A single line to 3 cashiers is ~3x faster than a separate line for each cashier (opens in new tab)

A couple of additional thoughts, pooling queues like this only works if the changeover time to process different types of things is low. So in the case of a grocery store where there is no separate changeover or batch setup time it works well. If you are pooling work to people though it breaks down if only certain people can do certain types of work or the change over time to switch to a different task exceeds a certain threshold.

The other thing is the title of this post is almost certainly incorrect. Switching to a single queue reduces average queue time, but it does not reduce work time. In order to be 3x faster you would have to reduce both. The other factor at play is that people continuously rebalance from slow lines to fast lines, which also helps mitigate some of the problems.

* some grammatical edits

So I am wondering why don't stores do this already. And I believe it is because of perceptions. They understand that time will be saved, however, they realize that most people will be scared by a long line.

One long line that moves fast will still appear terrible compared to a bunch of small lines that crawl. Because people don't look long enough to estimate the rate of movement. They see both lines as static (not moving).

http://blogs.msdn.com/b/ericlippert/archive/2009/08/20/queue...

From my brief understanding, when someone talks about Queueing theory they are not talking about a singular "theory" but they mean something much broader. It doesn't seem as if there is something here that needs to be proved or disproved.

This is a part of naming in mathematics that has always perplexed me.

edit: not sure why this would get downvoted, seems like a simple neophyte question

I don't know what the "par" function does, but assuming it doesn't do anything crazy, the answer for all three of those expressions should be exactly 150,000, because they just reorder the order of summation.

Do you mind writing out what you're doing in pseudocode or in words? Intuitively, this result doesn't seem obvious to me.

Imagine where you have a one line scenario - you watch which register people go to. Label people who went to registers A,B,C with A, B and C respectively. Then, repeat the situation, but instead of one line, use 3, where everyone labeled A stands in one line, B in the other, and C in the third.

The transactions play out exactly like before. I realize we're dealing with probabilities and expected values, but it's definitely not obvious to me.

I am also very curious why the total time to process 3000 customers with mean time 50 is not closer to 3000*50. Perhaps I have missed something on the technical side.

At first they were awesome because nobody used them, so you could zip right through and avoid the lines. But now, after they've been here for a few years, a lot more people feel comfortable using them but many of those people use them poorly and far too many people will use them even when they have an entire cart full of groceries. That's an entire cart full of stuff they have to scan without accidentally voiding the whole order (which I've seen happen multiple times), a lot of trial and error on trying to figure out how to scan their produce, etc, etc.

It has reached the point where I rarely bother with self checkout anymore unless there is absolutely no line for it because while the system works great when nobody else is using it, it doesn't scale that well because most people are terribly slow checkers relative to dedicated workers doing that job.

I love these, because I can be done in 10 seconds. The people in front of me in line to use these, however, are rarely able. It's actually faster to wait in the non-self-checkout line these days because the people in the self-checkout line use them so slowly.

(Also, self-checkouts suck. I bet their throughput is terrible compared to manned checkout lines. That teenage checkout girl is WAY better than I am at scanning stuff.)

To self-scan you need to register with the store, and in the beginning you're manually checked a couple of times. They track how many errors you have and on what kind of merchandise, and determine how trust-worthy you are and how often you should be manually checked.

I can't remember if this was already implemented or just a suggestion from somewhere, but the self-scanning devices could track your location in the store, both to analyze customer behaviour but also to monitor any suspicious activity. If you spend 15 minutes in the electronics department without scanning anything, maybe that warrants a manual check.

As a side note, I wonder how much time self-scanning and self-checkout really saves in the end, for the consumer, and how much of it is just letting us do more unpaid labour under the impression of efficiency.

hrabago's point is important, but it certainly doesn't justify the linkbait title. A single line will decrease the variance of the wait time. Since the customer's impression of the wait time is very non-linear, this might significantly reduce customer unhappiness. But that isn't some brilliant insight into the process of handling customers faster.

There is a good amount of psychological research on waiting, and people in lines are much happier if certain things can be relied on. One of these things is fairness, as in, my wait time should be as long as everyone else's. Another thing is knowing how long the wait will be, which reduces anxiety over the wait. Single queue feeders enable those two things to happen much better than multiple queues. So even if the math ends up being the same either way, the customer will likely be happier with the single queue.

Because when you pick a line you don't know which line will go the fastest ahead of time. Neither do others on average, so everyone ends up spending more time.

But I would fully expect the majority to find fault in it. And reasonably so. The system is in place and it is multiple queues. The consequence of bucking the system is, at its most polite, a sneer and a scoff.

Leading left hand turns at a vehicular intersection may be the wiser alternative, but to flout a trailing left hand turn and jump through at the green is dangerous, rude and illegal.

Spatially, its actually quite complex to make one long line (it will probably have to snake around your store, and you'll need those awful movable tape barriers everywhere to make sure everyone keeps in line - customers hate these) and then to make one long line split evenly into several end points is not easy either (doing this may also take up a lot of valuable floor space).

Also, you could just have a store layout inherited from the 60s and its too expensive to change it right now...

Oh, and airline ticket counters are routinely run this way.

Edit: Yelp says this line system has been eliminated. http://www.yelp.com/biz/target-emeryville-2

And they prefer to choose their own line rather than wait in a single-file line for the next available register—even though that set-up has proven to be faster, research on queuing shows.

Based on these data points, it would seem as though more crowded places use this optimization.

There are practical reasons to do that. That is common in realtime systems. Trying to isolate the cpu for a particular process. So that is available faster when that process needs it. You could also have n-realtime processes. You don't want them competing for the same CPU if you know ahead of time you can allocate a CPU for each one of them.

Another reason is caching. For example you can assign a CPU to process network interrupt requests from a particular network device. Then you might or might not want to also assign the process that consumes that data to that CPU.