A Scaling Law for Tours
To researchers who study human mobility, a tour is a chain of trips that starts and ends in the usual place of residence. A tour’s length is its number of intermediate stops. That simple definition can encompass suburban errands, tourist itineraries, and other circular outings. Now Xiao-Yong Yan of Beijing Jiaotong University and his collaborators have developed a model that can account for the distribution of tour lengths of thousands of individuals who used a phone app to plan and log trips in Los Angeles and New York [1]. The model could help urban planners site schools, shopping centers, and healthcare facilities more efficiently.
The trip data came from Foursquare, a location-based social network. Although the mean and variance of users’ tour lengths in Los Angeles and New York differed significantly, the distribution of lengths closely followed the same form: the product of a falling power law and a more steeply falling exponential. The shape reflects the tendency of individuals to disfavor long tours.
The model that Yan and his collaborators developed has three parameters: is the initial probability that an individual will terminate a tour after one trip, characterizes how the probability of termination decreases as the tour gets longer, and characterizes an individual’s propensity to explore new locations. Parameters and are determined from data. Parameter is determined by fitting the model to the data—provided that the model is a good fit. Yan and his collaborators found that the model did indeed reproduce the Foursquare data. It turned out that and govern the tour-length distribution and how spread out individuals’ movements are. Yan says that adjusting and through urban planning could lead to people taking fewer tours that include more stops, saving energy.
–Charles Day
Charles Day is a Senior Editor for Physics Magazine.
References
- X.-J. Lin et al., “Scaling law of individual urban tour behavior,” Phys. Rev. E 113, 034303 (2026).