Towards Autonomous and Distributed Traffic Signal Control

Abstract

The challenge of optimizing traffic signal control has significant implications for individual wellbeing, economics, and the environment. To tackle this, our thesis presents two core strategies. Firstly, we introduce a centralized approach rooted in the principles of Model Predictive Control (MPC). This centralized method utilizes a predictive traffic dynamics model to effectively establish a baseline performance for comparisons. In contrast, our primary focus is on the second strategy, which involves a distributed algorithm chosen for its scalability benefits in extensive traffic networks. A prominent instance of such a distributed algorithm is the Max Pressure (MP) algorithm, renowned for its theoretical maximization of throughput under specific assumptions -such as infinite queue lengths. To overcome this limitation, we incorporate a technique commonly employed in communication and queuing theory, referred to as the Lyapunov Drift-Plus-Penalty (LDPP) framework. While upholding that same assumption, the LDPP framework facilitates the integration of an additional penalty function designed to specifically address this constraint. Beyond mitigating the limitations of this assumption, this function also fosters collaboration among neighboring intersections by incorporating their actions. By adopting this approach, we successfully transform the original traffic signal control problem into a consensus challenge among neighboring intersections, departing from the assumption of independent intersection actions as seen in the MP formulation. This collaborative methodology strives for more globally optimal solutions. Moreover, we substantiate our approach with theoretical stability guarantees that limit the congestion size. To solve this resulting consensus problem, two algorithms are employed. The first is a consensusbased Alternating Direction Method of Multipliers (ADMM) formulation, while the second is a custom Greedy algorithm. Both algorithms are executed in a fully distributed manner. While ADMM approaches close-to-optimal solutions, the Greedy algorithm approximates the optimal solution with a significantly reduced computational cost. Simulation results validate the effectiveness of our proposed method, demonstrating significant enhancements of travel time by up to 30% compared to the MP algorithm. Additionally, average queue lengths experience a congestion reduction of 40%, particularly in networks with shorter inter-lane distances. Furthermore, we illustrate that our algorithm showcases performance similar to the centralized formulation.