  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.
