Savings in time and energy would come from replacing extremely heavy trains that stop at every station with lightweight vehicles that depart immediately and go directly from A to B, stopping only at one’s destination. No more waiting or stopping every few blocks.

Prices could be flexible, adjusting to congestion and smoothing demand with a reservation system. Some cabs could be upholstered with the finest leather and plated with gold for those New Yorkers who want a truly luxurious experience. Others could have a work table for those who want to write on the way to the office. Trendy models might come sporting graffiti designs by name-brand artists, created as an homage to the 1970s-era trains. But most would probably be slim, simple, and utilitarian. People would pay to reserve a slice of the pavement at a particular time; and the tunnels would be maintained by these fees.The prices would move up and down, adapting to demand.

The new system could be dramatically faster. The autonomous vehicles would take passengers from their initial station to the final one without stopping once. The stations would have to be redesigned, outfitted with little entrance and exit ramps that carry that cabs which carry the riders up to where the turnstiles are now. This way, the traffic would never stop flowing. The vehicles would stop only when they’re out of the flow of traffic. (They could then be recharged and stored at each station until another passenger comes along.) The vehicles might not run as fast as the current trains—which can go 50 miles an hour or more at top speed—but the lack of stops would pay off. (As every rider of the express trains knows, every stop really slows things down.)

Renting out the tunnels by the minute would also allow for new uses. There’s no reason the system couldn’t carry packages, food, or other freight in little autonomous trucks during off-peak hours.

This federated system of companies would be a return to an earlier era, when the subway tunnels and elevated trains were built by competing companies working with the city. The first elevated train lines were started in the 1860s, and the first subway tunnel opened at the turn of the century. A confusing system of leases and private contracts knitted together private industry and the city government until they were integrated around World War II.

[Readers respond: The NYC Subway Is Not ‘Beyond Repair’]

In that era, the tech of choice was the train, and the trains were big. Autonomous vehicles, by contrast, can be incredibly lithe, especially if you skip over the car-shaped models and head for the super-lightweight transports called “hoverboards” or “scooters.” These clever devices with computer-driven balancing look a bit like skateboards but carry enough battery power to go a dozen miles or more. Some cities are already filled with scooters that can be rented by the minute and driven on the streets. Now we just need autonomous ones that run in the subway system.