Percolation-based dynamic perimeter control for mitigating congestion propagation in urban road networks

Perimeter control regulates the traffic flows between different regions of a road network by coordinating the signal timings at region boundaries with the aim of improving the overall network performance. The method is proved to be effective in optimizing urban road traffic and is a crucial component of the modern intelligent transportation systems. A possible shortcoming of classical perimeter control is its limiting perception of congestion propagation dynamics, viewing congestion only through aggregated or local properties, e.g., traffic accumulation within the perimeter or queue length at each intersection. Furthermore, restricting traffic via gating by conventional perimeter control may trigger formation of congested queues at the control boundary. In this work, we tackle this problem with control at a dynamic perimeter where the geometry of the boundary evolves over time according to the congestion propagation dynamics. The proposed dynamic perimeter control utilizes percolation theory, a well-established theory for studying statistical physics of spreading phenomena, to analyze the evolving congestion and adapts the shape of the perimeter accordingly. The percolation-based dynamic perimeter effectively adjusts to propagating congestion and prevent small congestion pockets from merging into a larger congested cluster. We demonstrate the performance of the proposed approach in a typical grid network. Our results show that i) the percolation analysis is able to effectively characterize the spatio-temporal evolution of the congestion for the purpose of traffic signal control, ii) adjusting the control dynamically according to percolation-based analysis of congestion successfully balances the traffic leading to boosting the flow capacity of the network, and iii) the percolation-based dynamic perimeter control significantly improves the network traffic performance, compared to the classic fixed perimeter control. This study applies percolation theory and for the first time incorporates an account for the geometrical properties of congestion propagation in traffic signal control, aiming at preventing the emergence of large-scale connected jams.