Room for one more? Zoran Milich/Reuters

That’s what a new MIT study suggests. But applying this math to the real world is more complicated.

There are nearly 14,000 taxis in New York City, and sometimes that doesn’t seem like enough. But in a new study from MIT, researchers suggest that just 3,000 ride-sharing vehicles—be it a traditional taxi, an Uber/Lyft car, or a future autonomous robo-cab—could do the same job if each accepted up to four passengers. And if all passengers were willing to share their rides with nine other strangers in return for less traffic and lower cost, the city would need just 2,000 of such vehicles.

That would be welcome news for cities like NYC, where gridlock has gotten so bad the city has proposed to implement congestion fees. It could also be a boon for cities like Los Angeles or London that are trying to cut down on urban smog from vehicle emissions. (Of course, whether ride-hailing services and ride-sharing apps actually ease traffic or make it worse is still a matter of vigorous debate, hinging in large part on whether taking certain fleets off the road encourages more people to drive their own car.)

MIT’s “secret sauce,” as lead researcher Daniela Rus puts it in the Proceedings of the National Academy of Sciences, is an algorithm her team developed to find the most efficient routes for carpooling vehicles to pick up and ferry multiple passengers to their destinations in a single trip. It first lays out all the requests and available vehicles on a map in real time. Then it analyzes all possible trip combinations to find the best one before assigning passengers each vehicle. If a new request appears during the initial trip, the system calculates whether a cab should pick up that new party. It will also send idling cars to places with high demand based on historical information.

“One of the challenges is to create a solution that can deal with thousands of requests that appear at [once] in real time,” says Rus, director of the Computer Science and Artificial Intelligence Laboratory (CSAIL) at MIT. “We call our algorithm ‘anytime optimal,’ meaning our algorithm will be refined over time, ultimately converging to an optimal solution.”

To test the algorithm, the team ran simulations using public GPS data of 3 million taxi rides in Manhattan from one week in 2013. They found that if each cab carried up to four separate passengers, the wait time per passenger would average 2.7 minutes, and each rider’s trip would be delayed by roughly 2.3 minutes. With cabs or minibuses that can shuttle 10 passengers, that wait time would increase to approximately 2.8 minutes, while trip delays would average around 3.5 minutes. The algorithm would work with any ride-sharing service, and even with autonomous cars, according to the researchers.

While the math might check out, David King, a urban planning professor at Arizona State University, is doubtful that the numbers would play out that dramatically in the real world—if they play out at all. For starters, the researchers assume that each taxi trip in that dataset carries one passenger (the data doesn’t specify this) when in reality, a lot of cabs are already shared by a party of multiple passengers. “Families get in them, or a couple is going out to dinner, so it’s not just a matter of once this vehicle picks up Person 1, it can then pick up Persons 2, 3, 4, and 5,” because the first party may have already filled up half of the seats, he says. His own research indicates that the average occupancy number is 1.6, which means the 430,000 trips made in one day during that week in 2013 could have carried as many as 688,000 passengers. (For her part, Rus says the parameters of the algorithm can be adjusted and would be tested over time to find that optimal solution.)

Then there’s still the problem with why passengers hail taxis in the first place. “There’s a lot of interest in sharing taxis, and there has been for decades, but nobody ever does it” King says. “Taxis are a premium service, and the wealthiest use taxis the most because they have a high value of time and they value their privacy. The low-income use taxis when they don't have any other choice.”

So aside from the social challenge of getting strangers to get cozy in a small car, individual priorities might stand in the way as well. Not to mention, he adds, people may question the reliability of a 10-person ride-sharing cab that could be rerouted several times to pick up nine other people along the way.

And it’s not like NYC’s Taxi and Limousine Commission hasn’t tried ride-sharing before. In 2010, they piloted a limited “Share-a-Cab” program with a flat fee of $3 or $4 a head. A New York Times reporter shared her observations then:

On the program’s first two days, the only people lining up at the three pickup points were other journalists. Drivers did not slow as they passed by. So I approached people who were hailing their own cabs, pretended to be heading in the same direction and offered to share. After getting rejected for the 12th or 13th time, I started offering to pay the whole fare — not a cab share, a cab gift. That only creeped people out more. Eventually I was riding around in the back seat of my own taxi with the window open, yelling, “Come on, get in!” to anyone with a hand in the air.

That’s not to say there isn’t value in a study like this, says King. After all, ride-sharing programs from Uber, Lyft, and the like exist in many cities, and Google is also starting its own service. There’s a benefit in studying how this can apply to the taxi industry, he says, but “it's one thing to say we can improve efficiency with better matching; it's another to say it will reduce a vehicle fleet by a factor of five.”

Rus acknowledges that her team will do more research to figure out what other conditions to apply. “The algorithm is really quite general, and it was instantiated to this particular study, but that doesn't mean that this is the only thing that it can do,” she says. “It's really easy to play with the parameters and assumptions.” The algorithm is a mathematical way of comparing the benefits of ride-share to all parties to the inevitable tradeoffs, and different places would have to decide how they might want to implement it. While not all cities will see such dramatic results, she adds, even taking a more modest number of vehicles off the streets can make a big difference, traffic-wise.

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