When you go out to run errands on the weekend, you’re on a “tour” as defined by human mobility researchers. Same if you book a guided tour of a famous city or take a trip on a cruise boat that reaches multiple ports. A characteristic of such tours is that you begin and end up in the same place and take intermediate stops along the way. The number of stops is the tour’s “length.”
New model maps how people move
Now researchers from Beijing Jiaotong University in China have developed a model that describes the distribution of tour lengths for thousands of users of the Foursquare location-based social network. Their work is published in Physical Review E.
Modeling the patterns of human mobility is important in fields such as urban planning, animal foraging, transportation engineering and freight transportation. In the field of public health, movement of people is the primary driver of infectious disease, daily commuting patterns shape flu transmission in metropolitan areas, and, as COVID-19 showed, air travel determines how quickly a novel pathogen reaches continents.
Much about human mobility is already known from empirical studies, such as the frequencies of location visits obeying Zipf’s law, and the distinct number of locations visited over time following Heaps’ law.
Digging into Foursquare tour data
To go deeper, Xiao-Yong Yan and his colleagues—three altogether from Beijing Jiaotong University and one from the University of Leeds in the UK—used Foursquare users’ check-in records in New York and Los Angeles. Foursquare is a local search-and-discovery mobile app for those out running errands, exploring a city or out on the town.
In total, the researchers used data from trips in Los Angeles and New York City that totaled 255,204 trips generated by 15,499 users, about 10,000 in Los Angeles and 5,500 in New York. These users’ tours were each voluntary visits to various consecutive citywide locations, of significantly different lengths for each city; there were about 30,000 tours in total.
Despite the means and variances for each city being different, the researchers found the underlying location and time data quite valuable for analyzing individual human mobility.
Each user record in the two cities contains an individual ID, a timestamp, and geographic coordinates. The “home” base for each individual was chosen to be the most frequently visited location for that individual, and tours were then extracted from that user’s trajectory data.
What the tour length patterns show
The researchers first used the data to determine the distribution of tour lengths—the probability of a tour of a certain length as a function of that length.
They found the distribution could be well approximated by a truncated power law distribution—the product of two factors: the tour length to some negative power (parameter), times an exponential of (the tour length divided by another parameter).
This distribution captures what the data tell: (1) most individuals make only one or two stops before returning home, while a minority make several stops, and (2) the probability of very lengthy tours decreases drastically. The best fits to each city’s dataset gave remarkably close values for the two parameters mentioned above.
The scientists asked why individuals in different environments exhibit similar touring patterns. Is there some common mechanism involved?
Why earlier mobility models fall short
First, they found that generated tour length distributions of two existing models of human mobility “exhibit substantial discrepancies compared to empirical observations,” as they wrote in their paper.
They found that both models neglected the tour generation processes, and especially individual decisions to terminate a tour. So they developed their own touring model, calling it the tour terminate-continue (TTC) model.
They assumed that at every step the individual might decide to end the tour and return to their home base. Using their empirical data from Foursquare, their model process “included the relationship between the probability of terminating the tour and the length of the current tour.” The termination probability decreased with increasing tour length, a finding also found by an earlier research team.
The Foursquare data showed that the probability of terminating the tour decreases with increasing tour length, a feature captured by the TTC model but not by the two models mentioned earlier.
‘David’s Flower Service’: From theory to delivery truck routes
Phys.org asked one of the co-authors, Xiao-Yong Yan of the School of Systems Science at Beijing Jiaotong University, how their work would apply to my hypothetical David’s Flower Service. My company takes orders and delivers flowers in my beautiful city throughout the day. The delivery trucks start and end at the same location every day. During the day, they each go on trips, several trips a day for each, and deliver flowers to various locations around town.
Yan said such an example fits their paradigm very well and has been treated in closely associated work, the master’s thesis of the Physical Review E paper’s first author, Xu-Jie Lin.
“The core problem we address,” said Yan, “weighing the trade-off between minimizing total travel distance and managing the costs associated with long tours (such as driver fatigue or time constraints)—is directly relevant to your business.”
To apply our model, he said, you would need to collect the geographic coordinates of and the number of visits to the flower shop and all delivery destinations.
Their work, Yan said, “introduces a truck tour minimum cost model that balances two types of costs:” (a) total distance cost, proportional to the sum of all miles driven by all trucks, and (b) tour average distance cost, i.e. the average length of a single tour.” He added, “Keeping this lower helps reduce driver fatigue and ensures timely deliveries.” I don’t want my drivers getting injured in accidents.
Then, using their model, “companies can dispatch drivers based on dynamic conditions such as demand for real-time orders, availability of trucks, location of drivers, and distance to destinations,” said Yan, “allowing trucks to complete transportation tasks at one location and then move further to other locations on an optimal path, thus extending the average length of the tour and reducing the energy consumption and emissions of trucks.”
I’ll give it a try. In this economy I gotta keep trimming costs, you know.
Written for you by our author David Appell, edited by Sadie Harley, —this article is the result of careful human work. We rely on readers like you to keep independent science journalism alive.
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Publication details
Xu-Jie Lin et al, Scaling law of individual urban tour behavior, Physical Review E (2026). DOI: 10.1103/9d5z-9xxt. On arXiv: DOI: 10.48550/arxiv.2505.20590
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