Figure 5

Characterization of the distribution times of bus route 650I. (a) The time series (\(\Delta t^{*}\)) for five different trips of the bus route 650I shown in a logarithmic color scale. The largest values of \(\Delta t^{*}\) are approximately concentrated in the same regions. (b) The distribution of the values \(\Delta t^{*}\) for the same five trips are illustrated in logarithmic scale. We performed a power–law fitting for each distribution. We see that each trip has a different value for the power–law exponent α. The dashed lines are a visual guide with slope −3.0 and −2.0. In (c) we have the relation between the α exponent and the total time that the bus used to finish the scheduled trajectory. Each point represents a trip of line 650I and the dashed line represents the average behavior obtained from the Nadaraya–Watson regression. The large values of time trips for low values of α corroborates the correlation between Gini and time delay D (Fig. 4(b)), since distributions with \(\alpha \to 2.0\) must have Gini close to 1.0