Some expediters speak of recurring dreams in which time compresses, and they race against it. The machine jams, or prints out endless streams of paper. They walk into a familiar kitchen, but it’s full of unreadable tickets.

The work of an expediter can be a thrill, but it’s also high-pressure, competitive and comes with major responsibilities. “If one guest is sitting at their table without food, that’s not on the cooks,” Ms. Raben said. “That’s on you.”

If an expediter at Noodle Bar misses a shift, Mr. Kim said the team finds ways to fill in, but it’s a challenge. “There’s this very funny, comical dance that happens between manager and chef because we’re both doing two halves of the job,” he said. “We’re a step behind, we’re just not as on it as we should be.”

In some cases, no expediter may be preferable to a disorganized expediter, unfamiliar with the kitchen and its systems, who relays incorrect notes to servers about table positions, or forgets about an allergy.

“They don’t just lag, they screw things up,” said Erik Ramirez, the chef and owner of Llama Inn, a Peruvian restaurant in Brooklyn. During a busy brunch service years ago, one of his line cooks walked out and the expediter had to fill in and cook while a manager expedited.

“It’s a pretty big hiccup” anytime someone new jumps into the role, he said. “Tables will lag, people will complain about the food taking a long time. It can be rough.”

But in a restaurant they know inside and out, great expediters can peek into the dining room, peer across a full board of tickets, then organize the data in their heads and see directly into the future.