Validating Express Rail Optimization with AFC and Backcasting: A Bi-Level Operations–Assignment Model to Improve Speed and Accessibility Along the Gyeongin Corridor

This study develops an integrated bi-level operations–assignment model to optimise express service on the Gyeongin Line, a core corridor connecting Seoul and Incheon. The upper level jointly selects express stops and time-of-day headways under coverage constraints—a minimum share of key stations and a maximum inter-stop spacing—while the lower level assigns passengers under user equilibrium using a generalised time function that incorporates in-vehicle time, 0.5× headway wait, walking and transfers, and crowding-sensitive dwell times. Undergrounding and alignment straightening are incorporated into segment run-time functions, enabling the co-design of infrastructure and operations. Using automatic-fare-collection-calibrated origin–destination matrices, seat-occupancy records, and station-area population grids, we evaluate five rail scenarios and one intermodal extension. The results indicate substantial system-wide gains: peak average door-to-door times fall by approximately 44–46% in the AM (07:00–09:00) and 30–38% in the PM (17:30–19:30) for rail-only options, and by up to 55% with the intermodal extension. Kernel density estimation (KDE) and cumulative distribution function (CDF) analyses show a leftward shift and tail compression (median −8.7 min; 90th percentile (P90) −11.2 min; ≤45 min share: 0.0% → 47.2%; ≤60 min: 59.7% → 87.9%). The 45-min isochrone expands by ≈12% (an additional 0.21 million residents), while the 60-min reach newly covers Incheon Jung-gu and Songdo. Backcasting against observed express/local ratios yields deviations near the ±10% band (PM one comparator within and one slightly above), and the Kolmogorov–Smirnov (KS) statistic and Mann–Whitney (MW) test results confirm significant post-implementation shifts. The most cost-effective near-term package combines mixed stopping with modest alignment and capacity upgrades and time-differentiated headways; the intermodal express–transfer scheme offers a feasible long-term upper bound. The methodology is fully transparent through provision of pseudocode, explicit convergence criteria, and all hyperparameter settings. We also report SDG-aligned indicators—traction energy and CO₂-equivalent (CO₂-eq) per passenger-kilometre, and jobs reachable within 45- and 60-min isochrones—providing indicative yet robust evidence consistent with SDG 9, 11, and 13.