S. Patwardhan, Ş. Erkol, F. Radicchi, & M. Barthelemy

Proc. Natl. Acad. Sci. U.S.A. 123 (29) e2535998123,

Public transit agencies face the challenge of allocating limited resources across routes with varying demand. Analyzing bus systems across 19 metropolitan areas, we show that, despite differences in cities, agencies, and planning practices, realized operations exhibit a specific scaling pattern in service allocation. This regularity is not imposed by a universal planning formula, but emerges across institutional and urban contexts. We show that it can be understood through a constrained-optimization principle balancing passenger waiting time, crowding, and limited resources. The result connects urban transit to complex flow systems in physics and biology by highlighting a regime where demand fixes flows, and cities allocate service capacity. This framework explains unequal returns to investment across systems and guides efficient, equitable planning.

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