elevator arithmetics

I am fascinated by elevators. Each of the many times a day I employ one of the four means of horizontal locomotion in my workplace, I think about ways to further optimize speed of transportation, overall throughput or waiting time. My deliberations have nothing to do with my general unease about awkward situations involving co-workers, but date back to my first independent living experience in (or better said, on top of) an old peoples home. The only way to reach the ground floor was to traverse, by means of lift, 5 floors of old peoples home, smell of fumigation included.
The four top-notch high-speed hoists that now ease my daily displacements are a far cry from the sole elevator in front of whose door I remember often having waited for the better part of 10 minutes. Something good has come out of the sufferance, though. Having spent so much time awaiting (and understanding) the lift, I am now well equipped for elevator analysis.

Many people neither understand nor appreciate the two-tier elevator button system, by which one can indicate whether one wants to go up or down. One can only wish them to never have to wait for ones lift to grind its way up through five floors of a residence, taking a 1 minute break on every floor, only to do the same again on its way down. The two-button system is constructed to avoid redundant stops for multiple persons showing up after each other, on the same floor, when the lift travels to another floor in-between. The following situation exemplifies. Person A, wanting to go down, stops the lift on its way up. Person A gets on-board, and the lift continues its journey upwards to fetch person B, after which it starts going down. In the meantime, person C shows up on the same floor where person A got on. Had the lift initially not stopped because the two-tier button indicated that that A wanted to go down, and fetched person B directly, person A & C could have boarded in only one, rather than two, stops.

The above behaviour is all the more nasty the longer a lift stops on any given floor. A well placed door-closer button helps in situations in which the lift has been accidentally stopped (or colleagues change heart and/or continue chatting). This is the more appreciated the longer it takes for the doors to close; memories of the door-inhibitors in my first lift still let me lay awake at night.. 20 seconds ARGHHH… In my current workplace, the door closer button certainly features prominently on top of the ranking of most pressed buttons, even above the cafeteria one. Why this is so is everybody’s guess, but possible explanations are that this is an expression of peoples general unease of the elevator situation, or the haste with which business is conducted nowadays.
What I have been wrestling with, though, is whether the door closing buttons make an actual difference. My inbuilt clock tells me that the door does not close any sooner, despite repeated button pushing. I intend to investigate the matter, by way of stop-watch, shortly.

Once these rather trivial issues are addressed, one can get down to the high-art of elevator optimization.

Having multiple cabins, the responsible lift optimizer should not simply leave the lift where it stops. It clearly makes no sense to have more than one cabin waiting on the same floor, except in exceptional circumstances. Instead of leaving them to linger alongside, it would reduce waiting time for people on other floors, if a lift was waiting for them there already. By rule of thumb, a good approach would be to preposition cabins equidistantly from each other, such that the waiting time on any floor is minimized.

While this gives already a quite good result, there is still some room for manoeuvre. The equidistance scenario is only the best solution if people appear randomly on random floors. However, experience shows that that the lift load of different floors vary over time. Statistical analysis of past demand, can send lifts to those floors where demand has been highest around this time in the past.

The elevator enthusiast’s conundrum heads to its daily climax between 12.30-14.30h when one lift is cut off from the main system, to ferry passengers between the ground floor and the cafeteria only. Ostensibly this is to prevent guests entry into the organization, but one wonders why nothing is done about lunchers trying to penetrate from the cafeteria on. Since the measures’ merit for security is shaky at best, I wonder if they at least contribute to the systems’ efficiency, e.g. by providing extra capacity where it is needed most.
At first glance the measures seem to be a distortion. Capacity is reserved for one trajectory, to the detriment of all others. While those travelling from bottom to the top (and back), enjoy a quick ride, everybody else disposes only of three, instead of four, lifts at the crucial lunch time, when most people undertake their displacements.
But there are also reasons supporting the arrangement. Due to the high passenger volume from outside the trajectory ground-floor attic would be in constant demand anyway. This means that these resources are not diverted from the rest than would be the case under the normal arrangements. But the fact that the special lift cannot stop in-between means that unnecessary halts are avoided. Since the special cabin is almost always full, these stops would not serve any purpose, since nobody could get on.
An additional benefit is that by reserving resources for a trajectory in high demand, overall waiting time is reduced. Since a lift cannot know how many people are waiting when the button is pushed, equal treatment of all floors would prejudice a majority. It is better to go and get the 10 people downstairs than the single one on the second floor.

The ultimate measure to unload the system is to take the stairs though. A variant of this is to refrain from calling the lift wherever it suits, but to take the stairs to a high volume floor where the likelihood of getting a “free ride”, with someone who was there already, is higher. Practically, this is what I do in the morning after storing my bike in the garage on P1. Instead of calling the lift and divert resources, I climb to the ground floor, where almost everyday someone is getting on the lift anyway.