But with a shared fleet of autonomous cars, we'd be able to drastically increase the hours per day each cars was in use. Instead of driving your car to work and leaving it at the lot all day until you used it again, you'd only need the car for the duration of the drive. Then it'd go on to other things.

If car use were totally random throughout the day, and all trips were of relatively equal lengths, and there were no weird migratory patterns that resulted in many people all needing cars in the same place at once at the same time (say, at the start of rush hour), then it'd be easy enough to figure out just how many fewer cars we'd need.

But alas that's not how cities work, just ask anyone who has looked for an available Car2Go in a residential neighborhood on the late side of the morning commute. At peak times, everybody travels at once, and they tend to head in similar directions (from residential areas to downtown). It's for this reason that car- and bike-sharing systems have to "rebalance" their fleets at different points in the day, either offering members incentives to travel in unpopular directions (notably, uphill, in the case of bike sharing), or actively carting bikes around the city in vans in anticipation of where they'll be needed next.

So calculating just how many cars a city of the autonomous-driving future will need is a bit of a challenge, but, fortunately, a team of researchers at MIT, Stanford, and the Singapore-MIT Alliance for Research and Technology has taken a crack at it, giving us at least a preliminary sense of just how dramatic a shift this will be. Their conclusion: We'll only need about one-third the number of vehicles we have now.

In a new paper, the researchers take a look at Singapore, a city for which excellent data exists on how much people drive, to where, and how long it takes. Moreover, because Singapore is an island, the authors say, officials are limited in what they can do to alleviate congestion in the long run. As a result, the city is a promising candidate for a move to an autonomous, shared driving fleet. If it did, the authors estimate, the average Singaporean would save on the order of $15,000 annually, if you take into account not only the costs of car ownership, maintenance, and parking, but also the time people spend looking for parking, dealing with tickets, in line at the DMV, and other nuisances.

Based on their model, the authors, led by Kevin Spieser of MIT, calculated that at most times of the day, a relatively modest fleet of 200,000 vehicles would provide residents with cars within just a few minutes. The problems come at rush hour, when a fleet of 200,000 would send wait times skyrocketing above the hour mark. To keep wait times under 20 minutes during rush hour, they estimate Singapore would need a fleet of about 300,000. By comparison, in 2011 there were nearly 800,000 passenger vehicles in operation in the city.

Kevin Spieser et al.

So does that mean that in the cities of the future we'll need about a third of the cars that we have now? Not quite. Each city's demographics, geography, law, public transit, culture will shape just how dramatic a shift this will be. As they say, your mileage may vary.