How to fix crowded elevators at work

After a long day of work, all that my friend wants to do is go home.

But many days he is held up by the office building elevators, crowded from everyone leaving at the same time.

The worst part is that people on other floors “game” the elevators and exacerbate the problem. My friend writes to me:

So I work on the 8th and top floor of my building with 8 elevators. During rush hour at night, people are so desperate to get an elevator down, that they will press up on the elevator on the 6th and 7th floor and hop on to reserve a spot for the return trip going down. This means that sometimes an elevator that gets to the 8th floor is already full.

A crowd forms on the 8th floor, meaning the next time an elevator comes to the 8th floor, it will definitely get full and be a crowded, unpleasant ride. Worse, even then the elevator will have to stop on the 7th and 6th floors for people who pressed the “down” button, and so that slows everyone down even more. As you can see, this elevator system is quite annoying and hurts people on the 8th floor the most.

How can we make it more fair? Will having 1 elevator go directly to the top floor without stopping always be helpful at this time?

It took me a long time to find out how the elevators could be routed more efficiently. But there is an amazingly simple answer. As it turns out, my friend was on the right track with his idea of having an elevator go directly to his floor.

Optimal elevator strategy

In doing research for the answer, I came across an academic paper from over a decade ago that remarkably solves this exact problem.

In the paper Strategies for Serving Peak Elevator Traffic, G. F. Newell analyzes the problem of how to schedule elevators in an office building with a moderate number of floors (5 to 20).

Newell comes up with a mathematical formulation that accounts for the wait time to get an elevator plus the riding time once a passenger is on.

Newell compares several strategies and derives an optimal elevator strategy during the busy peak hours. The answer is this:

For very heavy traffic the optimal strategy is to have an elevator serve only one floor on each trip, since this maximizes the number of passengers which can be carried per unit time. [emphasis mine]

At first it might seem strange to have an elevator serve just one floor without making other stops. But on further reflection, it makes a lot of sense.

Having an elevator serve just one floor at a time is efficient for many reasons. First, elevators are empty on arrival so people can get on quickly. Second, the elevator wastes no time in stopping at floors and waiting for people to get on: the elevator goes directly down to the lobby so people can leave. And finally, no one would need to game the system: you just catch the single elevator that services your floor, and you will get out quickly enough. It’s an incredibly simple system that can save a lot of headache and time.

In my friend’s building, another solution is readily at hand too. There are 8 elevators, so each elevator could serve one of the different 8 floors as an express during rush hour.

Even smarter elevators

I should mention there are some minor refinements in this strategy if certain floors have only a few passengers.

In that case, Newell also suggests elevators could be designed even better if they could collect data on the weight of passengers boarding from each floor. The data could be used to create a time-dependent demand curve and would result in an even more efficient elevator scheduling.

However, in most buildings, sophisticated data may not be needed. Practically there is usually a rush hour where each floor has a lot of people wishing to exit. Thus, the strategy of having an elevator serve one floor per trip will be ideal.

If the peak traffic is predominantly from or to a lobby floor, some (most) elevators should be assigned to serve this traffic in a manner such that each elevator serves only a few floors on each trip, possibly only one, seldom more than two.

This strategy might not work in a hotel setting where guests enter and leave at all times of the day, but it would certainly work in an office building with a more clustered traffic pattern.

While the math is clear and straightforward, I am unaware of any companies that implement the optimal solution. But crowded elevators in office buildings can and should be fixed.