Staircases play an essential role in crowd dynamics, allowing pedestrians to flow across large multi-level public facilities such as transportation hubs, shopping malls, and office buildings. Achieving a robust quantitative understanding of pedestrian behavior in these facilities is a key societal necessity. What makes this an outstanding scientific challenge is the extreme randomness intrinsic to pedestrian behavior. Any quantitative understanding necessarily needs to be probabilistic, including average dynamics and fluctuations. To this purpose, large-scale, real-life trajectory datasets are paramount.

In this work, we analyze the data from an unprecedentedly high statistics year-long pedestrian tracking campaign, in which we anonymously collected millions of trajectories of pedestrians ascending and descending stairs within Eindhoven Central train station (The Netherlands). This has been possible thanks to a state-of-the-art, faster than real-time, computer vision approach hinged on 3D depth imaging, sensor fusion, and YOLOv7-based depth localization. We consider both free-stream conditions, i.e. pedestrians walking in undisturbed, and trafficked conditions, unidirectional/bidirectional flows. We report on Eulerian fields (density, velocity and acceleration), showing how the walking dynamics changes when transitioning from stairs to landing. We then investigate the (mutual) positions of pedestrian as density changes, considering the crowd as a “compressible” physical medium. In particular, we show how pedestrians willingly opt to occupy fewer space than available, accepting a certain degree of compressibility. This is a non-trivial physical feature of pedestrian dynamics and we introduce a novel way to quantify this effect. As density increases, pedestrians strive to keep a minimum distance $d\approx 0.6$m (two treads of the staircase) from the person in front of them. Finally, we establish first-of-kind fully resolved probabilistic fundamental diagrams, where we model the pedestrian walking velocity as a mixture of a slow and fast-paced component (both in non-negligible percentages and with density-dependent characteristic fluctuations). Notably, averages and modes of velocity distribution turn out to be substantially different. Our results, of which we include probabilistic parametrizations based on few variables, are key towards improved facility design and realistic simulation of pedestrians on staircases.

楼梯在人群动态中发挥着至关重要的作用，允许行人流经交通枢纽、购物中心和办公楼等大型多层公共设施。对这些设施中的行人行为进行可靠的定量理解是一个关键的社会必要性。行人行为固有的极端随机性使其成为一项突出的科学挑战。任何定量的理解都必须是概率性的，包括平均动态和波动。为此，大规模的现实轨迹数据集至关重要。

在这项工作中，我们分析了为期一年的前所未有的高统计数据行人跟踪活动，其中我们匿名收集了埃因霍温中央火车站（荷兰）内数百万行人上下楼梯的轨迹。这要归功于基于 3D 深度成像、传感器融合和基于 YOLOv7 的深度定位的最先进、比实时更快的计算机视觉方法。我们考虑自由流条件，即行人在不受干扰的情况下行走，以及交通条件，即单向/双向流。我们报告了欧拉场（密度、速度和加速度），展示了从楼梯过渡到着陆时行走动力学如何变化。然后，我们研究行人随着密度变化的（相互）位置，将人群视为“可压缩”的物理介质。特别是，我们展示了行人如何愿意选择占据比可用空间更少的空间，并接受一定程度的压缩性。这是行人动力学的一个重要的物理特征，我们引入了一种新的方法来量化这种影响。随着密度的增加，行人努力保持最小距离$d\approx 0。6$距离他们前面的人米（楼梯的两级台阶）。最后，我们建立了首个完全解析的概率基本图，其中我们将行人行走速度建模为慢速和快节奏分量的混合（两者的百分比都不可忽略，并且具有与密度相关的特征波动）。值得注意的是，速度分布的平均值和模式有很大不同。我们的结果包括基于少数变量的概率参数化，这是改进设施设计和楼梯上行人的真实模拟的关键。