Waiting: What The Best Way To Line It Up?
There's a blog-thingie about
lines going on. The question is, what's
the best way to feed lines into something like a bunch of checkout linse.
Interestingly for where the conversation
began, the Corporate HQ Whole Foods' doesn't have the
single line talked about, except for a special thing in the
takeout section.
The ultimate Big Line I've seen in Austin is at Fry's Electronics.
They very much have it down. I'm reimpressed every time I go.
A couple of comments on
Tyler Cowen's blog about it, One Line To Rule Them All:
I've never seen a good study of when single lines are to be preferred.
I have, in my Computer Performance class, but I've long since forgotten it ;-)
All I remember is that the answer is one line in most cases. One
exception, I think, involves the case where some people wait in the
feeder line for particular individual lines, gumming up the queue for
everybody else. There may be other exceptions for some kind of
feedback between lines. The above-mentioned Fry's doesn't let any of
those kinds of hangups happen, of course.
. . . he always said it didn't matter which lane you chose, your
average expected waiting time would be the same, and this was
according to the efficient markets hypothesis.
It's definitely true that it doesn't much if you take subways, busses,
or drive in N YC (or even walk, if it's close enough). It always comes to
a mean of 50-60 minutes. Spooky.
Posted by Jon Kay at June 29, 2007 04:38 PM
It takes me 45 minutes sometimes to get downtown by car less than a few miles away at most. It takes about 4 hours to get all the way to Boston. Go figure. Buses are slow and subways a bit faster. I will say, my new Maverick 5.0 gets me around town fast, but then I have to carry a seven pound chain and lock to make sure my bike isn't stolen.
Whole Foods in the new Time Warner building has two huge lines. One for under ten items and the other for more. It actually goes pretty fast with a person always directing traffic to several rows of cashiers. The worst is CVS and Duane Reade that have several cashiers and no plan for where customers stand as they block incoming traffic waiting for the cashiers to get free.
Now imagine just one line on a highway, waiting to go through the toll booth.
Oh goody! Something I actually know something about! (Like Jon, I picked it up doing Computer Performance. Be nice . . . or I'll start posting the mathematics.)
This is basic (sorry!) queuing theory. The worst approach is to require people to pick a line for a particular server, with no way to tell whether the people ahead are going to be quick or slow. Those multiple lines for the toll booths may make you feel good because they look short, but you are subject to finding yourself behind someone who has to dig thru all his pockets and all the around the car to find the toll.
The most efficient way (as in, the shortest times in the queue for everybody) is with multiple servers (cashiers, toll booths, tellers, etc.) and a single (1) queue. Then the occasional turtle doesn't inconvenience anybody except himself.
What wj said. As far as actually processing everyone in line as efficiently as possible goes, the single-line feeder queue works best. Average process time is reduced. What grates is that wait variability is almost eliminated, and cannot be affected by one's own choice.
Cowan's point is that individuals will skip such lines as they cannot improve their time-above-average with their individual choice. With a single-line primary queue, the only choice involved is whether to get in line, or not. Once in line, everyone's "processing time" becomes approximately the same (assuming the queue length is constant, but let's not niggle about side issues).
Someone who would otherwise gamble on their own choice of queue in a multiple-line setup improving their process time will often pass when that choice is removed, even though the average process time they face as a generic queue member has actually been reduced by the greater overall efficiency of a single-feeder queue. Call it ego, but their assumption is that their odds (not the result, but the odds) are always better when they can choose their own queue. They're usually wrong, but that's people for you--they perceive their odds and wait times as improved, even when they're not.
