Hierarchy of urban road networks from a scaling law perspective

Abstract

The efficient functioning of cities largely relies on their road networks that manifest a rich hierarchical structure, ranging from the highest-level motorways all the way down to the lowest-level footways, much like the vascular networks found in living organisms. As an infrastructure-related indicator, road length theoretically scales sublinearly with the population size of the city, which indicate that roads need to be planned grows slower than the population. However, scaling relations between the length of roads at each hierarchical level and city size remain unclear, which is a crucial practical problem for urban planning. Attribute to collective efforts from millions of volunteers worldwide, detailed hierarchy labels for roads are available from OpenStreetMap, providing a unique opportunity to study this problem. Based on large-scale infrastructure data for more than 1000 cities in the United States and China, we unveil that the total length of roads at most hierarchical levels scales sublinearly with urban population, echoing the economy of scale. However, metro lines and footways are two prominent exceptions that surprisingly manifest a superlinear scaling relation with the population, which signifies a faster growth than the urban population and cannot be explained by current theories. Despite drastic differences in the composition of roads across hierarchies and their spatial connection patterns, it is intriguing that scaling behaviors are quite consistent across these two countries. Such nonlinear urban scaling laws suggest that, for infrastructure planning, using conventional road length per capita can be either biased towards large or small cities, depending on whether the scaling exponent is greater or less than one. Using deviations from urban scaling laws, termed as the scale-adjusted metropolitan indicator (SAMI), which takes off size effect, is a more objective evaluation for whether a city has a shortfall or excess provision of certain types of roads. Furthermore, based on SAMIs across road hierarchy, we identify four groups of cities in the US and three groups of cities in China with distinct average SAMI profiles. In addition, regression analysis further reveals that longer-than-expected residential roads and footways, indicated by positive SAMIs, can help alleviate traffic congestion. By contrast, a longer-than-expected secondary roads might exacerbate it. Our scaling analysis through the lens of hierarchy provides a more comprehensive understanding on the relation between city size and road networks, offering valuable insights for improved urban planning.