Detecting the Critical Thresholds of an Urban Traffic System Using Percolation Theory

We employ high-resolution speed data to develop a percolation theory-based network analysis framework by integrating two identified critical thresholds. This framework effectively captures the dynamic behaviors of traffic networks before, during, and after the critical phase transition point. Our study reveals characteristic congestion thresholds around this critical phase transition for each studied network. Critical thresholds mark tipping points where small disruptions may trigger widespread congestion in traffic systems. Near these thresholds, traffic behavior akin to a first-order phase transition occurs during rush periods, while a second-order phase transition is observed during non-rush periods. These insights facilitate the establishment of critical thresholds for urban areas. Additionally, our framework identifies essential links, termed bottlenecks, which are crucial for maintaining the functional connectivity of urban transport networks and ensuring the required level of service in cities. Our findings indicate that these traffic bottlenecks consistently appear at the same times on different days. Notably, links with high betweenness centralities often act as persistent seeds of congestion at the onset and throughout rush periods. Finally, the results indicate that disturbances in links with low congestion index and low betweenness centrality are unlikely to cause catastrophic fragmentation or the decomposition of the giant component.