Sensitivity of Train Path Envelopes for Automatic Train Operation

Automatic Train Operation (ATO) aims to enhance punctuality, energy efficiency, and reliability by automating driving tasks. Specifically, for mainline railways, an ATO onboard component generates and tracks optimised train trajectories based on time targets or windows at critical network locations, known as timing points, across train routes. These timing points and their associated constraints are specified in the Train Path Envelope (TPE), computed to ensure conflict-free operations. The generation of TPEs relies on dynamic updates of the real-time traffic plan from the Traffic Management System and real-time train statuses (e.g., position and speed). Understanding how TPEs are affected by these updates is essential for effective ATO deployment. To address this, this paper proposes a sensitivity analysis using elementary effects of a TPE generation algorithm, evaluating its response to variations in real-time traffic plans and train status updates. A real-life case study on a Dutch rail corridor with heterogeneous traffic reveals that control timing points can be introduced into the TPE as headways decrease, to homogenise traffic by aligning speed profiles and thus resolving conflicts. Timing point locations remain mostly unchanged, while their associated time windows become more sensitive when placed further along the route. Operational tolerance, which defines the latest conflict-free passing time, becomes more sensitive to headway changes and the distance from the previous stop.