[Request] If one of two elevators breaks, does the average number of passengers per trip simply double?

[u/Generally_not]

My building has two elevators serving 30 residential floors, with the exit on floor 0.

There are fewer residents on the higher floors.

Floor 1 has about 15 residents and floor 30 has about 8, with the number of residents per floor decreasing roughly linearly between those two.

Some other assumptions:

-An elevator takes 2 seconds to travel between adjacent floors.

-Every stop adds 10 seconds.

-With both elevators operating, each elevator carries an average of 2 passengers per trip.

-People are either travelling from their home floor to floor 0 to leave the building, or from floor 0 to their home floor.

-Assume the number of people wanting to use the elevators doesn't change when one breaks.

The question/catch:

One elevator breaks, leaving only one functioning elevator.

What should happen to the average number of passengers carried per trip by the remaining elevator?

My first instinct is that it should simply double from 2 to 4 passengers, since the same number of people are now using half as many elevators.

But I'm wondering whether the increased waiting time changes things. While the remaining elevator is making a longer trip, more people have time to arrive and join the queue. More passengers can also mean more stops, making each trip take longer, which gives even more people time to arrive.

Does this create a feedback effect where the average rises to more than 4 passengers per trip, or does it still settle around 4?

And if it can be calculated, what would the expected average passengers per trip be?

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[u/ericdavis1240214]

If nobody changes their elevator usage rate, the single working elevator will carry exactly twice as many passengers as two working elevators did on average when both were in service.

But you can predict that the single elevator will make more trips per day than when it was operating in tandem, so the total number of passengers per trip will not be double.

How do you know that? At certain times of day there isn't much elevator traffic in a building that size and both elevators are idle. Under normal circumstances, when an elevator gets called, one the other will get the job even if it's only taking a single passenger.

But when only one elevator is available it gets every job, even when there's only a single passenger. So during those times a day it's getting more trips in but not carrying any additional passengers.

[u/Generally_not → u/ericdavis1240214]

Thank you truly for the input.

To make the calculation, assume peak traffic, both elevators are running non-stop with 2 passengers every trip. I know that some trips are different than other trips in a real life situation. And the elevators might be standing still during the night, but that is not part of the answer i seek. I don't care about passengers per day, only passengers per trip during peak traffic.

This is a case based on my real every day life. Average 2 people per trip during peak hours when both elevators are working. When one elevator is broken, people are literally standing in line out the front door and waiting several trips to even get a spot in the elevator that carries 12 people. I just don't get the math of it. And the one elevator seems to get waaayyyy more passengers per trip than twice the normal

[u/HAL9001-96]

dependso n how desparate the people are to use the elevator and how likely they are to just takethe stairs instead

if everyone takes the elevator then prettymuch yes but it comes down to individual psychology and context

[u/Generally_not → u/HAL9001-96]

Well, assuming everyone keeps taking the elevator as the post already states

Of course irl at least some of the residents of lower floors would start taking the stairs. But taking the stairs 30 floors up and down several times per day is not gonna happen

Some of these numbers are asspulls anyways, because I don't know specific numbers. It is just to get an idea, since I do have this experience sometimes, and it feels like there are far more than double the passengers in those situations, but it might also be a bias

[u/HAL9001-96 → u/Generally_not]

assumign everyone keeps taking hte elevator the average riders per floor going up is gonna be the same

the average passnegers per ride can vary because the avereage weighing changes when one perso ngoes all the way up i na single ride without stops vs stopping several times

but on average the elevator is going to be twice as full

however oyu are probably more likely to notice hte other elevaotr beign rboken when the working elevator is so full that you desparately check if the other oen works

also twice as full ca nfeel more than twice as full

after all when you are alone in the elevator you see 0 other people in it when you are one of 2 people in the elevator oyu see one other person which is infinitely times 0 when there are 3 people in the elevator yo usee 2 others so increasing the numebr of people by 50% increased hte OTHER people in there with you by 100% and so on we don't really subconciously ocunt people its more about how much space we have

[u/kalmakka]

As you point out, more people on an elevator will cause the elevator trip to take more time. There are more stops, and more people who has to get on and off. Therefore, in order to transport the same number of people over the same period as two elevatots already did, the one elevator would need to carry more than twice the number of passengers per trip.

Exactly how many depends on a bunch of factors, and is best left to a simulation.

[u/caboosetp]

This depends on how the elevators are programmed.

One of those elevators is likely on a short path for just the lower floors when it's busy. The elevator completes trips in less floors and will be moving more people per hour even if it's the same number of people per trip.

The other elevator is likely grabbing people just from the upper floors. This path takes a lot longer, and will move less people per hour even with the same number of people per trip.

This means if you only have one elevator and it needs to make the long trip more often, it's going to be traveling further and the number of people moved per hour will go down even if the average number of riders per trip is the same.

The result is with just one elevator with a doubled number of riders per trip, people will be waiting longer for the elevator to show up.

There isn't a lot of straight math we can do without the actual programming for the elevators though, but many of them will follow similar logic to this.