Scientifically, You Probably Are in the Slowest Moving Line

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News Posted: Thu, Dec 23 2010 9:40 AM
As you wait in the checkout line just before Christmas, your observation is correct. That other line is moving faster than yours. That's what Bill Hammack (the Engineer Guy), from the Department of Chemical and Biomolecular Engineering at the University of Illinois - Urbana "proves" in this YouTube video.

The video was released just in time for the final days of the holiday shopping season, as a lesson in queueing theory for the holiday season. Using the work of Agner Erlang, a Danish engineer who helped the Copenhagen Telephone Company determine the best level of service with the minimum number of operators, Hammack shows stores can determine the best number of cashiers in a store.

Ironically, the most efficient set-up is to have one line feed into several cashiers. This is because if any one line slows because of an issue, the entry queue continues to have customers reach check-out optimally. However, this is also perceived by customers as the least efficient, psychologically.

It does indeed imply that Fry's Electronics checked with Hammack before starting their practice of using one queue and multiple checkout lines.

In fact, scientifically, it can be proven that the other line is more likely to move faster than your line.  As shown in the video, in a system with three checkout lines, 2/3 of the time, the other lines will move faster than yours. Watch the video below.

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Inspector replied on Thu, Dec 23 2010 12:11 PM

LOL, nice thinking. I am one of those that will say making one line will make it longer :P

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LLeCompte replied on Thu, Dec 23 2010 12:46 PM

this makes a lot of since. Very interesting video.

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Sociology is awesome?

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CSauve replied on Thu, Dec 23 2010 7:46 PM

The title of this article is incorrect. The conclusion that the video comes to is "You are likely NOT in the FASTEST line." Since there are three lines, you could be in the 2nd fastest or the slowest.

In the article where you say

"In fact, scientifically, it can be proven that THE OTHER LINE is more likely to move faster than your line."

this should actually read;

"In fact, scientifically, it can be proven that ONE OF THE OTHER LINES is more likely to move faster than your line."

This article falls far short of what can be called "science".

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CSauve replied on Thu, Dec 23 2010 7:58 PM

Also, you've been slashdotted (mainly because timothy doesn't read half the crap he puts on the frontpage). Be prepared for the wave of people to pick apart this article.

Another problem with your conclusion is that single queues are not actually more efficient. This can be best spelled out by Idarubicin:

http://science.slashdot.org/comments.pl?sid=1923206&cid=34656506

What putting everyone into a single queue does is ensure that the distribution of waiting times is very narrow -- everyone will spend very nearly the same amount of time in the queue before reaching a cashier. However, this setup will almost always impair overall checkout efficiency (measured in customers per hour) by some amount; the average waiting time will be slightly longer. Each time a customer clears the cash desk and the cashier has to wait for the next customer to arrive, time is lost. Since the customer can't unpack his basket while the cashier is finishing with the previous customer, time is lost. It gets worse if a customer at the head of the queue doesn't realize that a cashier is available; everyone stands around waiting that extra bit of time. Yes, this can be offset by having a staff member playing shepherd, but that's extra expense for the store (and wouldn't it be better to have that employee actually manning a cash register?). As well, the store needs to be able to maintain a larger open space by the cash registers through which people can move, to get from the head of the queue to the checkout.

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RCook replied on Thu, Dec 23 2010 8:02 PM

@CSauve Thank you for being sane. My mind boggles at the stupidity of the people who write these headlines. Or maybe it's dishonesty, because exaggeration sells, right? I only came here because I was surprised at the word "slowest." If they had written "not the fastest" I would not have come here. But now I know they are idiots.

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i'm always fooled by article titles lol

"The old appeals to racial, sexual, religious chauvinism to rabid nationalist furver are beginning not to work. A new consciousness is developing which sees the earth as a single organism and recognizes that an organism at war with itself is doomed"- Carl Sagan

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This is exactly what is wrong with society. Slow people vote for people who lie, then they end up spending Millions of dollars on reasearch such as this!

