Stability of traffic breakup patterns in urban networks

We investigate the behavior of extended urban traffic networks within the framework of percolation theory by using real and synthetic traffic data. Our main focus shifts from the statistical properties of the cluster size distribution studied recently, to the spatial analysis of the clusters at criticality and to the definition of a similarity measure between whole urban configurations. We discover that the breakup patterns of the complete network, formed by the connected functional road clusters at criticality, show remarkable stability from one hour to the next, and predictability for different days at the same time. We prove this by showing how the average spatial distributions of the highest-rank clusters evolve over time, and by building a taxonomy of traffic states via dimensionality reduction of the distance matrix, obtained via a clustering similarity score. Finally, we show that a simple random percolation model can approximate the breakup patterns of heavy real traffic when long-ranged spatial correlations are imposed.

Figure 1

Largest (red), second (blue), and smaller clusters (third through $1000\text{th}$) (green) temporally averaged spatial distributions over London during the first 3 months of 2019 at four different hours: 8 a.m., 10 a.m., 5 p.m., and 8 p.m. The linewidth increases with the frequency with which edges belong to each of the main clusters: thinnest for 0.4, thickest for 1.0. A larger version is shown in Fig. S1.

Figure 2

Distribution of London traffic configurations over 3 months obtained from t-SNE and Fowlkes-Mallows similarity: Each symbol represents a single day at a specific hour.