Scaling laws of dynamic high-capacity ride-sharing

Abstract

This study discovers a few scaling laws that can effectively capture the key performance of dynamic high-capacity ride-sharing through extensive experiments based on real-world mobility data from ten cities. These scaling laws are concise and contain only one dimensionless variable named system load that reflects the relative magnitude of demand versus supply. The scaling laws can accurately measure how key performance metrics such as passenger service rate and vehicle occupancy rate change with the system load. The scaling laws strongly agree with experimental results, with the values of $R^2$ exceeding 0.95 across all scenarios. In addition, the scaling laws can accurately reproduce experimental results of dynamic high-capacity ride-sharing involving different road networks, supply–demand patterns, vehicle capacities, and matching algorithms, indicating these scaling laws could be general and applied to other cities. These scaling laws provide a reference for transportation network companies and governments to efficiently manage dynamic ride-sharing services. For example, according to these scaling laws, when the demand is relatively high, e.g., system load equals 3, ride-sharing services with a capacity of 2 passengers can only accommodate 50% of demand. In comparison, high-capacity ride-sharing services with a capacity of 4 passengers can satisfy 72% of demand. The findings provide valuable insights into the expected performance of ride-sharing, informing decisions about how to operate a fleet to improve transportation efficiency.