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Math Businesses Science

Scientifically, You Are Likely In the Slowest Line 464

Posted by timothy from the why-to-shop-online dept.
MojoKid writes "As you wait in the checkout line for the holidays, your observation is most likely 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 video. 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."
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Scientifically, You Are Likely In the Slowest Line More

Scientifically, You Are Likely In the Slowest Line

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  • Please, please, someone forward this to Jim Sinegal.

    • Re:Costco (Score:5, Insightful)

      by jschen ( 1249578 ) on Thursday December 23, 2010 @07:47PM (#34656508)
      Let's think about this a bit first. At a place like Costco, you may be trying to feed 20+ registers at a busy time. In terms of average wait time, it's better to have each line constantly full rather than to have someone have to move over to a register and start putting things up on the conveyor belt only after someone else cleared said register. One solution to this is that you specify have exactly one customer waiting behind each register, starting to load goods onto the conveyor belt. First of all, you now have the exact unfairness issue that multiple lines causes since one person might be behind someone with one item, and another behind someone with dozens of items. Might as well let them pick lines since you have the same result anyways, and don't need as much space dedicated to people forming a long line. If you still want to consider a single line, what about those far away stations (there must be at least one register 10 stations away or more)? And what if someone at one of those far away locations only has one or two items? Maybe we should switch to two customers behind each register before forming a big line? And how does a single line affect traffic in the store when you have 40+ people jamming up your main aisle on one side? Maybe we should have a line on each side? Or maybe it's best to let the customers sort through the situation, and just focus on having all open registers used to capacity, as currently is done.

      • Single queues have further disadvantages. It takes time to get to the newly opened register. About 1 customer in 5 is a doofus too slow to respond to the opening until someone starts poking him. Some stores even have to appoint a person (sometimes two) to point out the opening and get the head of the line moving (thus adding to overhead and the price the customer pays).

        Single queues to multiple checkouts work well when the number of checkouts is small and they're close together, and it especially helps if t

        • Re:Costco (Score:5, Informative)

          by pz ( 113803 ) on Thursday December 23, 2010 @10:26PM (#34657452) Journal

          Single queues to multiple checkouts work well when the number of checkouts is small and they're close together, and it especially helps if there's a tendency for occasional customers to take much longer than the average. (This happens when there are price checks, arguments over prices, or [in airports] itinerary changes.) It isn't a reasonable option for a WalMart with 40 registers.

          And you've actually done the theoretical study of this? People have. Many people. There's even a subspecialty of operations research / computer science / psychology called Queueing Theory.

          And the answer really is that a single line works best, even when you include all of the other factors for nearly every situation. If you have a prompter who can anticipate shortly before a given teller will be free, they can even eliminate the travel latency to get from the line to the teller. Naturally, there is an upper limit for fanout, but then it is still the case that a larger queue feeding multiple tellers is more efficient. Always. It is never, ever more efficient to have one line per teller. Ever.

          Please, please, please, someone tell the people at US Passport Control about this. The prompter agent always seems to work to keep the small queues in front of each control agent as long as possible when they should be close to zero at all times.

          The US Post Office seems to understand the idea, for which I am grateful. Most banks understand this idea as well.

          • Re:Costco (Score:4, Interesting)

            by bbtom ( 581232 ) on Friday December 24, 2010 @12:01AM (#34657828) Homepage Journal

            Please, please, please, someone tell the people at US Passport Control about this. The prompter agent always seems to work to keep the small queues in front of each control agent as long as possible when they should be close to zero at all times.

            The US Post Office seems to understand the idea, for which I am grateful. Most banks understand this idea as well.

            Passport control is an interesting one. Perhaps it's because I'm a UK citizen and I'm biased, but UK passport control always seemed slightly better organised than US in terms of queuing. At LHR Terminal 3, they just have one massive queue for UK/EU passport holders and one massive queue for foreign passport holders, then have a cluster of agents at the end, all close together.

