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 $T_c^{\mathrm{FW}}\sim {10}^4$ commuters, we observe the emergence of a urban freeway. The second threshold is larger and on the order $T_c^{\mathrm{RR}}\sim {10}^5$ 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.

Figure 1

(a) Example of Tucson (Arizona, USA, $540000$ inhabitants in 2020), an urban area with two urban freeways (green lines). (b) Example of Charlotte (North Carolina, USA, $860000$ inhabitants in 2020), an urban area with a ring road (red line) and several urban freeways (green lines). Latitude and longitude are in degrees.

Figure 2

(a) Fraction of U.S. urban areas with a urban freeway vs its number of commuters at the time of construction. Urban freeways appeared in urban areas with more than ${10}^4$ commuters. (b) Fraction of U.S. urban areas with a ring road vs the number of commuters at the time of construction. Ring roads appeared in urban areas with more than ${10}^5$ commuters. The error bars correspond to the uncertainties on the number of commuters in 1960.

Figure 3

One-dimensional model of a city of size $2R$. (a) We first consider the case where a city has two possible choices: to build either a urban freeway of size $2(R-L)$ or a ring road of length $2g(R-L)$. (b) We then consider the possibility of adding a ring road between points $\ell$ and $2R-\ell$ to a city which has already a freeway. The corresponding cost difference is $\mathrm{\Delta }{C}^{\mathrm{RR}}$. (c) Finally, we show the possibility of removing the urban freeway between $\ell$ and $2R-\ell$. The corresponding cost is $\mathrm{\Delta }{C}^{\mathrm{SC}}$.

Figure 4

Cost per road user for the construction of different infrastructures, as a function of the traffic demand (i.e., the number of car commuters).

Figure 5

Value per km of urban freeway for different external costs and critical value above which the freeway removal is economically sensible. We used values computed for the city of Seoul for estimating the land value cost (see text). The red surface (defined by ${\epsilon }^{\prime }>{\epsilon }_c$; the red line is above the critical green line) shows cities which typically have a urban freeway (population $>100000$) and would benefit to remove it (population $<1400000$).

Figure 6

Summary of the evolution of urban infrastructure (shown here in blue) when the population grows (the darker the denser) implying a growth of the number of commuters $T$. In the 1960s, urban freeways were built through city centers, followed shortly after by ring roads around the urban areas. Taking into account the detrimental aspects of urban freeways, cities tend to remove their urban freeways.