Optimization of Vehicle Trajectories Considering Uncertainty in Actuated Traffic Signal Timings

Abstract

This paper introduces a robust green light optimal speed advisory (GLOSA) system for fixed and actuated traffic signals considering a probability distribution. These distributions represent the domain of possible switching times from the signal phasing and timing (SPaT) messages. The system finds the least-cost (minimum fuel consumption) vehicle trajectory using a computationally efficient A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^\ast$</tex-math> </inline-formula> algorithm incorporated within a dynamic programming (DP) procedure to minimize the vehicle’s total fuel consumption. Constraints are introduced to ensure that vehicles do not collide with other vehicles, run red indications, or exceed a maximum vehicular jerk for passenger comfort. Results of simulation scenarios are evaluated against empirical comparable trajectories of uninformed drivers to compute fuel consumption savings. The proposed approach produced significant fuel savings compared to an uninformed driver behavior amounting to 37% on average for deterministic SPaT and 30% for stochastic SPaT data. A sensitivity analysis was 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 savings in fuel consumption. Specifically, the study demonstrates that the proposed system can be within 85% of the maximum savings if the timing error is ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm$</tex-math> </inline-formula> 3.3 seconds) at a 95% confidence level. Results also emphasize the importance of more reliable SPaT predictions as the time to green decreases relative to the time the vehicle is expected to reach the intersection given its current speed.