Quantifying Traffic Patterns with Percolation Theory: A Case Study of Seoul Roads

TL;DR

This paper applies percolation theory to analyze Seoul's traffic patterns, revealing how congestion transitions and correlations impact traffic resilience and network fragmentation during different times of the day.

Contribution

It introduces a novel application of percolation metrics to urban traffic analysis, emphasizing the role of correlations and temporal variations in traffic network robustness.

Findings

Lower $q_c$ and $ au$ during rush hours indicate low-dimensional traffic behavior.

Weight correlations significantly influence cluster formation and traffic state onset.

Real-world correlations differ from uncorrelated models, affecting traffic resilience.

Abstract

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 $q_c$ and Fisher exponent $\tau$. The transition point $q_c$ 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 $q_c$ and lower $\tau$ values during rush hours representing low-dimensional behavior. 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.