Percolation-Based Dynamic Perimeter Control for Urban Road Networks

Abstract

Perimeter control regulates the traffic flows between regions of a transport network by coordinating the signal timings on their 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 drawback of restricting the incoming traffic to a region is the susceptibility to formation of congested queues outside the perimeter. In this work, we tackle this problem with control at a dynamic perimeter where the geometry of the boundary evolves over time based on congestion clustering underpinned by percolation analysis. Here, we consider a conventional fixed perimeter control that can effectively optimize traffic flows within a hotspot region of the network. In the common event of queue spill-back from this perimeter, our proposed time-varying perimeter outside the fixed perimeter will be triggered to control the propagation of congestion. We utilize percolation analysis to examine the evolving congestion over time and adapt the dynamic perimeter accordingly, with the aim of preventing 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 performance, compared to the classic fixed perimeter control. This study, for the first time, applies percolation theory, a well-established theory in studying statistical physics of spreading phenomena, to characterize congestion propagation for signal control to prevent emergence of large-scale connected jams.

Keywords: Percolation theory, Congestion propagation, Macroscopic fundamental diagram, Traffic signal control, Dynamic perimeter control