  Dynamic ride-sharing services, including ride-pooling offered by ride-hailing
platforms and demand-responsive buses, have become an essential part of urban
mobility systems. These services cater to personalized and on-demand mobility
requirements while simultaneously improving efficiency and sustainability by
accommodating several trip requests within a single ride. However, quantifying
the advantages and disadvantages of dynamic ride-sharing, particularly
high-capacity ride-sharing, remains a challenge due to the complex dynamics
that depend on several factors, including matching algorithms, vehicle
capacity, transportation network topology, and spatiotemporal demand and supply
distribution. In this study, we conduct extensive experiments on an agent-based
simulation platform calibrated by real-world mobility data from Chengdu, Hong
Kong, and Manhattan. Our findings reveal a few scaling laws that can
effectively measure how key performance metrics such as passenger service rate
and vehicle occupancy rate change with a dimensionless system loading factor
that reflects the relative magnitude of demand versus supply. Moreover, our
results indicate that these scaling laws are universal for different network
topologies and supply-demand situations. As a result, these scaling laws offer
a means for urban planners, city managers, and ride-hailing platforms to
quantify the potential benefits and drawbacks of dynamic ride-sharing under
different circumstances and to design better operational and regulatory
strategies.

Systems and Control;Systems and Control