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Abstract

Ride-sharing services may substantially contribute to future sustainable mobility. Their collective
dynamics intricately depend on the topology of the underlying street network, the spatiotemporal demand
distribution, and the dispatching algorithm. The efficiency of ride-sharing fleets is thus hard to quantify and
compare in a unified way. Here, we derive an efficiency observable from the collective nonlinear dynamics
and show that it exhibits a universal scaling law. For any given dispatcher, we find a common scaling that
yields data collapse across qualitatively different topologies of model networks and empirical street
networks from cities, islands, and rural areas. A mean-field analysis confirms this view and reveals a single
scaling parameter that jointly captures the influence of network topology and demand distribution. These
results further our conceptual understanding of the collective dynamics of ride-sharing fleets and support
the evaluation of ride-sharing services and their transfer to previously unserviced regions or unprecedented
demand patterns.