Optimising timing points for effective automatic train operation

Automatic Train Operation (ATO) aims to partially or fully automate train driving, enhancing railway capacity, punctuality, and energy efficiency. However, a key challenge arises from the mismatch between discrete event-time decisions at the Traffic Management System (TMS) level, assuming fixed running times, and the continuous speed–distance trajectory optimisation at the ATO level, leading to possible misalignments between planned and executed train movements. To bridge this gap, this paper introduces a novel optimisation-based method that dynamically computes Train Path Envelopes (TPEs) based on multiple driving strategies, defined as time targets or windows over a sequence of timing points, which ATO-equipped trains must comply with to align their movements with traffic management constraints. The method follows a two-stage approach: First, a linear programming model determines conflict-free blocking time ranges across the multiple driving strategies. Second, a structured optimisation process establishes operationally feasible TPEs by determining departure tolerances and configuring intermediate timing points. By integrating a critical-block strategy, the optimised TPEs provide the flexibility needed for ATO while accommodating variations in train driving strategies. The method is validated through experiments and a real-life case study in The Netherlands, demonstrating that optimised timing points at critical track locations improve energy efficiency, enhance punctuality, increase capacity, and provide an approach to align traffic management with ATO.