So they got a huge gvment grant to sit around smoke a pipe and watch the first scene of Office Space, just to figure this one out? :P

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Yes @ office space reference

"The old appeals to racial, sexual, religious chauvinism to rabid nationalist furver are beginning not to work. A new consciousness is developing which sees the earth as a single organism and recognizes that an organism at war with itself is doomed"- Carl Sagan

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RBernstein replied on Thu, Dec 23 2010 10:20 PM

The conclusion is actually completely wrong, not just poorly stated. Most of the times you wait in line, you are in one of the faster lines. But on average, you are in an average speed line during any given minute you wait in line.

For a simple example, consider three lines that take one, two, and three minutes per customer. In a 12 minute period, 12 people go through the fast line, six go through the middle line, and four go through the slow line. So in a total of 36 line-minutes, 22 customers go through. So you have a 55% chance of being in the fast line, a 27% chance of being in the middle line, and an 18% chance of being in the slow line. On average it takes about 1.6 minutes to get through each customer.

Counterintuitively, even though only one third of the lines are moving fastest, and one third of the people standing in line at a given moment are in the faster line, more than half of the customers wait in the fast line. Of course the exact proportions depend on the exact distribution of delays, amount of stuff people buy, and other speed factors.

Now let's say there are usually four people in each line. The total wait plus checkout times are four minutes in the fast line, eight minutes in the middle line, and 12 minutes in the slow one. So the average customer spends 0.55*4 = 2.2 minutes in fast lines, 0.27*8=2.2 minutes in the middle one, and 0.18*12 = 2.2 minutes in the slow one, or a total of 6.6 minutes waiting, and therefore has a wait time better than someone in the middle line.

Realistically, some customers might look at how much stuff other customers are holding and how fast the clerk is working, so the faster lines might actually form a longer line. If that happens, you will both be in faster-moving lines on a disproportionately large number of visits, and also spend a disproportionate amount of time in faster-moving lines.

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mhenriday replied on Fri, Dec 24 2010 12:53 PM

You chaps are all wrong ! The slowest queue is the one I'm standing in. Thus, if you see me standing in one line, your optimum move is to move to another. If you could only do so before I got to that particular queue, you could help me out as well !...

Henri

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amino95 replied on Fri, Dec 24 2010 6:43 PM

Where is the evidence that people prefer the uncertainty, delays, and line cutting of multiple queues over the equity of a common queue that may appear longer?

Anyone who has shopped in a busy store knows from experience what it's like to be stuck with an indefinite delay behind someone trying to write a check, contesting a price, or processing a pile of coupons or other complexity. Give me the shared queue any day.

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amino95 replied on Fri, Dec 24 2010 6:45 PM

bsdect wrote "Those that aren't in a rush will get into any line."

Not true. Standing has a cost, both in time and expenditure of energy. People always do a cursory shop for shorter queues, if not an exhaustive one.

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JWernicke replied on Sat, Dec 25 2010 3:05 AM

I am also one of those poor souls who always get shafted no matter which queue I pick. Statistics and overhead be damned. Give me the shared queue (and one less wrong choice to make) plz k thx.

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yadda replied on Sat, Dec 25 2010 8:43 AM

Monty Hall strikes again. We are a selfish bunch. Off the cliff we go! No complements please.

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Dave_HH replied on Sat, Dec 25 2010 12:22 PM

RCook, feel free to use the exit. The headline was written in jest and the entire article has an entertainment factor about it too. In other words, lighten up. Same to you Rico-Suave. :)

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JBraun replied on Wed, Jan 5 2011 11:21 PM

Loved it. I know Bestbuy uses the single queue and sure enough when I first stepped in line I felt it was going to take forever. Great explanation on why my feelings were wrong.

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amino95 replied on Wed, Jan 12 2011 9:37 PM

And people will wait behind a dozen people in the "express lane" before standing behind two in a regular line.

The same holds true in airports, where they will eagerly sign up for an extra ten minutes in an obviously longer "frequent flyer / first class" lane, believing that the branding will somehow make it better.

Actually, the same holds true in moderate to heavy traffic on the highway. In the States, hordes will flock to the left lane expecting expeditiousness of snappy drivers only to crawl along for most of their trip with all the other sheep. This holds true even for daily commuters who repeat the same route at the same time of day for years at a time.

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