            In SFO and BOS, they have a queue for US and a queue for foreign, then they have fan-out queues for each agent. As you say, this is bad queuing theory.

            The strange thing is that even though the LHR queue is usually enormous, it seems to get processed extremely quickly. Perhaps it's just subjective and my brain is playing tricks on me (the combination of spending 6-10 hours in a tin box, followed by the feeling that "London! Home!" etc.), but it would be interesting to see how this works comparatively between UK and US.

            I wonder whether the bottlenecks that get built into airport (and international trains like Eurostar) terminals are deliberately built-in or planned around. I mean, there may be a bottleneck at passport control in order to make sure that people go through customs at a steady speed, or to provide an opportunity for CCTV operators to keep an eye on the queue to see if anyone is acting oddly.

            Or, as when I last flew to Boston, so some idiot can dance around, making a nuisance of himself and swear at the TSA/ICE guys, while the polite group of Brits stand in line with a mixture of embarrassment (at someone being a dick in public) and fear (that an armed TSA/ICE guy or cop is going to shoot the dude when he does something unpredictable: 'cos, you know, we've seen Westerns and cop shows).

      • Re:Costco (Score:4, Insightful)

        by rolfwind ( 528248 ) on Thursday December 23, 2010 @10:10PM (#34657382)

        A hybrid system. Do the same thing we do at our self-checkout line, there are 2 opposing sections of 3 kiosks facing eachother across open space. One line forms (usually), and the next-in-line goes left or right depending on what register is open.

        R| |R
        R| |R
        R| |R

        So, at a Costco, have 2 registers face eacher (conveyor belts across from each other in a space 2.5 carts wide) and use those line seperators airports and banks use to make a one cart wide line leading to both (this needs to be no longer than a few feet). Then a person can choose which line to join, and then can choose whether to go left or right -- probably as they see one or the other side paying sucessfully.

        Alternatively, at my Ikea, there are two registers, one right behind the other. So when a single line forms, the guy ahead of it can skip to the front register if free or it looks to be free. Same system as I described, basically.

        People still can make a choice (while forced queing would piss them off even if faster), get some of the benefits of a faster line if some grandma decides to pay with a check, and won't have any of the other hassles you describe like a massive, single long line.

  • Comment removed based on user account deletion

  • What's so new about single line queue? (Score:3, Informative)

    by BLToday ( 1777712 ) on Thursday December 23, 2010 @07:24PM (#34656302)

    I thought we've verify the efficiency of single line queue for many years.

    • Re:What's so new about single line queue? (Score:5, Informative)

      by Random BedHead Ed ( 602081 ) on Thursday December 23, 2010 @07:27PM (#34656338) Homepage Journal
      This is the norm in Britain. And it works. But trying to get people to do this in the States is like pulling teeth.

      • Re: (Score:3)

        by Binestar ( 28861 )
        Borders does this
      • Every post office and bank in my area does this, along with book stores, most of the eateries, airports, and nearly anywhere else. I hardly ever see multiple lines, regardless as to venue, in the last few years - in the states.

      • Yeah we do this on self checkouts here. It seems obvious that it's the most efficient method.

      • Some places yes but I wouldn't say its "the norm" - certainly none of the supermarkets does it and that's where it pisses me off. Stand for 15 minutes in a queue only for someone to open a new till for someone who's hasn't waited at all.

        I think as a nation, Britain has a real etiquette about queuing and I know I feel a real injustice when someone gets to skip it.

      • I usually see a chaotic oscillation (Score:5, Interesting)

        by presidenteloco ( 659168 ) on Thursday December 23, 2010 @08:10PM (#34656708)

        between single-line multi-server queue and multiple queues.

        This occurs in fast food restaurants with the row of cashiers.

