On the 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.