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Traffic conflict points (e.g., intersections, work-zones) cause travel delay, stop-and-go traffic, and excessive energy consumption. Efforts have been taken to improve traffic conflict point performance via trajectory control of connected automated vehicles (CAV) as the CAV technology emerges. One major challenge to these efforts is the complexity in optimization of CAV trajectories, particularly with joint signal timing optimization. This challenge poses barriers to real-time application requirements, scaling them up to address network level problems and drawing analytical insights into problem structures. To overcome this challenge, this paper aims to seek for an efficient and analytical solution to a joint vehicle trajectory and signal timing optimization problem. This problem simultaneously optimizes CAV trajectories and signal timing to minimize travel delay and energy consumption at a conflicting point with two traffic …