## 1 Introduction  
Cities represent the most efficient form of land use, often exhibiting high economic vitality, well-developed infrastructure, abundant public service resources, and a strong radiation effect. Therefore, cities in various countries continuously attract the inflow of migrant populations, leading to an expansion of the jurisdiction. Megacities with a population of 10 million or more and an area of over 10,000 square kilometers are increasingly emerging [1]. The continuous expansion of cities has been a historical characteristic over the past century, resulting in a distribution pattern of human civilization with megacities as hubs of politics, economy, and culture. The expansion of cities is also a trend in future development, which will induce the ongoing growth of existing megacities and the emergence of new ones [2]. Consequently, urban transportation infrastructure faces a severe challenge. Transportation infrastructure serves as a circulatory system, facilitating the internal flow of people and goods, as well as the internal and external exchange of materials among cities. Due to the influence of the geometric properties of the city, the marginal effect of newly built urban transportation infrastructure will be dramatically weakened as the area and population of the city expand to a certain extent [3]. This implies that to serve the same area and population, the mileage of transportation infrastructure in the newly extended fringe area of the city is much greater than that in the existing area of the city center. This phenomenon can be attributed to three primary causes. Firstly, the urban expansion area is far away from the urban geometric incenter, and longer transportation infrastructure is required to effectively connect with other areas [4]; secondly, the existing transportation infrastructure in the urban expansion area is relatively weak, and extensive supplementary construction is required to connect the existing transportation networks in megacities [5]; thirdly, the population in the expansion area is relatively dispersed, and a large amount of transportation infrastructure should be constructed to meet the transportation needs of the local population [6]. Due to diminishing marginal returns, the increase in transportation service capacity becomes smaller with each additional mile of similar infrastructure added in megacities. To maintain the function of megacities, the constructed mileage of transportation infrastructure worldwide has exhibited an almost geometric growth trend in recent decades. The transportation infrastructure requires significant costs for construction, operation, and maintenance. The construction, operation, and maintenance costs of transportation infrastructure remain high in megacities, which triggers the encroachment of expenditures on public services such as security, environment, education, and healthcare [7]. Currently, issues such as disordered public security, accumulated garbage, and high levels of homelessness are becoming common challenges for megacities worldwide. If the service capacity of transportation infrastructure can be effectively improved, and the construction, operation, and maintenance costs can be reduced, related expenses will be saved in megacities. If the expenses can be allocated properly, the security, environment, education, and public health of the city will be improved. The diminishing marginal effect of transportation infrastructure with the development of megacities can be effectively addressed through the coordinated planning of diverse transportation infrastructure [8]. Megacities can maximize the effectiveness of their transportation network by reasonably planning and integrating various types of infrastructure, such as municipal roads, subways, highways, expressways, railways, and high-speed railways. Passengers can take the subway to the train station, then board a train or high-speed train to their final destination. From there, they can transfer to a bus at a transit point to reach their final destination.