Scaling of multiple functional facilities covering comprehensive processes in cities

Many urban features are found to follow the scaling relationship with population size (Y = alpha N beta). It has been found that the infrastructures scale 5/6 sublinearly with population size, and the commercial facilities scale superlinearly. However, there is a lack of systematic research on the scaling of different types of functional facilities covering comprehensive urban processes, and the mechanism explanation for scaling of functional facilities is rare. Using data from 523 cities, this work presents the studies of the scaling of 22 types of functional facilities, taking into account the socio-economic level of cities. Results show that: (1) the scaling exponent of infrastructures such as road areas is 5/6, that of facilities such as banks, telecom halls, and libraries is 8/9, and the waterworks and delivery outlets scale linearly; (2) the scaling exponent of commercial facilities such as fastfood restaurants, gyms, and machinery plants is positively correlated with their service capability, varying 6/ 5-7/5; (3) the insufficient supply makes the decomposition facilities deviate from the 5/6 sublinear scaling; (4) urbanization and economic development increase the scaling exponents of commercial facilities; (5) economic development has a negative correlation with scaling exponents of infrastructures.