Optimizing Bus Bridging Service Considering Passenger Transfer and Reneging Behavior

This paper addresses the design of bus bridging services in response to urban rail disruption, which plays a critical role in enhancing the resilience and sustainability of urban transportation systems. Specifically, it focuses on unplanned urban rail disruptions that result in temporary closure of line sections, including transfer stations. Under this “transfer scenario”, a heuristic-rule based method is firstly presented to generate candidate bus bridging routes. Non-parallel bridging routes are introduced to facilitate transfer passengers affected by the disruption. Meanwhile, the bridging stops visited by parallel routes are extended beyond the disrupted section, mitigating passenger congestion and bus bunching at turnover stations. Then, we propose an integrated optimization model that collaboratively addresses bus route selection and vehicle deployment issues. Capturing passenger reneging behavior, the model aims to maximize the number of served passengers with tolerable waiting times and minimize total passenger waiting times. A two-stage genetic algorithm is developed to solve the model, which incorporates a multi-agent simulation method to demonstrate dynamic passenger and bus flow within a time–space network. Finally, a case study is conducted to validate the effectiveness of the proposed methods. Sensitivity analyses are performed to explore the impacts of fleet size and route diversity on the overall bridging performance. The results offer valuable insights for transit agencies in designing bus bridging services under transfer scenarios, supporting sustainable urban mobility by promoting efficient public transit solutions that mitigate the social impacts of sudden service disruptions.