Scaling of variations in traveling distances and times of taxi routes

TL;DR

This study analyzes the variability in taxi travel distances and times across five cities, revealing broad power-law distributions and differences between peak and nonpeak periods, highlighting the complexity of human mobility patterns.

Contribution

It introduces novel measures of trip variability and quantifies the scaling laws of travel distances and times relative to average routes during different periods.

Findings

Broad power-law distributions of distance and time ratios.

Higher exponents in peak hours indicating more variability.

Shorter trips with larger exponents during rush hours.

Abstract

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...