Why it takes so long for the lift to arrive

Here I am again, waiting for the lift and asking myself why it's taking so long. Granted, someone could have blocked the door, but then the lift next door would have had to step into the breach. The lengthy wait started me wondering about how lift controls actually work. Is some artificial intelligence involved? Or is it more like artificial stupidity?

The psychological explanation

Of course, it could be that the lift doesn't take very long; it might just be me. After all, I haven't been standing in front of the doors with a stopwatch and compiling statistics on waiting times. There are multiple psychological reasons why the wait often feels longer than it really is:

• Boredom: there's nothing to do. This focuses our attention on the lift arriving (or not arriving).
• Impatience: the lift always seems to take an especially long time when I have an important meeting or am really hungry.
• Misinterpretation of events: I always notice it more if the lift takes a long time compared to when it arrives immediately. This creates the impression that it generally takes a long time.
• Cultural conditioning: everything is trimmed down for efficiency these days. We are made to believe that we're missing out if every minute of our lives isn't busy. This is even more pronounced (in German) in Germany and Switzerland.

Nevertheless, I'm sure I'm not imagining the waiting times. There must be technical reasons for them.

Algorithms for a constantly changing situation

Programmers are well acquainted with what comes next: algorithms. An algorithm is a sequence of instructions. It tells the lift which system it should follow to carry out its tasks. For example, the algorithm could be: go up to the top floor and serve all guests that want to travel in this direction. Then go to the ground floor and do the same. Or: always go to the person who is on the nearest floor to you. Or: go to the person who has been waiting the longest.

It's clear that different algorithms are quicker in different situations. A complex algorithm could calculate the best transport plan for a given situation (there's a presentation on this by mathematician Jörg Rambau (in German)) in a reasonable timescale (less than a second). But the problem is that the situation is constantly changing. While the lift is serving a floor, it receives new tasks from people who have pressed a button inside or outside the door.

This is the biggest reason for unusually long waiting times every now and then. Even the best algorithm can't know what will happen next. For example, if you're standing in front of the door and a lift going in the right direction has just passed you, you're out of luck. The lift has already determined its route and won't turn around now. That would confuse or even annoy the people already in the lift.

Which lift algorithms are efficient?

So everyone will be the victim of an unfavourable situation now and then. You might therefore ask: which algorithm is the most efficient on average, i.e. in vastly different circumstances?

Three mathematicians at the University of Vienna conducted a study (in German) to examine exactly this. The following algorithms have been empirically tested:

1. Simple algorithm: the lift travels from ground floor to top floor and back. It stops if someone wants to get out or someone is waiting to get in. It works like a public bus service.
2. Nearest neighbour: when a lift is idle, it travels to the nearest waiting person rather than stubbornly going right to the top and back to the bottom again. If multiple lifts are idle, the one nearest a person waiting is activated.
3. A variant of the above: the person who has been waiting the longest is prioritised rather than the nearest person. Although you probably have to be a mathematician to see this as a variant of the nearest neighbour algorithm.
4. Random target: an empty lift seeks out a random target.
5. Sectors: the building is divided into sectors of several levels. Every lift is allocated a specific sector. It only carries out tasks from and to these sectors, along with those involving the main entrance, which has the largest volume of people (mainly on the ground floor).

The simulation was done on different scenarios: different buildings (numbers of floors, numbers of lifts with varying capacities and speeds) and different volumes of people. The mathematicians also considered peak times. In office buildings, everyone wants to go up from the main entrance in the morning, while everyone wants to come back down in the evening.

Unsurprisingly, the simple algorithm is the slowest. By a long way. However, I was surprised that the randomly-controlled mechanism is just as efficient as nearest neighbour. And it's actually better than the sector algorithm. The problem with sector allocation is that the lift passes people who are waiting when it could just have easily picked them up. This drawback is particularly problematic at peak times. And peak times are decisive, as all algorithms are more or less satisfactory with low volumes of people.

The lift which travels to the person who has been waiting the longest is the fairest, but not the most efficient. It also potentially prevents extremely long waiting times, even though it's worse overall. Unfortunately, the study's authors don't have any data on that.

Different types of controls

The paper doesn't make it clear which principle the waiting people's calls follow. There are systems with just one button («I need the lift»), those with two buttons («I want to go up/down») and even some where you can choose the floor in the process.

Two buttons enable all algorithms to work more efficiently than one because lifts only stop when they're already travelling in the right direction. However, two-button controls can result in losses in efficiency of up to 30% (in German) if someone accidentally presses the wrong button. Logically, this can't happen with one-button controls.

If you can choose your floor, the system knows from the start which people are heading to the same destination. This information is used to minimise intermediate stops. This means reducing the journey time rather than waiting times. This is especially practical in high-rise buildings. Although this can increase waiting times, conveying capacity can be increased by 15–20%.

By the way: if the lift is voice-operated and never arrives, it's because the person is speaking in a Scottish accent, as the video below shows.

Unanswered questions

What I didn't find out was which algorithms are actually used where. What is clear is that there are very different lift systems based on their age and requirements. Self-learning systems are also being used now. They constantly monitor the number of people on different floors and their destinations and adapt based on this information. Critical peak times can therefore be managed more successfully.

So now there's just the final unanswered question on lift controls to address. Does the «close doors» button actually work, or is it just a placebo that's only there to keep you occupied while you're waiting? My theory? Lift manufacturers keep the answer a secret so that we shorten the waiting time ourselves by talking about it.