Scaling of spatio-temporal variations of taxi travel routes

The importance of understanding human mobility patterns has led many studies to examine their spatial-temporal scaling laws. These studies mainly reveal that human travel can be highly non-homogeneous with power-law scaling distributions of distances and times. However, investigating and quantifying the extent of variability in time and space when traveling the same air distance has not been addressed so far. Using taxi data from five large cities, we focus on several novel measures of distance and time to explore the spatio-temporal variations of taxi travel routes relative to their typical routes during peak and nonpeak periods. To compare all trips using a single measure, we calculate the distributions of the ratios between actual travel distances and the average travel distance as well as between actual travel times and the average travel time for all origin destinations during peak and nonpeak periods. In this way, we measure the scaling of the distribution of all single trip paths with respect to their mean trip path. Our results surprisingly demonstrate very broad distributions for both the distance ratio and time ratio, characterized by a long-tail power-law distribution. Moreover, all analyzed cities have larger exponents in peak hours than in nonpeak hours. We suggest that the interesting results of shorter trip lengths and times, characterized by larger exponents during rush hours, are due to the higher availability of travelers during rush hours. Thus, drivers are more motivated to shorten their trips in order to take new passengers in rush hours compared to non-rush hours. We also find a high correlation between distances and times, and the correlation is lower during peak hours than during nonpeak hours. The reduced correlations can be understood as follows. Due to the high availability of passengers in peak periods more drivers choose long distances to save time compared to nonpeak periods. Furthermore, we employed an indeterminate traffic assignment model, which supports our finding of the power-law distribution of the distance ratio and time ratio for human mobility. Our results can help to assess traffic conditions within cities and provide guidance for urban traffic management.