Applying Ollivier-Ricci curvature to indicate the mismatch of travel demand and supply in urban transit network

•The Ollivier-Ricci curvature in differential geometry for transit network optimization.•Dividing public transport supply and demand based on ORC and spatiotemporal big data.•A case study in Beijing compares ORC with traditional betweenness centrality. Urban transit networks need to be upgraded in accordance with urban development. While methods have been studied to design an optimal transit network given the locations of stations, these methods focus on the whole network as the optimization object. However, the strategy to improve parts of an existing transit network based on the gap between travel demand and infrastructure supply is rarely investigated. Different parts of the same network should not have the same priority to be upgraded. An evaluation method is required for this purpose to decide which parts of a transit network should be upgraded first. We argue that Ollivier-Ricci curvature, a concept from differential geometry, can serve as the evaluation method. The basic hypothesis is that Ollivier-Ricci curvature indicates the theoretical attractiveness of the fastest path between any two nodes, thereby capturing the internal structure of the transit network. Meanwhile, travel demand and behavior can be approximated by urban mobility big data. By comparing the theoretical attractiveness and the flow volume between a path between two stations, the traits of lines with mismatched supply and demand are identified, and macro strategies are suggested. A case study in Beijing demonstrates how the proposed method works out followed by a comparison with traditional betweenness centrality analysis.