Traffic systems are complex systems that exhibit non-stationary characteristics. Therefore, the identification of temporary traffic states is significant. In contrast to the usual correlations of time series, here we study those of position series, revealing structures in time, i.e. the rich non-Markovian features of traffic. Considering the traffic system of the Cologne orbital motorway as a whole, we identify five quasi-stationary states by clustering reduced rank correlation matrices of flows using the $k$-means method. The five quasi-stationary states with nontrivial features include one holiday state, three workday states and one mixed state of holidays and workdays. In particular, the workday states and the mixed state exhibit strongly correlated time groups shown as diagonal blocks in the correlation matrices. We map the five states onto reduced-rank correlation matrices of velocities and onto traffic states where free or congested states are revealed in both space and time. Our study opens a new perspective for studying traffic systems. This contribution is meant to provide a proof of concept and a basis for further study.

中文翻译：

---

交通系统时间相关性中的准平稳状态：以科隆轨道高速公路为例

交通系统是表现出非平稳特征的复杂系统。因此，临时交通状态的识别具有重要意义。与通常的时间序列相关性不同，这里我们研究位置序列的相关性，揭示时间结构，即交通的丰富非马尔可夫特征。考虑到整个科隆轨道高速公路的交通系统，我们通过使用 $k$-means 方法对流的降秩相关矩阵进行聚类来识别五个准静止状态。具有非平凡特征的五种准平稳状态包括一种假日状态、三种工作日状态和一种假日和工作日混合状态。特别是，工作日状态和混合状态表现出强相关的时间组，在相关矩阵中显示为对角线块。我们将这五个状态映射到速度的降阶相关矩阵和交通状态，其中在空间和时间上都显示出空闲或拥塞状态。我们的研究为研究交通系统开辟了新的视角。此贡献旨在提供概念证明和进一步研究的基础。