Spatial properties of congestion in street networks: a geometric version of Braess's paradox

Abstract: Streets networks are the primary facilitators of movement in urban systems, allowing residents to navigate the different functional components of a city. Since navigability is a key ingredient of socioeconomic activity, roads represent one of its most important infrastructural components and a large body of work has elucidated its structural properties.  One such important metric, intricately related to the flow of people and goods and services, is the betweenness centrality. The betweenness centrality, a path-based global measure of flow, is a static predictor of congestion and load on networks. We demonstrate that its statistical distribution is invariant for any street network in any city irrespective of topography, geography or urban planning choices. This invariance is a consequence of spatial embedding of the street network in a 2D plane leading to an underlying tree structure for high betweenness nodes that controls the majority of the flow. Furthermore, these high congestion streets display increasing spatial correlation as a function of the increasing density of streets. Counterintuitively building more streets does not alleviate congestion but diverts it further to the city center. This hints at a geometric flavor for the well-known Braess's paradox from transportation theory. Urban policy planners are thus better served in investing in multimodal transportation systems and innovative policies such as congestion pricing, than merely building more “traditional” connectivity. We confirm our analysis through empirical results on street networks from 97 cities worldwide as well as 200 years of street data for Paris.

Time permitting, I shall also discuss our ongoing collaboration with Google AI where we study global mobility flows at high resolution. Initial results include a surprisingly rich signature of urban indicators such as pollution, health, and transportation as a function of the spatial structure of intra-city flows.