Understanding individual routing behaviour

Abstract

Knowing how individuals move between places is fundamental to advance our understanding of human mobility (González et al. 2008 Nature 453, 779-782. (doi:10.1038/nature06958)), improve our urban infrastructure (Prato 2009 J. Choice Model. 2, 65-100. (doi:10.1016/S1755-5345(13)70005-8)) and drive the development of transportation systems. Current route-choice models that are used in transportation planning are based on the widely accepted assumption that people follow the minimum cost path (Wardrop 1952 Proc. Inst. Civ. Eng. 1, 325-362. (doi:10.1680/ipeds.1952.11362)), despite little empirical support. Fine-grained location traces collected by smart devices give us today an unprecedented opportunity to learn how citizens organize their travel plans into a set of routes, and how similar behaviour patterns emerge among distinct individual choices. Here we study 92 419 anonymized GPS trajectories describing the movement of personal cars over an 18-month period. We group user trips by origin-destination and we find that most drivers use a small number of routes for their routine journeys, and tend to have a preferred route for frequent trips. In contrast to the cost minimization assumption, we also find that a significant fraction of drivers' routes are not optimal. We present a spatial probability distribution that bounds the route selection space within an ellipse, having the origin and the destination as focal points, characterized by high eccentricity independent of the scale. While individual routing choices are not captured by path optimization, their spatial bounds are similar, even for trips performed by distinct individuals and at various scales. These basic discoveries can inform realistic route-choice models that are not based on optimization, having an impact on several applications, such as infrastructure planning, routing recommendation systems and new mobility solutions.

Keywords: city science; complex systems; human mobility; transportation.

Figure 1.

From trajectories to route choices. (a) A sample of the trajectories analysed from the four cities, shown in grey, outline their urban road networks. Coloured trajectories spanning between the same pair of points represent seven routine trips. In each routine trip, a coloured line represents a distinct route choice. (b) A set of trajectories belonging to a car. Each trajectory starts at the circle marker and ends at a square marker. (c) By clustering the endpoints of the trips, we find three significant places. Two routine trips are shown with a solid black arrow. (d) We finally discover, for each routine trip, the different route choices performed by the driver. In this example one routine trip has three route choices (purple, green, red), the other has two (cyan, orange). (Online version in colour.)

Figure 2.

Individual patterns of route choice. (a) The distribution of the number of routes used for a routine trip. For most routine trips this number is low, despite the fact that these trips span over a period of up to 18 months. The markers show the empirical histograms about routine trips grouped by city. The solid curve shows the best lognormal fit, obtained on aggregated data generated in all four cities. (b) The probability density distribution of number of trips performed in a routine trip; the solid line is a kernel density estimation. (b,d,e) Share the axes and are on the same scale. (c) Maximum point distance between the optimal route r_opt, as suggested by the online routing service, and the favourite user route r_usr. For the other three curves, we consider all the alternative routes returned by the service and all the routes ever used by the driver, choosing for each element the route that deviates the least from its counterpart, respectively and Notably, 34% of the routes chosen are not any of the shortest paths and over 53% of the preferred routes are not optimal. (d) The number of trips performed during a routine journey versus the normalized Gini coefficient related to how many times each route choice is used. The two quantities show a weak correlation (Pearson's r = 0.48, p = 4.2e–255). The more a driver travels between two locations, the more likely it is for them to have a route of preference. (e) The probability density distribution of the normalized Gini coefficient G_n; the solid line shows a kernel density estimation. (Online version in colour.)

Figure 3.

The boundaries of human routes. Coordinates are projected to a cartesian coordinate system using the spatial reference system EPSG:2062. Each trajectory (x, y) is roto-translated and scaled into so that the source and destination of each trip are (0, 0) and (1, 0), respectively. (a) A 1% random sample of the trips, shown as partially transparent lines connecting consecutive positions. (b) The probability density function of the trajectory positions during a journey. Significant detours in all directions are uncommon but not unheard of. (c) Ninety-five per cent of the positions are within the region shown in the figure. The figure shows a sample trajectory, as a dotted line, the ellipse that fully contains it, as a dashed line, the focal distance as a dash-dot line and the major axis as a solid line. (d) The probability density function of the eccentricity of the ellipse containing each trip, shown as a solid blue line, and for comparison, the same quantity measured for the optimal trips, shown as a dashed green line. While both groups of trajectories are characterized by high-eccentricity, optimal trips are slightly less eccentric than actual user trips, suggesting that the former deviate slightly more from the ideal origin-destination straight line. (Online version in colour.)