Fig 1.
(a) For a given agent located at a random location x, there is no subway station located at a distance less than d0 with probability 1 − p (in the data used here d0 = 1km). In this case the journey to work located at the central business district (CBD) is made by car (dashed line). (b) With probability p there is a subway station in the neighborhood of x and the agent has to compare the cost Gcar of car (dashed line) and the cost GMRT of MRT (the trip is depicted by the red line) in order to choose the less costly transportation mode to go to the CBD.
Fig 2.
The most advantageous mode of transport depends on the value of time of individuals and the distance to the urban center.
The limit between the two areas evolves with congestion: the larger the traffic (curves from blue to green) and the larger the area in which rapid transit is beneficial compared to car driving. The grey solid vertical line corresponds to the size of the urban area and indicates the critical value of time (dashed red line) below which rapid transit is advantageous in the whole agglomeration whatever the value of congestion. The values of the parameters are chosen here as: Cc = 15 $, vc = 40 km/h, vm = 30 km/h, f = 30 minutes (see Material and methods for a precise description of all data).
Fig 3.
Comparison between the observed car modal share T/P and the share of population p living near rapid transit stations (less than 1 km) for 25 metropolitan areas in the world.
The red line is the prediction of our model (R2 = 0.69). Given the absence of any tunable parameter the agreement is satisfactorily, and discrepancies are probably mostly due to the existence of other modes of transport (walking or cycling), lower car ownership rates, or a higher cost of the MRT, etc.
Fig 4.
Comparison between the annual transport-related CO2 emissions per capita and the effects of congestion, area size and rapid transit density predicted by our model.
The red line is the linear fit of the predicted form y = αx where α ≈ 0.064 CO2tons/km/hab/year (the Pearson coefficient is 0.79). We had no congestion estimate for Seoul and Tokyo and we used an average congestion rate τ = 50%. The error bars are computed for a typical error of 10% on p and τ.
Fig 5.
Average commuting time measured for different cities versus the predicted value of our model (Eq 18).
We perform the fit on the single parameter g using Eq 18, leading to an average value g ≈ 0.203 (the Pearson correlation is here 0.65). The existence of large fluctuations around our prediction is probably connected to the spatial organization of the city and the structure of the transportation networks.