Optimization of Emergency Bus Bridging Service with Mixed Diesel–Electric Fleets under Metro Disruptions

Abstract

Metro service disruptions occur frequently in large cities, making emergency bus bridging services essential for maintaining network functionality and reducing passenger delays. With the rapid electrification of urban bus fleets, traditional bus bridging strategies face new challenges related to electric bus state-of-charge (SOC) limits and charging availability, which are often ignored in existing models. This study develops a mixed-fleet optimization framework for emergency bus bridging services that jointly considers diesel buses and electric buses (EBs). Two models are formulated: a standard feeder model (SFM) providing all-stop services, and a combined feeder model (CFM) that supplements standard feeders with limited-stop direct services to serve high-demand origin–destination (OD) pairs. Both models explicitly incorporate EB SOC constraints, charging requirements, and coordinated fleet deployment. A case study based on the December 2023 rear-end collision on the Beijing Subway Changping Line demonstrates that both models can generate feasible emergency response plans under realistic operational and charging constraints. Compared with the SFM, the CFM reduces total system cost from RMB 76,802.99 to 76,752.93. This improvement is driven by a reduction of RMB 322.98 in passenger delay cost, which outweighs an increase of RMB 272.93 in operator cost. Sensitivity analyses are further conducted to evaluate model performance under varying demand patterns, disruption durations, direct-service capacities, and charger availabilities. Results indicate that the CFM performs best under concentrated demand, long-distance trips, and moderate disruption durations, highlighting its effectiveness in reducing passenger delays for high-impact OD flows.