  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 (OD) 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 in rush hours compared to non-rush hours...
