Wednesday, February 16, 2011

Elevators: the curiosity

This blog post is intended to serve as a reminder for myself as well as a teaser for everyone else.

First a bit of history of the trigger. The old elevators in the buildings in Belgium are pretty peculiar - they have no doors. Yes, if you are surprised, I was too - when I first arrived - back in Russia (and in Soviet Russia) they had the doors - either the sliding ones or closing ones. So this optimization was weird and a bit frightening.

However, over time I got used to this, and even found it kind of cool to watch the wall as in the evenings the elevator was pulling me up to the 14th floor where I live, and down to the ground in the mornings.

All is good - but the regulators came. Apparently these door-less elevators were considered unsafe by someone. I can imagine either someone got squeezed in some unpleasant way, and hence the reaction. Net result: a seemingly IR-laser based emergency stop mechanism (if you reach your hand towards the wall as the elevator is moving and cross the surface, it stops) - which is pretty cool; and the decrease in speed of the elevator.

It's the latter which is utterly uncool and is a trigger for this - it, at least perceptually has noticeably increased my waiting time in enough number of the mornings to start wondering "why".

And I started to ponder - what is the best mathematical model for expressing my annoyance with this situation in numbers ? And it seems it is a curious one, much more involved than I'd expect at the first glance.

Some reading links on the topic:

So, in short it seems to be a pretty fun modeling topic - even if we do not get into the mechanical problems and keep ourselves busy only with traffic handling problems.

The analytical question, which, after this pre-investigation I am afraid is not so trivial is the function T(v,p) - where the function value is the upper bound on my waiting time when needing to go down from my 14th floor in the morning, "v" is the elevator velocity and the "p" is the probability interval. i.e. T(1,0.95) == 40 would mean that with the 95% probability I would have to wait less than 40 seconds, assuming the speed of the elevator of 1 m/s.

1 comment:

Nighty said...

Back in high school, somewhere in the 90's, I had the opportunity to walk around at the Philips Nat-Lab in Eindhoven. They had a very cool solution for this. They called it a "belt elevator", but googling for this doesn't produce anything useful.

Basically it was a belt that continuously ran along two parallel elevator shafts: up one, and down the other. To this belt were then affixed small (think single person) "elevator cells" for lack of better word, which would always maintain their upright position and continuously pass the holes in the wall where people could get on or off. No doors necessary (I assume security was a consideration when building this contraption), and if one cell is full, you just waited a couple of seconds for the next to arrive.