        This is because some people are "blind" to the fact that there is a single line
        situation in effect. These people can be divided into:
        1. The generally oblivious. Mindless automatons or cellphone talkers.
        2. The socially clueless. Somewhere on the autism spectrum, they don't
        understand that queuing is a complex social interaction with rules and etiquette.
        3. The obnoxious. Sees the situation but overtly butts in front to stand in front
        of one of the cashiers directly, thus forcing others to break rank and sneak in
        behind him, since the discipline is shot.
        4. The "will be first up against the wall when the revolution comes" devious, who
        form their own line like #3 but do it by carefully assessing the situation then actively
        pretending that they are in category 1.

        So it goes to multiple queues for a while, then some opportunist realizes they
        can line up ambiguously in between two cashiers to snag whichever comes open
        first, and we're back to single-line til a type 1 to 4 person arrives.

      • I always found it annoying because the British queues at say an airport were normally out the terminal door while the continental queues were half the size because they formed 2 queues for the 2 airline reps at the front. Same for Tesco self service tills. We form 1 long queue in the middle for four tills (2 tills per bank, so there should be 2 queues) hoping to take the next available computer till. While the trolley queues are all single file. Are you saying then a single file is better for both exampl

    • Re: (Score:3)

      by icebike ( 68054 )

      I thought we've verify the efficiency of single line queue for many years.

      Me too.

      I further doubt that most people still think single queue, multiple servers is perceived by customers as the least efficient. People have seen it work well at banks, Airport Security, Post offices, and other places. (Did I just say post offices were efficient?).

      The bad rap it gets is usually from the jump-in-front people who perceive the lack of an opportunity to queue-hop as removing one option under their control. Just often enough to enforce this belief, the die-hard queue hopper will get servic

  • Lots of locations in the US have discovered this. Fry's, REI, and just about any bank or credit union, to name a few.

    • Re: (Score:2)

      by EdIII ( 1114411 )

      To add, I don't think it is perceived as slower psychologically either.

      With Fry's they actually have a person directing the next customer in line to the next available cashier. First time I encountered it, I perceived it as faster, due to an increased appearance of organization.

  • I noticed they did this at fry's. Probably for this reason alone.

    • Re:Fry's (Score:4, Interesting)

      by pspahn ( 1175617 ) on Thursday December 23, 2010 @07:40PM (#34656460)

      I'm sure the fact that they can have a more impressive impulse purchase rack also factors in. They can have a greater variety of items by not having the same small selection of stuff at each register.

      Microcenter also does this (at least here in Denver), though it's a much smaller store than any Fry's I've ever been to (even the old ones).

      • I remember an article (probably here) ages ago about Tesco club cards etc. Tesco stopped doing the impulse crap after their research showed it wasn't actually any use. It does give a slightly classier feel if there aren't stupid sweets at the checkouts.

  • Paging Monty Hall (Score:5, Funny)

    by schmidt349 ( 690948 ) on Thursday December 23, 2010 @07:26PM (#34656330)

    See, you have three checkout lines to choose from. You can't see the register from where you are, but at two of the three lines the cashier is a goat...

  • Ironic? (Score:5, Insightful)

    by timeOday ( 582209 ) on Thursday December 23, 2010 @07:27PM (#34656340)

    Ironically, the most efficient set-up is to have one line feed into several cashiers... However, this is also perceived by customers as the least efficient, psychologically.

    That's a shame, since it's obviously the most fair, and eliminates the annoyance of jockeying into different lines to maybe get a faster one. I guess people like the chance of getting lucky occasionally, even at the cost of utility (average wait time) and fairness? Hmmm, our economy makes so much more sense now.

  • Obvious (Score:5, Insightful)

    by Arancaytar ( 966377 ) <arancaytar.ilyaran@gmail.com> on Thursday December 23, 2010 @07:27PM (#34656346) Homepage

    This is because if any one line slows because of an issue, the entry queue continues to have customers reach check-out optimally

    How is that ironic? Doesn't everyone know that? There is no customer configuration in which a single queue isn't more efficient than multiple queues, in average or worst-case waiting time or throughput. You could probably model that and prove it mathematically without needing simulation or experiments.

