Why Mathematicians Love Programming Elevator Actions

By Wesley Fenlon

Even 100 years after their invention, we're still tweaking elevators to minimize our waits and get us where we're going faster. And we still hate waiting for them.

You stand poised for action in the lobby, eyes darting back and forth between the doors in front of you. Any moment now one of them will open. But which one? You wait to hear that wonderful Ding! that means arrival, doors opening, salvation from the interminable boredom of a 30 second wait. When you hear it you'll spring into action, rushing into the elevator and jamming on the button for your floor. The doors close. And then you wait again.

It's a ritual we all know by heart, but it's amazing how much math and planning go into the 18 billion elevator rides taken annually in the United States alone. When everything goes right, you won't even have to wait 30 seconds for the doors to open. According to Theresa Christy, a mathematician and researcher at Otis Elevator Company, 20 seconds is the magic number for an elevator wait. And that number hasn't changed in about 50 years.

You'd think we'd have faster elevators five decades after 20 seconds became the target waiting time, but speed isn't really the issue. It's all about the number of stops elevators have to make and juggling the wait times for people on every floor of a building. A recent profile of Christy in the Wall Street Journal reveals just how much math goes into every imaginable elevator use scenario.

When Christy programs elevators, she has to take into account the size and weight of elevators and how many people can fit in them. Building owners want to install as few elevators as possible, since they take up a great deal of space. Passengers in various countries prefer different amounts of personal space. So, for example, more Japanese riders will crowd into elevators than Americans, but they want to know in advance which elevator they'll be getting into, so they can line up in front of the right set of doors.

The elevator code has to strike a balance between convenience for riders and convenience for waiters. If an elevator has already made three stops, should it make a third to pick up someone who's been waiting for 30 seconds and inconvenience its current passengers? Christy runs simulations to analyze the decisions elevators make according to their programming, then tweaks that programming to better her score.

She compares it to a video game; we hope she's never played Mass Effect. NPR's Marketplace calls her work an art. We think either label works--it's an underappreciated, endlessly challenging job that will never have a perfect solution. Christy's short Marketplace interview is an interesting look into a job that most of us would never think about, despite how much it affects our daily lives.