Supplementary material from "Cohesive urban bicycle infrastructure design through optimal transport routing in multilayer networks"

Bicycle infrastructure networks must meet the needs of cyclists to position cycling as a viable transportation choice in cities. In particular, protected infrastructure should be planned cohesively for the whole city and spacious enough to accommodate all cyclists safely and prevent cyclist congestion -- a common problem in cycling cities like Copenhagen. Here, we devise an adaptive method for optimal bicycle network design and for evaluating congestion criticalities on bicycle paths. The method goes beyond static network measures, using computationally efficient adaptation rules inspired by Optimal Transport on the dynamically updating multilayer network of roads and protected bicycle lanes. Street capacities and cyclist flows reciprocally control each other to optimally accommodate cyclists on streets with one control parameter that dictates the preference of bicycle infrastructure over roads. Applying our method to Copenhagen confirms that the city's bicycle network is generally well-developed. However, we are able to identify the network's bottlenecks, and we find, at a finer scale, disparities in network accessibility and criticalities between different neighborhoods. Our model and results are generalizable beyond this particular case study to serve as a scalable and versatile tool for aiding urban planners in designing cycling-friendly cities.