This paper presents a large-scale traffic signal optimization system, OSaaS, that uses low penetration rate vehicle trajectory data to improve traffic signal timing. The system eliminates the need for vehicle detectors and relies solely on vehicle trajectory data to optimize traffic signals. It uses a probabilistic time-space (PTS) diagram and a stochastic point-queue model to reconstruct the spatial-temporal traffic state from historical data. This allows for the optimization of traffic signal parameters to reduce delays and stops at intersections. The system was tested in Birmingham, Michigan, and demonstrated a 20% reduction in delay and 30% reduction in stops at signalized intersections. The system is scalable, sustainable, and efficient, and can be applied to every fixed-time traffic signal in the world. The paper also discusses the challenges of using low penetration rate data and the importance of accurate traffic state estimation for effective traffic signal optimization. The results show that even with low penetration rates, the system can effectively reconstruct traffic states and improve traffic signal timing. The system uses a closed-loop approach to continuously monitor and optimize traffic signals based on historical data. The paper also discusses the potential for real-time adjustments to traffic signals under certain conditions. The results demonstrate that the system can significantly improve traffic flow and reduce congestion in urban areas.This paper presents a large-scale traffic signal optimization system, OSaaS, that uses low penetration rate vehicle trajectory data to improve traffic signal timing. The system eliminates the need for vehicle detectors and relies solely on vehicle trajectory data to optimize traffic signals. It uses a probabilistic time-space (PTS) diagram and a stochastic point-queue model to reconstruct the spatial-temporal traffic state from historical data. This allows for the optimization of traffic signal parameters to reduce delays and stops at intersections. The system was tested in Birmingham, Michigan, and demonstrated a 20% reduction in delay and 30% reduction in stops at signalized intersections. The system is scalable, sustainable, and efficient, and can be applied to every fixed-time traffic signal in the world. The paper also discusses the challenges of using low penetration rate data and the importance of accurate traffic state estimation for effective traffic signal optimization. The results show that even with low penetration rates, the system can effectively reconstruct traffic states and improve traffic signal timing. The system uses a closed-loop approach to continuously monitor and optimize traffic signals based on historical data. The paper also discusses the potential for real-time adjustments to traffic signals under certain conditions. The results demonstrate that the system can significantly improve traffic flow and reduce congestion in urban areas.