Predicting the future development scale of high-speed rail through the urban scaling law

High-speed rail (HSR) has become a significant mode of intercity travel due to its numerous socioeconomic and environmental benefits. Although some countries, such as China and Spain, have developed comprehensive HSR networks, many other nations are also investing or interested in developing their HSR infrastructure. However, concerns are arising about the high cost of HSR development and operation and whether the massive investment in HSR is justified. Furthermore, it remains unclear what HSR scale is appropriate to maintain travel demand and financial sustainability, considering the socioeconomic heterogeneity among different regions. To address this research gap, this study introduces a novel analytical framework that examines the relations between the scales of HSR and socioeconomic and demographic characteristics, including the size of the urban population, using 294 Chinese cities as an example. By applying the machine learning method based on the theory of urban scaling law, we find that the existing scale of HSR varies considerably among different tiers of cities. Although some large cities have underutilized the scale of the HSR systems in terms of service frequencies, platforms and rail lines, others have overutilized it, especially in terms of the building area of HSR stations in Tier-1 cities. In addition, by comparing the predicted scale changes of HSR in 2035 and 2050 with the actual system planning documents, we confirm that while some cities’ (i.e., Shanghai and Shenzhen) predicted outcomes of system’s scale are consistent with that of the actual civic HSR development plans, inconsistencies are also found in other cities, such as Yangzhou and Wuhan. Overall, the study provides valuable empirical evidence and implications for policymakers to improve decision-making on the future HSR scale and guidance for future development.