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Figure 1 | EPJ Data Science

Figure 1

From: Traveling heterogeneity in public transportation

Figure 1

Model and processing of bus travel data. (a) Conceptual representation of the trajectories of a trip performed by a bus. On the route, in relation to the original data, the variation of time (Δt) and distance (Δs) between each consecutive GPS point is illustrated. (b) The same path in (a) is shown, however, it is divided into constant lengths (\(\Delta s^{*}\)) and the new time values (\(\Delta t^{*}\)) between each constant length are calculated from a linear interpolation. (c) The Lorenz curve \(L(s)\) generated artificially to follows the Pareto Principle is illustrated. This curve is constructed by performing the cumulative sum of the constant distances (\(\Delta s^{*}\)) all divided by total length on the x-axis. On the y-axis we have the cumulative sum of the descending order time values (\(\Delta t^{*}\)) normalized by the total time. The function \(y=x\) (dashed line) is the equality line \(E(s)\) and two times the area defined between the Lorenz curve and the equality line is numerically equal to the Gini coefficient. The Gini value accounts for the heterogeneity of travel times distribution. The continuous vertical line points to the 80/20 ratio of the Pareto Principle

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