The Propagation of Congestion on Transportation Networks Analyzed by the Percolation Process

Percolation theory has been widely employed in network systems as an effective tool to analyze phase transitions from functional to nonfunctional states. In this paper, we analyze the propagation of congestion on transportation networks and its influence on origin–destination (OD) pairs using the percolation process. This approach allows us to identify the most critical links within the network that, when disrupted due to congestion, significantly impact overall network performance. Understanding the role of these critical links is essential for developing strategies to mitigate congestion effects and enhance network resilience. Building on this analysis, we propose two methods to adjust the capacities of these critical links. First, we introduce a greedy method that incrementally adjusts the capacities based on their individual impact on network connectivity and traffic flow. Second, we employ a Particle Swarm Optimization (PSO) method to strategically increase the capacities of certain critical links, considering the network as a whole. These capacity adjustments are designed to enhance the network’s resilience by ensuring it remains functional even under conditions of high demand and congestion. By preventing the propagation of congestion through strategic capacity enhancements, the transportation network can maintain connectivity between OD pairs, reduce travel times, and improve overall efficiency. Our approach provides a systematic method for improving the robustness of transportation networks against congestion propagation. The results demonstrate that both the greedy method and the PSO method effectively enhance network performance, with the PSO method showing superior results in optimizing capacity allocations. This research is crucial for maintaining efficient and reliable mobility in urban areas, where congestion is a persistent challenge, and offers valuable insights for transportation planners and policymakers aiming to design more resilient transportation infrastructures.