Similarity and economy of scale in urban transportation networks and optimal transport-based infrastructures

Designing and optimizing the structure of urban transportation networks is challenging. This study proposes a method inspired by optimal transport theory and the principle of economy of scale that requires little input information to generate networks similar to public transportation infrastructures. Unlike standard approaches, it does not assume an initial backbone network; instead, it extracts the network directly from a continuous 2D space using only a few origin and destination points, generating networks from scratch. Analyzing a set of urban train, tram and subway networks, we find a noteworthy degree of similarity in several cases between simulated and real infrastructures. By tuning a single parameter β, the method can reproduce a range of subway, tram and train networks and suggest potential improvements in transportation properties. The algorithm’s outputs naturally provide a principled quantitative measure of similarity between two networks, enabling automatic selection of similar simulated networks. We empirically validate that urban transportation systems can exhibit network topologies consistent with optimal transport-based optimality principles, as also observed in biological systems. By adapting a classical optimal transport framework to realistic travel demand settings with minimal inputs, we model network structures and compare them with real data across multiple cities. We observe that the optimal networks obtained with our approach often show similar cost and performance to those observed in real systems.