The algorithms and strategies behind minimizing your elevator wait time

Theresa Christy, a mathematician and Otis Elevator Research Fellow, explains the science behind your elevator experience. 

Sometimes, when you’re in a hurry, waiting for an elevator can feel like an eternity. And pushing the button a few extra times just doesn’t do a thing. Why is that elevator up on the fourth floor, and not here? There is actual, serious science guiding this path.

Theresa Christy, a mathematician and Otis Elevator Research Fellow, sat down with us to explain the science behind designing elevators with minimal wait times. 

Below is an edited transcript of our conversation.

What is an appropriate wait time for elevators?

We try to aim for an average of 20 seconds if you’re in a grade A office building. If you’re in a residential building, that average is a little longer. That’s because, traditionally speaking, people in residential buildings are more relaxed, they’ll wait a little bit longer before they get frustrated or feel that the elevator isn’t coming.

Is there a formula that tells you, ok, if the building is this size with this many people in it, here’s how many elevators you’re going to need? 

That’s a tricky question. The answer is yes and no. There is a formula that will help guide you to that direction. But the formula, which has been in existence for a long time, is called the round trip time, and it goes with something called handling capacity. It’s a probability formula based off of statistics and it gives you, on average, what percent of the population you can handle with how many elevators. So if you tell me there’s a thousand people in the building and I’m looking for a 12 percent handling capacity, then I need to have 120 people being moved every five minutes. I need to have enough elevators to do that. That can be worked out with a formula.

The problem is that those formulas are generalized. Nowadays, we have something new, called destination dispatching, and now people are no longer just pressing an up button or a down button, they are actually using a keypad or a touchscreen and they’re putting in their destination. So instead of saying up, they’re going to put seven and then that little device is going to come back to them and say, ‘ok, you wait for car A.’ Doing this allows us to group people by destination, it lowers the amount of stops on average that a person would make but it also renders our tried and true formulas no longer valid.

Might that mean you will need fewer elevators because they will move more quickly?

Yes, that is the holy grail of elevator dispatchers – that we can use fewer elevators and handle the same amount of people.

The kind of math you do to figure out the questions of elevators, is that applicable in other fields? Do you share your findings with other fields?

We do share, but we don’t share the exact formulas that we use or the exact methodology and that’s because elevator companies consider their dispatching to be kind of like a cook’s favorite recipe that they’re known for and that only they can make, and they don’t want to give it out because then everyone can make it. So the actual nitty gritty of things is kept secret.

What are some of the fields that you have learned something from?

Well, we basically like to look at transportation, whether it’s buses, trains, whether it’s delivering packages like UPS or FedEx and also things like network and how packets of electronic data are moving over the network and how they’re routed to get them to the best place. The problem we have when we read all of this information is that packages don’t mind going past their destination and then being brought back to it. Neither do electronic bits … but people do. So there have been some dispatching algorithms proposed where you get in, you tell the elevator you want to go to floor three, but it might bring you first to floor 5 and then bring you back to floor 3. Well, elevator companies tend not to do that. People don’t like it and it’s become sort of an unwritten rule that a dispatching algorithm won’t do that even if we might get a little bit better performance overall.

The human element must play a big role anyway in what you do because sometimes if the wait is short, but if I’m late for a meeting, the wait feels really long to me.

Absolutely. That’s something we call perceived waiting time. With the destination systems, if I tell you that the car that’s coming for you is Car A, you will have a tendency to stand in front of it. Whereas if you didn’t know which car, you might just stand in the middle and have to wait until one of the cars come and opens its doors. Well, that walking time, that time you’ve spent coming towards your elevator, that’s a time that might only be a few seconds, but you’re doing something and you’ve already got this idea that I know which car is coming, the system’s got me registered. It tends that people are willing to wait a little bit longer because they don’t really realize they’re waiting a little bit longer. The other things we’ve found is that when there are mirrors in the elevator lobby, they also tend not to notice the wait quite so much.