Traffic Signal Timing and Trajectory Optimization in a Mixed Autonomy Traffic Stream

This study introduces a methodology for cooperative signal timing and trajectory optimization at intersections with a mix of connected automated vehicles (CAVs) and human-driven vehicles (HVs). We represent joint signal timing and trajectory control as a mixed-integer non-linear program, which is computationally complex. The developed methodology provides a balance between computational efficiency and solution quality by (a) linearizing the nonlinear constraints and reformulating the problem with a tight convex hull of the mixed-integer solutions and (b) decomposing the intersection-level program into several lane-level programs. Hence, a unique controller jointly optimizes the trajectories of CAVs on a lane and the signal timing parameters associated with that lane. This setting will allow finding near-optimal solutions with small duality gaps for complex intersections with different demand levels. Case study results show that the proposed methodology finds solutions efficiently with at most 0.1% duality gap. We compared the developed methodology with an existing signal timing and trajectory control approach and found 13% to 41% reduction in average travel time and 1% to 31% reduction in fuel consumption under different scenarios.