Ms. Baer calls them “pedestrian safety and sanity managers” because they improve the quality of life. They unblock crosswalks and intersections, deter jaywalking and even help to lessen honking. And they keep people safe; no injuries have been reported while they have been on duty, she added.

Though pedestrians come first, Mr. Martin, 49, has also talked down irate drivers stuck in gridlock. He leans over to chat about local sports teams. He listens to their woes. They have somewhere else to be. They are going to miss a flight. One man said he had to get to his pregnant wife.

While Hudson Square is the only city neighborhood with pedestrian managers stationed at intersections, they are also used on a limited basis near construction sites, shopping malls and the Barclays Center in Brooklyn.

Other neighborhoods, Ms. Baer said, have expressed interest in starting similar operations.

The pedestrian managers are hired and trained by Sam Schwartz Pedestrian Traffic Management Services, a company run by Mr. Schwartz, a former city traffic commissioner. The company has 250 traffic managers working in New York, New Jersey and three other states.

The city’s Transportation Department requires pedestrian traffic managers to have at least five years’ experience working in law enforcement or in directing traffic and pedestrians at construction sites, and to receive specialized training.

The pedestrian managers in Hudson Square complete a two-day safety course, which reviews traffic rules, verbal commands and hand motions and gives pointers on avoiding being drawn into arguments. Then they are sent into traffic for on-the-job training.

Carl Vitale, who teaches the safety course, said some people have dropped out when they realize just what the job demands. “It’s not for everyone,” he said.