Optimization of Vehicle Trajectories Considering Uncertainty in Actuated Traffic Signal Timings

This paper introduces a robust optimal green light speed advisory system for fixed and actuated traffic signals when a probability distribution is provided. These distributions represent the domain of possible switching times from the Signal Phasing and Timing (SPaT) messages. The system finds the least-cost vehicle trajectory using a computationally efficient A-star algorithm incorporated in a dynamic programming procedure to minimize the vehicle's total fuel consumption. Constraints are introduced to ensure that vehicles do not, collide with other vehicles, run red lights, or exceed a maximum vehicular jerk for passenger comfort. Results of simulation scenarios are evaluated against comparable trajectories of uninformed drivers to compute fuel consumption savings. The proposed approach produced significant fuel savings compared to the uninformed driver amounting to 37 percent on average for deterministic SPAT and 28 percent for stochastic SPaT. A sensitivity analysis is performed to understand how the degree of uncertainty in SPaT predictions affects the optimal trajectory's fuel consumption. The results present the required levels of confidence in these predictions to achieve most of the possible savings in fuel consumption. Specifically, the proposed system can be within 85 percent of the maximum savings if the timing error is (within 3.3 seconds) at a 95 percent confidence level. They also emphasize the importance of more reliable SPaT predictions the closer the time to green is relative to the time the vehicle is expected to reach the intersection given its current speed.