    • Agreed, I think this was very well understood a long time ago.

    • The case where single queue is going to be worse is at a place like Wal-mart, where there's going to be quite a few people hopping in ahead of you without repercussion (and the line is usually going to be hundreds long at any given time). They don't use single queue because they don't want to hire security to keep people out of the front of the line.
    • For reasons why the "single-queue" isn't as efficient, see this comment [slashdot.org]

  • I always thought the one line/multiple cashiers was the most efficient, that way you don't have a single point of failure.

    Before this became popular, every time I went to the Best Buy checkout was the exact time somebody wanted to argue over the fucking extended warranty on their $50 DVD player.

  • I rather like the self service lines. Maybe it's just me but the baggers always put my squish ables in with my canned goods it seems like.

  • Woot! Microcenter in my area has this ... though these days it still has long lines due to inefficiency of the security locker for small & high value products being purchased by newbies.

    Still the last good place in my area to sell good and sometime hard to find odd toys & parts locally. The impulse buy at the the single queue is harder to resist though.

    Santa Baby, a Fryes in my state Please!

  • Scientifically, the title is bogus (Score:5, Informative)

    by Galestar ( 1473827 ) on Thursday December 23, 2010 @07:36PM (#34656416) Homepage
    Watching the video, the conclusion that the video makes is "...You are likely not in the fastest line".
    That does not necessarily mean that the reverse (the title) is true -- and yet they somehow jump to that conclusion with the title "...You are likely in the slowest Line."

    Can we get some people who actually understand this magical thing called "logic" to start editing Slashdot?
  • I tried positioning myself between two queues at the checkouts of my local supermarket to try to merge the lines, someone behind me asked which line I was in and when I replied "both" they sure did give me the stink eye. People just don't want to act in their own best interests.

  • Incorrect headline (Score:3, Insightful)

    by matthewncohen ( 1166231 ) on Thursday December 23, 2010 @07:39PM (#34656436)
    The video actually says that, mathematically, you are likely (2 out of 3 times) not to be in the fastest line.

    In his example of three lines, there is still a 2/3 chance that you are not in the slowest line. So unless "one in three" has become "likely," the headline demonstrates a failure at basic maths.

  • Finally! I love the idea and I thought this should be done for all lanes since I first stood in line for a self checkout machine. Sure the queue looks long but the checkout speed is optimized. Supermarkets, certain retailers and home improvement centers frequently feature self checkout lanes that are fed by a single line. Even if a person has a hard time using the machine, you are pretty much guaranteed the others are speedily checking out and will be done in minutes.

    I have always thought it stupid that man

    • Supermarkets, certain retailers and home improvement centers frequently feature self checkout lanes that are fed by a single line. Even if a person has a hard time using the machine, you are pretty much guaranteed the others are speedily checking out and will be done in minutes.

      Ditto. The "pretty much guaranteed" checkout time is the sole reason I use self-checkout whenever possible.

      Ron

  • You're likely not in the fastest... (Score:5, Insightful)

    by Idarubicin ( 579475 ) on Thursday December 23, 2010 @07:46PM (#34656506) Journal
    You're likely not in the fastest line (when compared to your neighbors), but -- unlike the poorly worded story headline -- you're equally likely not in the slowest line. Consider a situation involving three queues: the one you're standing in, and the two (one on each side of you) that you can readily observe. Assign a random speed to each queue/cashier. Do this multiple times. Look at the results. On average, and entirely unsurprisingly, one time in three you'll be in the fastest line; one time in three, you'll be in the slowest line. (And in the remaining third of cases, you'll fall in the middle.)

    What's this mean? Two thirds of the time at least one neighboring line will be moving faster than you, and you'll curse and stew and froth about your terrible misfortune. But look on the bright side -- two times out of three, at least one of the neighboring queues will have exactly the same burning jealousy towards your swifter, more efficient checkout.

    Ironically, the most efficient set-up is to have one line feed into several cashiers.

