Exploring urban travel routes' characteristics from a geometric perspective

Understanding routing behavior is essential for the design, implementation, and operation of a transportation system. Conventional transportation studies have paid great attention to discrete choice models which can quantify the relative influence of relevant attributes (e.g. travel time, travel distance, travelers' socioeconomic characteristics, etc.) However, these studies have been questioned because of their lack of real data to support and verify the conclusions. In recent years, with the development of mobile positioning technology, rich travel trajectory data are accessible, making it possible to mine travel routes' characteristics and rules from the data directly. In this paper, with the assistance of massive floating car data collected from three cities, we investigate characteristics of urban travel routes from a geometric perspective. We first define the number of heading directions that a traveler changes per kilometer in a trip as an index called geometric fragmentation to quantify routes' geometric characteristics, then find the statistical laws of routes' geometric fragmentations, and analyze their relationship with travel distances. Results indicate that: 1) travelers tend to choose less fragmentized routes. They most frequently change direction averagely once per 2.5 kilometer, and 76% of travel routes averagely change direction no more than once per kilometer; 2) routes with longer travel distances are less fragmentized, and the relationship between routes' geometric fragmentations and travel distances can be well approximated by a power function with a negative exponent; 3) The real routes' average geometric fragmentation is about 40% bigger than the fewest turns routes, and 40% smaller than the shortest length routes; 4) the above geometric characteristics of travel routes are irrelevant to the forms of urban road networks.