In one of his first moves, Mr. Rodi hired nearly two dozen developers to fix PBSC’s software problems and then to bring the system into the age of the mobile Internet. He is also crisscrossing the globe to find new customers and to keep existing ones. Mr. Rodi says he is willing to spend tens of millions if necessary to revive the company’s fortunes.

“Will we have success with it?” he said. “Yes, sir, we will have a success with it.”

When Montreal introduced its bike-sharing system in 2009, city officials simply wanted to make commuting easier. The city would be blanketed with almost 10,000 bike stations to fill in gaps not covered by trains, subways and buses.

But the Montreal City Council didn’t want to pay for the system, the Société de Vélo en Libre-Service, known more commonly as Bixi. So, like other cities, it funded the service in part through user fees and advertisements plastered on the bikes. To pay for the rest, officials were counting on creating an international business that would sell its proprietary bike-share technology to cities around the world.

Montreal’s system wasn’t the first large-scale municipal bike-sharing program, a distinction usually attributed to Copenhagen, which started one in 1995. But Bixi was considered one of the most innovative, with technologies specifically designed for bike sharing.

One of the biggest attractions was the bike itself. Rather than using inexpensive equipment that proved vulnerable to vandalism and breakdowns, the industrial designer Michel Dallaire came up with a durable, if costly, aluminum bike. Modifications thwarted thieves from easily unbolting parts.

“That bike, nobody can argue with his bike,” said Josh Squire, the chief executive of CycleHop, a bike-share operator that does not use the Bixi technology.