Tail reliability of metro bus bridging under spatially correlated road closures

Flood-induced metro disruption can disable rail service and replacement-bus corridors. We examine how spatial dependence in binary passability shapes the mean and lower tail of service from a fixed pre-event bus-bridging plan, and whether shortfalls arise from allocation or candidate-path disconnection. A vehicle-hour-constrained model is evaluated in a controlled stress test using the public Line 5 topology, constructed surface corridors, and nominal demand. At target closure probability 0.529, a distribution-informed plan served 44.59% of demand, compared with 38.80% for the best tested failure-blind rule using the same 540 vehicle-hours, leaving a 5.79-percentage-point matched-budget advantage. At target closure probability 0.35, increasing dependence length from 0 to 12 km raised mean service from 44.98% to 67.92%; bottom-decile service fell from 20.25% to zero. All four dependence kernels reproduced this divergence, with variation in magnitude. Increasing the training sample from 70 to 1,120 scenarios changed mean and bottom-decile service by 0.26 and 0.03 percentage points; no tested conditional value-at-risk (CVaR) weight produced a detectable tail improvement. Added destinations improved tail service; paired marginal gains fell from 22.17 to 0.50 points. After local calibration, the framework can help distinguish tail risk addressable through allocation from risk requiring additional reachable response options.