Integrated optimization of train routing and timetable of rail transit network with time-varying passenger demand

Urban rail transit is operated with network scenario mostly. Train routing determines spatial service range on the network, which will affect whether passengers transfer during the trip. Timetable determines arrival and departure time of each train at each station. To achieve balance between demand and supply and enhance service quality, simultaneous optimization of train routing and timetable is of significant importance for rail companies with the network. This will reduce the waiting time of passengers effectively, and the stations where train serve will be convenient for most passengers. However, existing studies in train operation planning with time-varying passenger demand haven’t addressed this aspect adequately. To bridge this gap, we develop an integrated optimization model for the Train Routing and Timetable Problem (TRTP) within a rail transit network, considering the dynamic of passenger demand and passenger path choice. Our objective is to minimize the operating costs for companies and to reduce the total waiting time experienced by passengers. The constrains of TRTP include time constraint, path constraint and train constraint. What’s more, the compatibility of headways on different routings is the focus when modeling. To verify the effectiveness of our proposed model, we conduct a numerical experiment with CPLEX. After that, the results of integrated optimization and staged optimization are compared to show the beneficial of integration with train routing and timetable. Moreover, we devise an algorithm tailored to this problem to solve the model, and a network case study is presented. As a case study, we apply the model to Guangzhou Metro Line 3 to validate its performance further, which is a Y-type line, the most common example of operation with network of urban rail transit in China. The results of our study demonstrate that the proposed integrated optimization model can achieve a reduction in operating costs and total waiting time for passengers effectively, providing convenience for passenger travel.