    Alanis Morissette called; she wants her misused word back. Anyway...the above statement ain't necessarily so. 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.

    In other words, the one-queue system is less efficient in terms of staff costs, less efficient in terms of average customer waiting time, and less efficient in terms of use of floor space. The only advantage is the one alluded to -- it eliminates the slow cashier/slow customer/bad luck penalty, and ensures that everyone has roughly the same wait. (And for that, I actually do prefer this system -- but I don't pretend that it's really more effiicient. I accept that I'm paying a small premium in average waiting time - and writing off a chance to ever be in a lucky fast line - to avoid the risk of occasional long waits.)

    • On average, and entirely unsurprisingly, one time in three you'll be in the fastest line; one time in three, you'll be in the slowest line.

      While I agree with the rest of your post, this isn't quite right. In actuality, each person picks a line based on how long it is at the moment. By this criteria, the probability that you will pick a given line is proportional to the speed of the line, and you will most likely pick a faster line.

      You could of course use a different measure of efficiency, such as measuring the square of each customer's wait time to approximate frustration. Then in certain circumstances (like banks, where transactions can take

      • In actuality, each person picks a line based on how long it is at the moment.

        No way. I pick lines based on the gender, age, and contents of their baskets.

        How I judge these factors, and any additional factors I might observe, will be withheld for the sake of political correctness. :)

    • On average, and entirely unsurprisingly, one time in three you'll be in the fastest line; one time in three, you'll be in the slowest line. (And in the remaining third of cases, you'll fall in the middle.)

      Don't give me any of that "It's how you play the game" positivist commie-pinko crap.

      *I* must win, and everyone else MUST lose. Regardless if it is fastest cashier line or thermonuclear war.
      Any other solution is simply unacceptable injustice and it makes baby Jesus cry.

  • I wonder if it has anything to do with the large blood stained machette that I carry when I go shopping ... :-)

  • WTF is this noise? (Score:3, Insightful)

    by KillerCow ( 213458 ) on Thursday December 23, 2010 @07:51PM (#34656552)

    FIRST... no he dose not prove that you are in the SLOWEST line. He demonstrates that it's most likely that you are NOT IN THE FASTEST LINE. The exact same argument can be used to show that you are likely NOT IN THE SLOWEST line [of course, Slashdot editors and readers have never written any kind of mathematical proof, so the concept of "similarly" is foreign to them].

    SECOND... this is elementary probability... barely even high-school level.

    Given 3 lines
    WLOG, randomly choose one
    there is 1/3 probability that your line is the fastest
    therefore there is 2/3 probability that your line is not fastest
    therefore it is more likely that you are not in the fastest line

    THIRD... there is nothing ironic about the single queue being fastest. This is obvious to anyone who has even set next to someone who's brother's dog licked someone who accidentally clicked on the wiki page for queuing theory.

    I cannot believe that this drivel got posted. Apparently, Slashdot is now for remedial math. AND the poster (and editors) didn't even get it right! Slashdot editors fail remedial math.

    I know this site went to shit about 7 or 8 years ago, but all nerd cred is forever lost in my eyes. It is now just for 12 year old mouth breathers who have no idea what they are talking about.

    Logging into my account that I created when I officially gave up on this website. I am not going back to routing *.slashdot.org to 0.0.0.0 so that I am never tempted to return here on a lark.

  • It's actually worse than the video shows (Score:5, Insightful)

    by Solandri ( 704621 ) on Thursday December 23, 2010 @07:54PM (#34656578)
    If you have 3 lines, you'd think that 2/3rds of the time there's another line which moves faster. But if you're in a slower line, you're spending more time in that line. So with three lines, you're only in the fastest line for 1/3rd of your purchases. But you're in the fastest line less than 1/3rd of the time. The way Fry's does it with a single queue is pretty much the best way (I can think of an exception for those 10 items or fewer lines).
  • We always knew that throughput and response time do not agree. but what about having a display at the EFTPOS displaying customer clearance rate for every single line? In that way customers can perceive themselves as making an informed decision as to which queue they want to be cleared in, while more efficient queues can in fact get more of the workload. And since the customer made the active choice which queue he/she wants to be in, they will feel more personally responsible for whatever speed the queue is
  • I believe there's also a throughput bonus from societal pressures - you're less likely to take time bagging, fiddling with your wallet, etcetera when you notice ten people standing behind you. This is being adopted more and more in the UK through self-service stations in supermarkets.

