Sharing rides could drastically improve the efficiency of car and taxi transportation. Unleashing such potential, however, requires understanding how urban parameters affect the fraction of individual trips that can be shared, a quantity that we call shareability. Using data on millions of taxi trips in New York City, San Francisco, Singapore, and Vienna, we compute the shareability curves for each city, and find that a natural rescaling collapses them onto a single, universal curve. We explain this scaling law theoretically with a simple model that predicts the potential for ride sharing in any city, using a few basic urban quantities and no adjustable parameters. Accurate extrapolations of this type will help planners, transportation companies, and society at large to shape a sustainable path for urban growth. Mobility of people and goods has been vital to urban life since cities emerged more than 7,000 years ago 1 . Indeed, the success, prosperity, and livability of cities are directly related to the effectiveness of their mobility systems 2 . However, due to fixed schedules, limited coverage, and low quality of travel experience, public transportation systems accommodate only a fraction of the urban mobility demand 3 . The rest is satisfied by private vehicles and taxis, inefficient transportation modes that move only 1.3 passengers per vehicle on average 4,5 , causing the road congestion observed in most cities worldwide, with immense economic and societal costs 6 . Enhancing transportation efficiency is a key to rendering sustainable the urban growth predicted for the coming years 7 . The emerging sharing economy 8, 9 promises to improve the efficiency of individual, on-demand transportation. Bridging the gap between shared but inflexible public transportation and flexible but not shared private transportation, novel services such as those provided by Uber TM , Lyft TM , and ZipCar TM can significantly contribute to reducing road congestion and emissions. But the realizability of such potential benefits depends on the answer to a fundamental unsolved question: How compatible in space and time -and thus shareable -are individual mobility patterns? While recent literature 10-15 has unveiled spatial and temporal regularity of individual mobility patterns, very little is known about their mutual similarity. In a previous study 16 , we introduced the notion of a shareability network to quantify the spatial and temporal compatibility of individual trips. The nodes in the network represent trips, and links between them mark trips that can be shared. Two trips are defined to be shareable if they would incur a sharing delay of no more than ∆ minutes, relative to a single ride (see Supplementary Information) . Let the shareability metric S denote the fraction of individual rides that can be shared. We found 16 that taxi trips in New York City offer a shareability well above 95% for ∆ = 5 min, and that S increases rapidly with the number of trips available for sharing. But that previous study 16 left a key question unresolved: Might the results be peculiar to New York City? There was good reason to suspect so, given that New York is singular in several respects, namely, its large population, its small geographical area, and its enormous density of taxi traffic. In what follows, we study ride shareability in three other major world cities -San Francisco, Singapore, and Vienna -for which extensive data is available. Although these cities differ greatly from each other and from New York City in their traffic characteristics, population size, and geographical area, we find they all obey the same empirical law governing the potential for ride sharing. To the best of our knowledge, the existence of such a seemingly universal law has not been reported before. We explain the mechanism underlying this law of ride sharing using a simple mathematical model. The model's prediction accounts for more than 90% of the variance in the data, and does so without any adjustable parameters.
A similar study has been presented by REF calculating shareability curves using millions of taxi trips in New York City, San Francisco, Singapore, and Vienna, showing that a natural rescaling collapses them onto a single, universal curve.
Scaling Law of Urban Ride Sharing
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