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Assume a skyscraper and a passenger that only uses the elevators. All elevators go from the first to the last floor. Does the length of time the passenger wait (on average) depend on the floor? (i.e. is average wait time of passenger on the 10th floor shorter than that for a passenger on the 30th floor?).

  • Let's consider most common scenario: the majority of elevator designs are developed from Up Peak Round Trip Time calculations.

  • Elevator traffic pattern: down peak traffic

  • There are 3 elevators in building (1 big, 2 small). But considering that relative estimation is required the quantity of elevators I think doesn't mater.

I believe this question can rely on Queueing theory. But I can't create this tag. There is also simulation software for design of buildings and elevators.

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Yes. Lower floor passengers will have a lower expected wait time.

This is because the only way to exit the building is from the first floor. And every user of the elevator will need to exit the building at least once. This makes the first floor the most likely end point for any given passenger. Since the elevators will only move in response to a request, there will be a higher portion of waiting elevators waiting in place on the first floor. Which means a shorter wait time for a passenger on the 2nd floor as compared to, say, the 100th floor.

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    $\begingroup$ It's not that simple, because the elevator doesn't wait on any random floor. In a business building, at 5pm (when people begin to leave work), elevators will wait on different floors to optimize throughput, while most elevators will be on first floor at 8am (when people arrive at work). $\endgroup$
    – Jacen
    Nov 26, 2015 at 17:18
  • $\begingroup$ @jacen: You have made several assumptions about the elevator behavior that are not contained in the question. $\endgroup$
    – Mowzer
    Nov 26, 2015 at 22:46
  • $\begingroup$ What the OP asked and what reality is are different things. I prefer that reality be answered. During peak down times, the controllers may well select higher floors over lower ones because more people are anticipated to be there, or simply because that allows the elevator to minimize the number of inefficient up/down cycles to lower floors (i.e. might not even fill the elevator). $\endgroup$ Nov 28, 2015 at 18:11

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