  • I could be the first person ever to be modded up for saying "Best Buy FTW!!!"

  • Honest question... I'd really like to know. I've *always* seen the single line feeding into multiple cashiers as going far faster, on average.

  • MOST of the stores I go to have single-line queueing, supermarkets being a conspicuous exception. Usually it's done by setting up rope barriers on stands, with a "line starts here" sign.

    TSA security and airline check-in work with a single queue. Walt Disney World has been operating that way literally for decades.

    And MOST of the places that don't, almost do: clerks at McDonald's, CVS, etc. are trained to say "I can help whoever's next" as soon as they are free, which has much the same effect.

  • But you know who this sucks for? (Score:3)

    by TheABomb ( 180342 ) on Thursday December 23, 2010 @08:34PM (#34656874)

    The poor register jockeys making a flat hourly rate no matter how many customers get through their lines. The harder they work, the more work they make for themselves, particularly if they're sharing all the customers. (Anyone who's worked in any sort of real job surrounded by slackers knows this.) At least with your own customer queue, you can kind of see an incentive to get them all through, even if more keep showing up. As an added bonus, a manager might notice the ten people waiting to get through the lazy bitch's line (although in my experience, that just results in the efficient one being told he's "not taking initiative" or some similar bullshit.)

  • The single queue issue. (Score:3)

    by Restil ( 31903 ) on Thursday December 23, 2010 @09:04PM (#34657060) Homepage

    The problem most people see with a single queue is that the line is LONG. Our minds have issues thinking of the fact that 4 lines with 4 people waiting each is the same as one line with 16 people waiting. We also give up the illusion of choice with the longer line. With multiple lines, we
    can look at the quantity of products in the baskets, the perceived speed of the cashier, if there's a second employee at that register helping to bag groceries, etc. Of course, none of that matters if one of the people you're stuck behind is trying to pay with food stamps and has selected the wrong size of product, and needs to run back quickly to exchange it with the correct size.... or if someone's check won't read, or whatnot.

    The other issue with a longer line is that you need space for it. Fry's is set up to handle the long queues, but look how much space that whole arrangement takes up, not to mention the fact that people at fry's don't tend to purchase 100 small items, which fascilitate the need for a conveyor belt and bagging system. The grocery store probably couldn't get away with much less space for the registers than they're already using, so providing space for a long queue would require them to take in more of the store for that purpose. Best they can do easily is provide the express lanes (which would work even faster if they only accepted cash).

    -Restil

  • line with fewest women (Score:4, Insightful)

    by contrapunctus ( 907549 ) on Thursday December 23, 2010 @10:28PM (#34657460)
    i pick the line with fewest women in them because they always seem to want to write a check and don't start pulling the checkbook out of their purses until after all items have been scanned... don't want to be sexist but there it is

  • One line, always (Score:3)

    by xnpu ( 963139 ) on Friday December 24, 2010 @12:15AM (#34657858)

    Don't we all learn in school why 1 line is faster? I sure did. Not to mention that any place where it really matters (e.g. airports) do this already. Who cares what a handful of people who didn't pay attention in school "feel" about it "psychologically". What about me? Do you have any idea how distressed I get when there's multiple lines to choose from? And no way to know for sure which line performs best?

  • . Ironically, the most efficient set-up is to have one line feed into several cashiers.

    Since irony indicates a result the opposite of what you'd expect, and logic tells us that the one-line option is the most efficient... how's it ironic?

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