In an article published in PNAS [1], a team directed by Marc Barthelemy (IPhT) shows that urban bus systems obey a robust scaling law, in which service frequency emerges as a power-law function of passenger demand and route duration
Using data from roughly 3,000 bus routes worldwide, they reveal that cities operate in distinct universal regimes controlled by budget constraints and crowding effects, with exponents reminiscent of those found in physical systems governed by optimization and capacity allocation.
This work places public transport networks within a broader statistical-physics perspective, showing how scaling laws can emerge from simple optimization principles under capacity and budget constraints.