Path-choice-constrained bus bridging design under urban rail transit disruptions

Although urban rail transit systems play a crucial role in urban mobility, they frequently suffer from unexpected disruptions due to power loss, severe weather, equipment failure, and other factors that cause significant disruptions in passenger travel and, in turn, socioeconomic losses. To alleviate the inconvenience of affected passengers, bus bridging services are often provided when rail service has been suspended. Prior research has yielded various methodologies for effective bus bridging services; however, they are mainly based on the strong assumption that passengers must follow predetermined bus bridging routes. Less attention is paid to passengers’ path choice behaviors, which could affect the performance of the bus bridging services deployed. In this paper, we specifically take passengers’ path choice behaviors into account and address the bus bridging optimization problem under urban rail transit disruptions. Incorporating a PS-logit model to estimate the probabilities of passenger path choices, we propose a mixed-integer nonlinear programming model to simultaneously determine the selection of bus bridging routes and vehicle deployment on selected bridging routes, with the objective of minimizing the cost associated with passenger travel time and unsatisfied demand. To solve this computationally challenging large-scale nonlinear model, we design a customized variable neighborhood search algorithm framework. A case study based on the Shanghai rail transit system is conducted to demonstrate the applicability and feasibility of the proposed approach. The results indicate that our approach can provide an effective bus bridging scheme that considers passenger path choice, which facilitates rapid response to rail disruptions. Our scheme substantially outperforms the current bridging designs that do not consider passenger path choice behaviors by significantly reducing the number of unserved passengers.