Paul Makepeace ;-)

October 11, 2005

Lift game theory

Posted in: Tech

The natural reaction to seeing a lift (a.k.a. elevator) with its doors open and full of people is to make a bolt for it, squeeze in before the doors close. This to avoid the tedious wait for another lift to chug down and grind its weary cogs open.

Having recently been using some very slick lifts in a busy building it's occurred to me that this behaviour is subject to a subtle assumption about lift dynamics.

What's interesting here is that if some of these variables are changed, this behaviour of running for a soon-to-depart lift actually works against users in the sense of potentially making their journey longer. What's even more interesting is that this situation arises when there is more than one lift and those lifts run faster than your average vertical conveyor. That is, with an apparently better provision of lift service you're better off not running for it.

So how does this peculiar situation occur? Consider two lifts both in the lobby of a hotel. Someone hits the Up button and so one of lift's doors duly opens. A couple of people step in and press for floors 3 and 6. A third person a little way off spies the doors open and makes the customary dash for it, just getting in as the doors close. The new entrant selects floor 2.

You may have spotted where this is going. For the first two people, their journey is now slower having taken a passenger who's stopping before their floors. Conversely, had the third person selected floor 7 her journey would've been slower by having to stop at a couple of floors first.

What's the alternative lift catching strategy? When there is more than one lift waiting at a given floor, a faster strategy for all users is to spread themselves out over the available conveyances. This means simply allowing the first lift to close and get under way before hitting the call button. (In every lift I've ever tried this on pressing the call button is either ignored if the doors of a lift are already open, or, arguably a mis-feature in the lift's programming given this discussion, the doors of a closing lift re-open.)

So with more lifts ready and waiting a better strategy is to let the existing lift set off, and catch another. I asserted earlier that the jump-in-quick behaviour could be wrong if the lifts are fast too - how so? Even if a lift isn't ready and waiting, it may very well be soon in the case of a speedy adjacent lift (this idea does require at least one other working lift: of course it'll be quicker to join a single lift than wait for it to return). For example, a second lift on the third floor being called to the lobby. The wait time for the call may very well be less than the cumulative waiting for the other occupants' stop-off on the ascent. This effect is probably more pronounced for those working on higher floors who have probabilistically more to lose getting into a crowded lift.

Posted by Paul Makepeace at October 11, 2005 14:15 | TrackBack

You'd have loved it at HSBC, then. I worked in their big building in Docklands earlier this year and found the lifts fascinating. Much more interesting than my actual job there, although that probably says more about working for a bank than it says about lifts.

Over 40 or so floors, the lifts come in banks. All lifts stop at the ground floor but then only cover a limited range of upper floors. To get from, say, the 11th floor where I worked to the 33rd floor, you would have a choice of routes, all of which would involve changing lift at some point.

The upper floor lifts had a top speed of something like 7 metres per second, according to the display screens inside. It was quite amusing to see the display screens blue-screen-of-death'ed on occasion. Didn't seem to affect lift operation, luckily.

Don't know how the lift software worked but I suspect it was some kind of evolutionary or neural net type program.

It did often work out better to miss a crowded lift and get the next. That strategy could just as easily fail, though, if a load of people get in the lift you've waited for. Or if everyone in the lift busy lift gets off at the same floor - more likely than you'd think, given that often groups of colleagues travel together to meetings, lunch, etc.

Other variables are that some floors are far more popular than others (eg gym vs trading floor vs canteen); certain times of day (eg lunch time) are busier than others; upper bank lifts are faster than lower bank lifts (no idea why)

Anyway, I used to get a kind of perverse enjoyment out of being able to just wedge my foot in the door of a nearly-departed lift and seeing all the ever so polite bankers trying to restrain themselves from tutting and muttering out loud. :-)

Posted by: Adrian at October 11, 2005 17:26

In Takashimaya (massive 14 storey department store) in Shinjuku you enter on the 2nd floor (with 3 floors below you) and the first set of lifts are so busy you are always better off taking the first available lift, even if it's going down. In fact, if you can be bothered, the escalator is faster still for the first 8 or 10 floors. What happens is the lift arrives on the 2nd floor full of people coming up from the 3 floors below it, or it stops on the way down, or it misses the floor entirely because the lift detects it's too full to take any more passengers. Basically it's very annoying because I only ever want to go to HMV or the restauarants on the top three floors :-/

Posted by: Nik Makepeace at October 15, 2005 10:03
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