Exploring the relationship between the spatial distribution of roads and universal pattern of travel-route efficiency in urban road networks

Abstract

Urban road networks are well-known to exhibit universal characteristics and scale-invariant patterns, despite the different geographical and historical contexts of cities. Previous studies on the universal characteristics of urban road networks have mostly focused on their network properties but have often ignored the spatial network structures. To address this research gap, we explore the underlying spatial patterns of road networks. We examine the travel-route efficiency in a given road network across 70 global cities, which provides information on the usage pattern and functionality of the road structure. The efficiency of travel routes is measured by analyzing the detour patterns, as determined by the detour index (DI). The DI is a long-standing popular measure, but its spatial pattern has been barely considered so far. In this study, we investigate the behavior of DI with respect to spatial variables by scanning the network radially from a city center. Through empirical analysis, we first discover universal properties in DI throughout most cities, which are summarized as a constant behavior of DI regardless of the radial position from a city center and a clear collapse into a single curve for DIs for various radii with respect to the angular distance. Especially the latter enables us to determine the scaling factor in the length scale. We further reveal that the universal pattern is induced by the center-periphery spatial structure of urban roads through the model study of an artificial road network. In addition to exploring the universality of DI, we delve into the specific characteristics of DI associated with the unique internal structure of individual cities. By visualizing the spatial DI network on city maps, we identify distinct city-specific DI characteristics. The case studies of selected cities demonstrate that our proposed method of spatial DI networks has the potential for practical implications in analyzing individual cities.