Quantifying traffic patterns with percolation theory: a case study of Seoul roads

Urban traffic systems are characterized by dynamic interactions between congestion and free-flow states, influenced by human activity and road topology. This study employs percolation theory to analyze traffic dynamics in Seoul, focusing on the transition point \(q_\textrm{c}\) and Fisher exponent \(\tau\). The transition point \(q_\textrm{c}\) quantifies the robustness of the free-flow clusters, while the exponent \(\tau\) captures the spatial fragmentation of the traffic networks. Our analysis reveals temporal variations in these metrics, with lower \(q_\textrm{c}\) and lower \(\tau\) values generally during rush hours representing low-dimensional behavior, within the broader context of the positive correlation between \(q_\textrm{c}\) and \(\tau\). Weight–weight correlations are found to significantly impact cluster formation, driving the early onset of dominant traffic states. Comparisons with uncorrelated models highlight the role of real-world correlations. This approach provides a comprehensive framework for evaluating traffic resilience and informs strategies to optimize urban transportation systems.