基于抽样车辆轨迹数据的信号控制交叉口排队长度分布估计

排队长度是评价信号控制交叉口运行状态的重要参数之一。现有大多数基于抽样车辆轨迹数据的排队长度估计方法可以实现周期级排队长度估计，但是需要信号配时、渗透率或车辆到达分布等实践中难以获取的输入信息。此外，这类方法在低渗透率条件下往往难以确保估计结果的准确性和可靠性，极大地限制了其实用性。因此，提出一种抽样车辆轨迹数据驱动的时段级信号控制交叉口排队长度分布估计方法，可不依赖任何交通流理论模型和前述输入信息实现排队估计。首先，通过理论推导可以证明时段内抽样车辆的停车位置分布和排队长度分布之间可互相转化；然后，提出一种扩展的核密度估计方法来拟合并平滑抽样车辆停车位置分布，从而有效地适应不同日期和周期的轨迹叠加所带来的波动，提高方法的适用性；最后，基于前述推导和拟合的停车位置分布实现时段排队长度分布、平均排队长度和百分位排队长度估计。分别采用仿真和实证数据对上述方法进行验证和评价。结果表明，通过叠加5 d相同时段的抽样轨迹数据，15 min的平均排队长度估计误差仅为1.59 veh，相对误差仅为9%。同时，面向不同分析时长，只要给定超过100 veh抽样车辆的观测样本，无论渗透率高低，所提出的方法在定时或自适应信号控制交叉口都可实现时段排队长度分布的准确估计，其成果可进一步用于信号控制交叉口运行可靠性评估以及多时段定时信号控制的鲁棒优化。

Queue Length Distribution Estimation at Signalized Intersections Based on Sampled Vehicle Trajectory Data

Queue length is one of the most important indicators for the operational evaluation of signalized intersections. Most of the existing queue-length estimation methods using sampled vehicle trajectories are cycle-based, requiring input information such as signal timing program, penetration rate, or vehicle arrival distribution, which are difficult to obtain in practice. In addition, these methods tend to produce inaccurate and unstable results under low penetration rates, which greatly constrains their application. Therefore, a time-of-day (TOD) based queue length distribution estimation method solely using historical sampled vehicle trajectories is proposed in this paper. This method is purely data-driven and does not rely on any traffic flow models or the aforementioned input information. First, we found that the queuing position distribution of the sampled vehicles and the queue length distribution are convertible. Then, the extended kernel density estimation (KDE) method was employed to fit and smooth the queuing position distribution, which can accommodate the fluctuation caused by various aggregations of days and cycles, thereby improving the applicability of the proposed method. Finally, based on the aforementioned derivation and the fitting results of the queuing position distribution, the queue length distribution of the analysis period was estimated, as well as the average and any percentile of queue length. The proposed method was evaluated using both simulation and empirical data. The results show that using trajectory data for 5 weekdays, the mean absolute error of the average queue length during 15 min is 1.59 vehicles, and the mean absolute percentage error is 9%. Meanwhile, given more than 100 sampled vehicles, the proposed method can produce precise estimates for the queue length distribution over a wide range of analysis intervals at fixed-time and adaptive control intersections, regardless of the penetration rate. This implies that the presented work could be applied to the reliability evaluation of signalized intersections as well as robust optimization of fixed-time signal timing plans in the time-of-day mode.