Optimizing the geometry of transportation networks in the presence of congestion

Urban transport systems are gaining in importance, as an increasing share of the global population lives in cities and mobility-based carbon emissions must be reduced to mitigate climate change and improve air quality and citizens' health. As a result, public transport systems are prone to congestion, raising the question of how to optimize them to cope with this challenge. In this paper, we analyze the optimal design of urban transport networks to minimize the average travel time in monocentric as well as in polycentric cities. We suggest an elementary model for congestion and introduce a numerical method to determine the optimal shape among a set of predefined geometries considering different models for the behavior of individual travelers. We map out the optimal shape of fundamental network geometries with a focus on the impact of congestion.