Figure 4

Gini coefficient by time of day and delay. (a) The variation of the Gini coefficient with time during the day. The continuous lines (blue for Fortaleza and red for Dublin) represent the average Gini (\(\mu_{\mathrm {gini}}\)) for bins equally spaced for all trips of the workdays of a week in Fortaleza and Dublin. The shaded area around the average represents \(\mu_{\mathrm {gini}} \pm \sigma_{\mathrm {gini}}\), in which \(\sigma_{\mathrm {gini}}\) is the standard deviation of the Gini for bins equally spaced. The plot corroborates the expectation that the largest values of Gini are in the rush hours. (b) The correlation between Gini coefficient and fraction of time delay for Fortaleza. Each point represents a trip and for each one a delay value D is calculated. The D measures the deviation of the expected value for the total time of that bus trip. The continuous line represents the Nadaraya–Watson non-parametric regression and the dashed line is the linear regression. The linear regression shows a relation of \(G = 0.38 + 0.24*D\) and the inset is the distribution of travel delay values. (c) The same correlation as (b) for Dublin. The linear regression shows a relation of \(G = 0.44 + 0.13*D\) and the inset is the distribution of travel delay values