An SD-LV Calculation Model for the Scale of the Urban Rail Transit Network

The planning for the scale of the urban rail transit network (URTN) is one of the key tasks of URTN planning. The scale should match the urban development (UD). A reasonable scale can improve travel efficiency, increase economic activities, and promote UD, while an unreasonable scale may consume more urban resources, fail to meet urban transportation demands, and even inhibit UD. Currently, the URTN scale is primarily determined by qualitative analyses and static indicators, which leads to the scale does not match UD perfectly. To determine a reasonable scale, a System Dynamics–Lotka–Volterra (SD-LV) model is constructed. The SD model is adopted to simulate the dynamic interaction between the URT and UD. The LV (Lotka–Volterra) model is employed to calculate the scale, in which the mutualism coefficients are proposed to characterize the mutualistic relationships between the URT and UD. The model is validated by using a dataset of the Beijing URTN from 2017 to 2021. The simulation errors of the URTN scale range from −4.3% to 1.32%, which demonstrates the robustness and effectiveness of the proposed model. The study offers quantitative theoretical insights for determining the reasonable scale of the URTN.