Uber be damned. One of the most iconic sights for visitors to New York City is the vast numbers of yellow taxis that line the streets of Manhattan.
Mathematical modelling from a team led by Mohammad Vazifeh from the Massachusetts Institute of Technology, however, reveals that around 40% of the vehicles that comprise the city’s taxi fleet are superfluous.
In a paper published in the journal Nature, Vazifeh and colleagues outline a new model for determining taxi efficiency, based on 150 million trips taken in a single year, that shows that more than one-third of the current fleet could be removed without requiring changes to regulation, business models or customer habits.
The model changes a critical assumption in previous attempts to establish a viable answer to what mathematicians call the “minimum fleet problem”. Earlier approaches have based calculations on ride-sharing – that is, two or more passengers occupying a vehicle at the same time, but being delivered to geographically different locations. Vazifeh’s team ditched that assumption, and used instead the notion of vehicle-sharing – wherein each taxi is in continuous use for 24 hours a day, driven in three eight-hour shifts.
(In this scenario, routine car maintenance is assumed to take place periodically on weekends, when the number of passenger requests drops.)
The researchers approached the problem by identifying the essential variables involved in each taxi journey – pick-up time and location, drop-off time and location, and how much time passes between a passenger being ready for pick-up, and pick up actually occurring.
Journey times were calculated using GPS data arising from real New York City streets rather than an idealised model.
Setting the variable for waiting time turned out to be the greatest challenge in the model, because it also determined a number of other real-world outcomes, including costs to the fleet operator, customer satisfaction, and traffic flow.
At one end of the scale, the researchers explained, setting the waiting time to an impossible zero seconds resulted in the assumption that taxis simply materialise and disappear at the start and end of journeys. This was not only unfeasible but also prohibitively costly.
On the other hand, they show, increasing the wait time into the region of hours results in the need for a much smaller fleet – but also produces what they term, euphemistically, “operational and traffic efficiency problems” – a phrase that could be understood to mean “a very large number of very angry New Yorkers”.
For the sake of the exercise, thus, Vazifeh and colleagues set optimal waiting time at 15 minutes.
Putting all the variables together and running the numbers, based on the previously collected data, the results were impressive.
“The efficiency breakthrough provided by network-based optimisation, when compared to current taxi operation in New York City, [revealed] the number of circulating taxis can be reduced by an impressive 40%, and kept fairly constant through the day,” the researchers conclude.
Two other conditions, however, informed the results – a high level of knowledge on the part of the operators concerning journey destination as well as start-point, and a centralised dispatch system.
The researchers then ran the numbers again, varying these conditions. When knowledge of destinations was absent in a large number of vehicle hires before the passenger is picked up, and when dispatch is through localised hubs, the total taxi fleet could still be reduced by 30% without loss of service.