Introduction: territorial heterogeneity of mobile demand
Variations in mobile data consumption at the territorial level are well known to network architects. They are most often attributable to the number of active mobile devices in the locations concerned. However, analyses of mobile traffic data also seem to indicate that consumption per user varies in different urban contexts. We were able to measure this using aggregated data at the relay antenna level (anonymous) collected during the ANR ABCD [[1]] and ANR CANCAN [[2]] collaborative projects. Data was collected over four years (2014, 2016, 2017, and 2019). Aggregates of total traffic by application category used at each antenna in France were calculated on a daily basis.
In 2014, mobile traffic consumption by a user in a town with 10,000 inhabitants was 77% of that of a user in a town with 100,000 inhabitants and 60% of that of a customer in Paris.
Methodology: spatial alignment and mobile traffic interpolation
To map the daily demand recorded at each base station (BTS), mobile traffic data must be spatially aligned with administrative zoning. To do this, the geographical locations of the base stations were used to approximate their coverage (Voronoi tessellation). The recorded mobile traffic was then assigned to each target geographic unit via weighted spatial interpolation. Figure 1 illustrates this assignment: we assume that average daily traffic is uniformly distributed within its Voronoi cell. Each antenna contributes to the given municipality with a fraction of its traffic proportional to the intersection between the corresponding Voronoi cell and the boundaries of the geographic unit.
Figure 1. Example of coverage of the municipality (in black) and approximate mobile network coverage (orange); the dot represents the location of the antenna.
Definition of units of analysis and scope of the study
For the purposes of this study, the analysis focused on examining urban contexts. In the absence of a consensus definition of a city, the two geographical divisions used by INSEE (French National Institute of Statistics and Economic Studies) for geostatistical analyses were used: municipalities and urban units (continuous built-up areas). Municipalities with a population of less than 2,000 were excluded. The analysis covers 4,979 municipalities and 2,354 urban units. This covers all towns and villages in metropolitan France and encompasses 70% and 75% of its population (approximately 48 and 50 million residents), respectively.
The wide variety of city sizes, spanning several orders of magnitude, makes direct analysis impossible. To remedy this, cities were grouped into 60 classes based on their population, using a logarithmic scale. For each class, the average daily mobile data traffic for all cities in the class was calculated for each day observed.
Results
The analyses confirmed that mobile Internet usage per capita is lower in smaller cities. The relationship between mobile traffic per capita and city size (population) follows a power law:
where t is the daily individual demand for mobile network traffic measured in a city and population is the number of inhabitants recorded in the census. The multiplier k and the exponent α are the parameters of the model.
Figure 2: Normalized daily mobile traffic and resident population for 4,837 municipalities (top) and 2,296 urban units (bottom), for four different years (columns). The adjusted power laws (orange lines) appear linear in the log-log diagrams. The gray dots are samples per city and per day, and the black dots are the averages per bracket used to eliminate heteroscedasticity in the data.
As shown in Figure 2, a similar relationship is observed for each year analyzed. The exponent α is always greater than 1 (see Figure 3), which implies positive returns to scale: the larger the city, the higher the amount of traffic consumed individually by users.
For example, in 2014, a user in a municipality with 10,000 inhabitants consumed 77% of the traffic of a user in a municipality with 100,000 inhabitants, and 60% of that of a user in a metropolis with 1 million inhabitants. In the most populous cities, people use mobile digital services significantly more than in smaller towns.
Mobile internet consumption follows a superlinear power law. It therefore more closely resembles the socio-economic characteristics of cities, such as wealth production (GDP), innovation (number of patents), wage levels, housing costs, crime rates, etc., which have an α > 1, than to the satisfaction of individual needs (e.g., water or energy consumption), which grows proportionally to the number of inhabitants (α = 1) [[3]].
Empirical data from numerous studies indicate a systematic acceleration of social and economic life with the size of the city, an acceleration that stems directly from the network of social interactions. Indeed, there is an increase in connectivity per capita in large cities, which amplifies propagation processes, such as the dissemination of information and ideas [[4]]. The consumption of mobile digital services therefore contributes to this urban dynamic.
Temporal evolution of model parameters
This study also allows us to observe the evolution of this relationship through changes in the values of two model parameters (Figure 3). The multiplier k can be interpreted as the average individual consumption, while the exponent α allows us to estimate the differences in usage intensity between small and large cities. Over the six-year period, both values increase. Data consumption grows year on year (k > 0), but the gap between cities according to their population widens (the exponent α is constantly increasing).
Figure 3: Evolution of parameters k and α of the power law model of total traffic and population over the years, for municipalities and urban units.
Conclusion: challenges for digital regional planning
This simple relationship, which allows mobile traffic in a city to be estimated based on a single variable (the number of residents), is of interest to mobile network planners. However, the superlinearity of app consumption based on city size places operators in a situation where they must balance two conflicting objectives. On the one hand, growing inequalities across the territory raise fears of a new form of “digital divide.” On the other hand, areas with the highest demand require better coverage in order to maximize user satisfaction.
The challenge is therefore to cover the territory in order to guarantee access for all, while meeting the specific needs of each territory. Indeed, the similarity of the relationship observed with other socio-economic variables that also follow the power law in the urban context indicates that the appetite for mobile applications may be associated with a higher density and pace of social and economic interactions in large cities.
[1] https://anr.fr/Project-ANR-13-INFR-0005
[2] https://cancan.roc.cnam.fr/
[3] Ribeiro, F.L. & Netto, V.M. (2025). Urban Scaling Laws. In: Rybski, D. (ed.) Compendium of Urban Complexity. Understanding Complex Systems. Springer, Cham. https://arxiv.org/pdf/2404.02642
[4] Schläpfer, M. et al. (2014) The scaling of human interactions with city size. Journal of the Royal Society Interface, vol. 11, no. 98 https://royalsocietypublishing.org/doi/10.1098/rsif.2013.0789
