Scaling Laws of Collective Ride-Sharing Dynamics

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.