Traffic light optimization with low penetration rate vehicle trajectory data

Traffic congestion at signalized intersections incurs substantial costs in the United States, estimated at roughly $22.9 billion annually. Improper traffic signal operation is a major contributor to these costs. While traffic signal retiming is a cost-effective method for mitigation, the high cost of installing and maintaining vehicle detectors has hindered widespread implementation of advanced traffic control systems. Most intersections rely on fixed-time signals, often not regularly optimized, leading to outdated timing plans and increased congestion. Connected vehicle services provide an alternative source of data—vehicle trajectory data—offering advantages over traditional detectors. Vehicle trajectory data has a wider coverage area and provides richer information (delay, number of stops, travel paths) than fixed-location detectors. This study leverages this readily available data to optimize fixed-time traffic signals without relying on roadside detectors, addressing the challenge of sparse and incomplete observations inherent in low penetration rates of connected vehicles. Existing studies focusing on connected and automated vehicle (CAV) traffic signal control often assume unrealistically high CAV penetration rates. This research aims to optimize traffic signals using currently available penetration rates, requiring innovative approaches to address the limitations of sparse data.

Many studies have explored traffic signal control with CAVs, but they typically assume high penetration rates, unlike real-world scenarios. Several studies have developed statistical methods to estimate traffic flow parameters (volumes, queue lengths) from trajectory data, but these methods are mainly for monitoring and lack explicit traffic flow models needed for optimization. Stochastic traffic flow models could predict traffic flow under different signal parameters, but most existing models aren't compatible with vehicle trajectory data due to differences in coordinate systems (Eulerian vs. Lagrangian). Models using both Eulerian and Lagrangian coordinates become complex in higher dimensions. The limited number of studies using trajectory data for traffic signal optimization have employed heuristic methods with limited scalability.

This paper proposes a stochastic traffic flow model using Newellian coordinates, based on Newell's car-following models. A simplified point-queue model under these coordinates captures the spatial-temporal traffic state via a probabilistic time-space (PTS) diagram. This simplification ignores stochastic and heterogeneous driving behavior, focusing on uncertainty from stochastic demand and sparse observations at low penetration rates. The model's low dimensionality allows direct calibration with vehicle trajectory data, enabling estimation algorithms to estimate unknown traffic states and parameters. The research developed a large-scale traffic signal optimization system (OSaaS), a closed-loop system encompassing monitoring, modeling, diagnosis, and optimization. Each retiming iteration involves delay and stop calculations from trajectories, parameter estimation (penetration rate, arrival rate) using the proposed model, and diagnosis of optimality gaps. Optimization algorithms update signal timing parameters for intersections with improvement potential. This allows for dynamic optimization every few weeks, compared to the current practice of 3–5 years. The method of moments estimator is used for parameter estimation, matching average delay from the model with trajectory measurements. The system was tested in Birmingham, Michigan using GM vehicle trajectory data. The Newellian coordinates system uses free-flow arrival time and the number of unit traffic flows as coordinates, enabling the conversion of vehicle trajectories to a point-queue representation. A stochastic point-queue model, which assumes that the vehicle arrival follows a Bernoulli distribution, is then established. This model can be easily projected back to the spatial-temporal space using the probabilistic time-space (PTS) diagram. Using the MM estimator, the penetration rate is estimated by matching the model-estimated average delay with the observed average delay. The traffic state is derived using the estimated parameter. For multi-movement corridors, a centralized formulation is used to estimate the penetration rate of multiple movements, considering the congestion level of each movement. The traffic signal optimization uses a coordinate-descent algorithm which aims at minimizing a performance index which is the linear combination of total delay and number of stops weighted by a certain coefficient.

The Newellian coordinate system and the stochastic point-queue model successfully represent and model the traffic flow using vehicle trajectory data. The method of moments estimator effectively estimates the penetration rate and arrival rate parameters. The OSaaS system accurately reconstructs the spatial-temporal traffic state, evidenced by an average Intersection over Union (IoU) of approximately 70% between the ground truth and reconstructed queueing areas. The system's diagnosis module effectively identifies intersections with optimality gaps, both for isolated intersections (cycle length, green splits) and corridors (coordination opportunities). The city-wide field implementation in Birmingham, Michigan, encompassing 34 signalized intersections, resulted in significant performance improvements. Adams Rd. showed a 12% reduction in average control delay and an 18% decrease in the average number of stops. Old Woodward Ave. exhibited a more substantial reduction in delay (over 15% during the AM peak) and stops (over 14% during the PM peak). The aggregated time-space diagrams before and after offset optimization visually demonstrate the improved traffic signal coordination, showing fewer stops and delays along the corridors. The results indicate substantial improvements in traffic flow metrics after implementing the new signal timing plans generated by the OSaaS system.

The OSaaS system effectively addresses the limitations of current traffic signal optimization practices by leveraging readily available vehicle trajectory data. The system's ability to operate without roadside detectors makes it cost-effective and highly scalable, potentially applicable to every fixed-time traffic signal globally. The use of a probabilistic model accommodates the inherent uncertainty in low penetration rate data, showing that useful inferences can be drawn. The system's closed-loop nature enables continuous monitoring and adaptive adjustments to changing traffic conditions. The significant improvements observed in the Birmingham, Michigan field implementation validate the effectiveness of the proposed approach. The superior performance of the offset optimization method compared to traditional green-band methods highlights the advantages of explicitly considering vehicle distribution and using a comprehensive objective function (total delay and stops).

This paper introduces OSaaS, a cost-effective and scalable traffic signal optimization system using low-penetration rate vehicle trajectory data. The system eliminates the need for roadside detectors, enabling widespread implementation. Field tests demonstrated significant reductions in delay and stops. Future research could explore real-time adjustments based on trajectory data and investigate the impact of incorporating different performance indices and priorities for various movements.

The accuracy of real-time traffic state estimation is limited by the low penetration rate of connected vehicles. The model's simplification, neglecting stochastic and heterogeneous driving behaviors, might introduce some limitations. The assumption of stationary traffic state within certain TOD might not perfectly capture all traffic dynamics.