Fig. 4: Variation of energy efficiency estimates of transport operations over density.

a Metro operations. b Private vehicular travel. This figure consists of two panels comparing the elasticity of unit energy consumption with respect to output for two modes of urban transport: metro operations and private vehicular travel. Elasticity is defined as the percentage change in energy use per passenger-kilometre resulting from a one percent change in total output, measured in million passenger-kilometres. Negative values indicate energy efficiency improvements as output increases. a (distinct coloured lines with shaded regions) presents elasticity estimates for metro operations, disaggregated by network size. Three separate curves are shown, corresponding to small, medium, and large networks, defined using the lower quartile, median, and upper quartile of the network length distribution, respectively. The curves are generated from model-based simulations using a flexible translog specification, with 95% confidence bands displayed as shaded ribbons. All three curves remain negative across the full range of operational density, indicating that increases in output lead to reductions in unit energy consumption. However, the curves rise with density, suggesting that the magnitude of efficiency gains declines as usage increases. The flattening of the curves at high densities points to a tendency toward constant energy intensity in heavily used systems. Notably, larger networks exhibit less negative elasticity values, that is, smaller energy efficiency gains, possibly reflecting operational complexity or scale-related inefficiencies. b (overlapping coloured lines with shaded region) presents the corresponding analysis for private vehicular travel. Unlike the metro case, only a single curve appears to emerge, as disaggregation by network size yielded no meaningful variation. In contrast to metro systems, the elasticity curve remains statistically not different from zero across the density range. This suggests that road-based private vehicle operations do not exhibit gains from densification, that is, higher utilisation is associated with declining energy performance, and network size has no discernible effect on these estimates. Overall, these visualisations highlight a key contrast between transport modes. While metro systems benefit from densification, particularly smaller networks, private vehicular travel displays diseconomies of density, with increased usage associated with similar levels of unit energy consumption. The figure underscores the differing energy efficiency dynamics of infrastructure-fixed versus demand-responsive transport systems in urban contexts.