In one corner, employees watch flat-screen televisions that depict various attractions in green, yellow and red outlines, with the colors representing wait-time gradations.

If Pirates of the Caribbean, the ride that sends people on a spirited voyage through the Spanish Main, suddenly blinks from green to yellow, the center might respond by alerting managers to launch more boats.

Another option involves dispatching Captain Jack Sparrow or Goofy or one of their pals to the queue to entertain people as they wait. “It’s about being nimble and quickly noticing that, ‘Hey, let’s make sure there is some relief out there for those people,’ ” said Phil Holmes, vice president of the Magic Kingdom, the flagship Disney World park.

What if Fantasyland is swamped with people but adjacent Tomorrowland has plenty of elbow room? The operations center can route a miniparade called “Move it! Shake it! Celebrate It!” into the less-populated pocket to siphon guests in that direction.