Optimization of Bridging Bus Timetable and Vehicle Scheduling under URT Disruption

After the occurrence of a disruptive event in an urban rail transit (URT) network, passengers' travel is affected, and a large number of passengers are stranded in the stations. These stranded passengers have to be evacuated urgently. With its flexible deployment, a bus bridging service has become an effective solution to evacuate stranded passengers. In order to avoid large passenger flow at stations, in addition to evacuating the static passenger flow stranded at the disrupted stations, the bridging buses need to focus on the dynamic passenger flow arriving at the turnover stations along the short-turning trains. In this paper, we propose a mathematical model to optimize the timetable and vehicle scheduling of bridging buses considering the adjustment of rail transit operations. The model aims to minimize passenger waiting time, the number of lost passengers, and the amount of bridging buses used. The model makes buses operate flexibly on different routes, taking the bus capacity and number of buses into account. By creating an improved ε-constraint method, the Pareto front of the problem is solved using the model with a commercial solver. Finally, the accuracy and validity of the model is verified by applying an example based on China's Hangzhou rail transit line 4. The results show that the bridging bus timetable and scheduling plan generated by the model effectively solved the problem of large passenger flow at turnover stations. In addition, compared with bridging buses with an even headway timetable, the results demonstrate that bridging buses with an uneven headway timetable, which considers coordination with rail transit, could reduce the passenger waiting time and the number of lost passengers. The model has better performance with an uneven headway timetable in the face of large passenger demand. The computational experiment shows that the total passenger waiting time and the number of bridging buses was reduced when the bus capacity was increased. However, the effect on passenger waiting time and the number of lost passengers was limited when the number of buses available at bus depots was increased.