Cancel-Run Frontiers for Delayed Trains Under Railway Performance Regimes

This study examines how small schedule buffers and overtaking permissions affect cancelor- run decisions for delayed trains under the Performance Regimes (PRs) applied in European countries. For a given primary delay (r0) and a remaining run time r, secondary delays caused to following services are computed. Primary and secondary delays are then mapped into PR-minute equivalents through country-specific thresholds, caps, and rates, and compared with a cancellation yardstick derived from path-cancellation rules. Four operational scenarios are assessed on identical timetables: (S1) no overtaking, no buffer; (S2) station overtaking, no buffer, (S3) no overtaking with sub-threshold buffer(s), and (S4) station overtaking combined with sub-threshold buffer(s). For each scenario, a strategy-conditioned frontier (θ) is obtained, as the smallest primary delay at which cancellation becomes cost-preferred to continuing. Outputs include per-country frontiers, a comparative strategy analysis identifying regions in where buffering or overtaking widens or shrinks the safe-to-run region. The framework separates timetable-propagation mechanics from policy parameters, enabling reproducible cross-country comparisons and actionable guidance without assuming operating-cost inputs. The processes are simulated using an original Python-based simplified timetabling software.