Table 2. This table displays the predicted theoretical behavior and the empirical observations versus the population size P for different quantities: Ltot is the daily total driven distance, A is the area of the city, LN is the total length of the road network, δτ is the daily total delay due to congestion, Qgas is the yearly total consumption of gasoline and
is the total CO2 emissions emitted yearly due to transportation. In the third (fourth) column, we show the predicted values of the exponent of P using the value of α (of a) measured on US data. In the fifth column, we show the value of the exponents directly measured on data about US and OECD cities. The measured values are in good agreement with the prediction. In particular, the exponents for LN and δτ are consistent with our prediction that their difference should be 1/2.
Predicted value of the exponents | ||||
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Quantity | Theoretical dependence on P in self-consistant case | self-consistent case | fitting case | Measured value |
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1 | 1 | 1.03 ± 0.03 (r2 = 0.95) |
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2δ = 0.64 | a = 0.85 | 0.853 ± 0.011 (r2 = 0.93)38,39,40 |
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0.765 ± 0.033 (r2 = 0.92)38,39,40 |
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1 + δ = 1.32 | 1.22 | 1.270 ± 0.067 (r2 = 0.97)38,39,40 |
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1 + δ = 1.32 | 1.22 | 1.262 ± 0.089 (r2 = 0.94)38,39,40 |
1.212 ± 0.098 (r2 = 0.83)41 | ||||
1.33 ± 0.0326 | ||||
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0.5 | 0.5 | 0.42 ± 0.02 (r2 = 0.83)38,39,40 |
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1 − δ = 0.68 | 1 − a/2 = 0.58 | 0.595 ± 0.026 (r2 = 0.90)38,39,40 |