Statistics Question -> Elevator Question

[GreenPrint]

I don't really know how to phrase this question. But what floor in a building takes the less time to wait for an elevator?

Like for example. Say that there's a building with two elevators in it. Each floors are the same height. Each elevator travels at the same speed. The first floor has a high probability for the elevator to be at that floor because it't the floor that all people from outside are most likely to call the elevator from to get onto floors above. Assume that the elevator has equal probability to be at any of the other floors except the first one.

My initial thought that the elevator would have less wait time on the middle floor or perhaps a floor closer to the bottom. I believe this to be so because the elevator can only be called half the length of the building.

For example if you called the elevator on the first floor it's possible the elevator is on the top floor and has to travel down the whole building. In the middle floor the greatest distance that the elevator could travel is half the building.

So what floor would have the less wait time? Like I don't know the exact figures or anything but just thinking about it I would assume it's the middle floor or one closer to the ground because of the fact that the elevator has a high probability of being on the first floor.

Thanks

 

[Simon Bridge]

It's an interesting question that has been the source of a lot of study and simulations.

eg.
http://www.tandfonline.com/doi/abs/10.1080/10798587.2010.10643067
http://stackoverflow.com/questions/16079949/big-buildings-elevator-number-and-work-process
... etc. Lots of papers considering different statistical models etc.

As well as what you have considered, the problem also depends on the programming for the elevators - will a car stop at every floor where someone has called it or will it leave some to another car? When a car is empty - what happens: does it just sit at the last floor waiting to be summoned or go to a specified parking level or what?

A lot of the studies are designed to help make these policies so that people don't have to wait all that long.