Evolution of road infrastructure in large urban areas

Most cities in the United States and around the world were organized around car traffic. In particular, large structures such as urban freeways or ring roads were built for reducing car traffic congestion. With the evolution of public transportation and working conditions, the future of these structures and the organization of large urban areas is uncertain. Here we analyze empirical data for U.S. urban areas and show that they display two transitions at different thresholds. For the first threshold of order T_{c}^{FW}∼10^{4} commuters, we observe the emergence of a urban freeway. The second threshold is larger and on the order T_{c}^{RR}∼10^{5} commuters above which a ring road emerges. In order to understand these empirical results, we propose a simple model based on a cost-benefit analysis which relies on the balance between construction and maintenance costs of infrastructures and the trip duration decrease (including the effect of congestion). This model indeed predicts such transitions and allows us to compute explicitly the commuter thresholds in terms of critical parameters such as the average value of time, average capacity of roads, and typical construction cost. Furthermore, this analysis allows us to discuss possible scenarios for the future evolution of these structures. In particular, we show that because of the externalities associated with freeways (pollution, health costs, etc.), it might become economically justified to remove urban freeways. This type of information is particularly useful at a time when many cities are confronted with the dilemma of renovating these aging structures or converting them into other uses.