。但是，大多数相关研究假设探测车的穿透率很高或采样间隔较短。本文提出了一种基于层次化的多目标优化框架，基于孤立的信号交叉口处的车辆轨迹，对固定时间的交通信号进行了优化，适用于低分辨率的轨迹数据。在交通流量不足和稍微过饱和的情况下，都可以优化周期长度和绿色分割。过饱和阶段的数量和平均车辆延迟分别用作主要目标和次要目标。请注意，过饱和阶段的队列无法释放。随着时间的流逝，过饱和阶段的队列长度和流量延迟将变得无限大。对过饱和的相数的考虑有助于增加车辆的吞吐量，并减少队列长度和交通延迟。提出了在多个周期的同一时期内采样轨迹数据的汇总以及相同比率原理（SRP），以弥补探测车低穿透率的局限性。明确规定了具有变化的信号定时的采样轨迹的演变。提出了一种采样轨迹密度方法来识别过饱和相。然后，通过线性化和枚举循环长度，制定了混合整数非线性规划（MINLP）模型并将其转换为一系列混合整数线性规划（MILP）模型。仿真研究验证了所提出的模型优于Synchro Studio中模型的优点。敏感性分析表明：（1）提出的模型适用于泊松车辆到达。（2）当收集到足够的采样车辆轨迹时，该模型可以处理长达15 s的采样间隔；（3）采样轨迹的数量对建议模型的性能产生影响，而不是对探查车辆的渗透率产生影响，特别是在交通流量不足的情况下；（4）当采用较短的采样间隔时，初始信号定时计划的周期长度对所需的采样轨迹数量没有明显影响；（5）所提出的模型对流量不足和稍微过饱和的初始信号时序计划的质量不敏感。所提出的模型还通过现场数据来实现，以证明其在现实世界中的适用性。