The development of technologies for reliable tracking of pedestrian trajectories in public spaces has recently enabled collecting large data sets and real-time information about the usage of urban space and indoor facilities by human crowds. Such an information, nevertheless, may be properly used only with the aid of theoretical and computational tools to assess the state of the crowd. As shown in this work, traditional assessment metrics such as density and flow may provide only a partial information, since it is also important to understand how “regular” these flows are, as spatially uniform flows are arguably less problematic than strongly fluctuating ones.

Recently, the Congestion Level ($CL$), based on the computation of spatial variation of the rotor of the crowd velocity field, has been proposed as an assessment metric to evaluate the state of the crowd. Nevertheless, the $CL$ definition was lacking sound theoretical foundations and, more importantly, was of very difficult interpretation (it was difficult to understand “what” $CL$ was measuring). As we believe that such theoretical shortcomings were limiting also its relevance to applied studies, in this work we clarify some aspects concerning the $CL$ definition, and we show that such an assessment metric may be improved by defining a dimensionless Congestion Number ($CN$).

As a first application of the newly defined $CN$ indicator we first focus on the cross-flow scenario and, by using discrete and continuous toy models, idealised “limit scenarios”, more realistic simulations and finally data from experiments with human participants, we show that $CN\ll 1$ corresponds to a crowd with a regular and safe motion (even in high density and high flow settings), while $CN\approx 1$ indicates the emergence of a congested and possibly dangerous condition. We finally use the $CN$ indicator to analyse and discuss different settings such as bottlenecks, uni-, bi- and multi-directional flows, and real-world data concerning the movement of pedestrians in the world’s busiest railway station.

公共场所行人轨迹可靠跟踪技术的发展最近使我们能够收集大量数据集和有关人群使用城市空间和室内设施的实时信息。然而，只有在理论和计算工具的帮助下才能正确使用此类信息来评估人群的状态。如本研究所示，密度和流量等传统评估指标可能仅提供部分信息，因为了解这些流量的“规律性”也很重要，因为空间均匀的流量可以说比剧烈波动的流量问题更少。

最近，拥塞级别（$C\mathrm{大号}$)，基于人群速度场转子空间变化的计算，已被提出作为评估人群状态的评估指标。尽管如此，$C\mathrm{大号}$定义缺乏坚实的理论基础，更重要的是，解释起来非常困难（很难理解“什么”$C\mathrm{大号}$正在测量）。由于我们认为这种理论缺陷也限制了它与应用研究的相关性，因此在这项工作中，我们澄清了有关$C\mathrm{大号}$定义，并且我们表明可以通过定义无量纲拥塞数（$C否$).

作为新定义的第一个应用$C否$我们首先关注交叉流场景，通过使用离散和连续的玩具模型、理想化的“极限场景”、更现实的模拟以及最终来自人类参与者的实验数据，我们表明$C否\ll \mathrm{1个}$对应于有规律和安全运动的人群（即使在高密度和高流量设置下），而$C否\approx \mathrm{1个}$表示出现了拥挤且可能存在危险的情况。我们最终使用$C否$指标来分析和讨论不同的设置，例如瓶颈、单向、双向和多向流量，以及关于世界上最繁忙的火车站行人移动的真实数据。