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A single line to 3 cashiers is ~3x faster than a separate line for each cashier

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Re: A single line to 3 cashiers is ~3x faster than a separate line for each cashier

#141
post #113

Earlier quoted context omitted.

Yes, and it is how real stores work, which is the point.

Except that the "primary" queue doesn't feed into the shortest register queue, it feeds into the register queue that the person at the front of the primary queue anticipates will empty the fastest. That's the premise that underlies the whole article: people get in the line they predict will move the fastest, and everyone uses different variables and judgment to make that prediction. Those variables and those predicti…

>everyone uses different variables and judgment to make that prediction. Those variables and those predictions don't show up when your model is based on distributions.

Sorry but that's simply not true. everyone uses different variables and judgment to make a phone call, yet phone calls follow an exponential distribution! everyone uses different variables and judgment to hit the internet, yet network traffic follows a Lavalette distribution. everyone uses different variables and judgment to buy stocks, yet equity prices follow a lognormal distribution.

Individual behavior in aggregate will almost always follow some distribution, regardless of each individual using different variables and judgment for himself. The whole point of statistics is to uncover the underlying probability distribution given tons of (seemingly random) data. Math does the opposite ( ie. given the distribution, a mathematician can tell you how to derive nice things like the moment generating function & the first & second moments & density functions & related family of distributions & so on, & in general give you n sample variates that fit the distribution. By saying "everyone uses different variables and judgment" you are in essence saying its just too complicated, but even if that were true, that is just another distribution ( white noise )

Re: A single line to 3 cashiers is ~3x faster than a separate line for each cashier

#142
post #141

Earlier quoted context omitted.

Except that the "primary" queue doesn't feed into the shortest register queue, it feeds into the register queue that the person at the front of the primary queue anticipates will empty the fastest. That's the premise that underlies the whole article: people get in the line they predict will move the fastest, and everyone uses different variables and judgment to make that prediction. Those variables and those predicti…

>everyone uses different variables and judgment to make that prediction. Those variables and those predictions don't show up when your model is based on distributions. Sorry but that's simply not true. everyone uses different variables and judgment to make a phone call, yet phone calls follow an exponential distribution! everyone uses different variables and judgment to hit the internet, yet network traffic follows a…

Thanks for explaining it that way, I think I understand better now.

Would you agree, though, that customers wouldn't simply enter the shortest available line?

Re: A single line to 3 cashiers is ~3x faster than a separate line for each cashier

#143
post #79

scala> import org.apache.commons.math.distribution.{ExponentialDistributionImpl=>expo} //pc = process customer, with a mean time mu per customer scala> def pc(mu:Int):Double= new expo(mu).sample // q = queue of n customers with mean process time mu scala> def q(n:Int,mu:Int):Double=(1 to n).map(_=>pc(mu)).sum scala> // put 3000 people in 1 queue with mean process time 50 scala> (1 to 1000).map(_=>q(3000,50)).sum/1000…

[deleted]

Re: A single line to 3 cashiers is ~3x faster than a separate line for each cashier

#144
post #43
post #27

FYI: This is an example of the branch of mathematics called queueing theory. http://en.wikipedia.org/wiki/Queueing_theory It's a fascinating study requiring a good knowledge of probability to use beyond the simplified models. It turns out from the math that throughput using a single queue is better than using multiple queues.

Not trying to be condescending but doesn't it surprise anyone here that this is _not_ obvious? At least on this site, there are still people doubting or debating this. 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 appe…

Stores are focused on individual wait times, not on total throughput.

Re: A single line to 3 cashiers is ~3x faster than a separate line for each cashier

#145
post #27

FYI: This is an example of the branch of mathematics called queueing theory. http://en.wikipedia.org/wiki/Queueing_theory It's a fascinating study requiring a good knowledge of probability to use beyond the simplified models. It turns out from the math that throughput using a single queue is better than using multiple queues.

This is a bit of an aside, but something I've always wondered is: why does this branch of mathematics get labeled as Queueing "theory"? 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…

It's a common enough construction. Quantum theory, set theory and so on.

Re: A single line to 3 cashiers is ~3x faster than a separate line for each cashier

#146

Earlier quoted context omitted.

This is a bit of an aside, but something I've always wondered is: why does this branch of mathematics get labeled as Queueing "theory"? 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…

It's a common enough construction. Quantum theory, set theory and so on.

Realize this is a worthless comment, but I couldn't stand the exclusion of graph theory.

Re: A single line to 3 cashiers is ~3x faster than a separate line for each cashier

#147
The parallel vs serial queuing problem is very well established within the operations research community.

And, IIRC, it's not that there's much impact to average performance, but rather that the variation (sigma) drops by a factor of n.

Re: A single line to 3 cashiers is ~3x faster than a separate line for each cashier

#148
post #141

Earlier quoted context omitted.

>everyone uses different variables and judgment to make that prediction. Those variables and those predictions don't show up when your model is based on distributions. Sorry but that's simply not true. everyone uses different variables and judgment to make a phone call, yet phone calls follow an exponential distribution! everyone uses different variables and judgment to hit the internet, yet network traffic follows a…

Thanks for explaining it that way, I think I understand better now. Would you agree, though, that customers wouldn't simply enter the shortest available line?

>Would you agree, though, that customers wouldn't simply enter the shortest available line?

I don't agree with that at all. In reality, some would and some wouldn't do what you suggest. If all of them did exactly what you are suggesting ( some sort of extreme rational agent), the distribution wouldn't be exponential. But then, all human beings don't buy low & sell high, nor do all of us withdraw money from the same ATM at the same time, nor do we make phone calls at the same time, or hit the internet at the same time. Aggregate behavior distributions modelling aggregate behavior of individual humans work well except in very extreme conditions such as 911 when everybody does indeed make the phone call at the same time thus jamming up the airwaves and killing the shape of the nice Erlang distribution at the telephone exchange.

Re: A single line to 3 cashiers is ~3x faster than a separate line for each cashier

#150

Earlier quoted context omitted.

It's a common enough construction. Quantum theory, set theory and so on.

Realize this is a worthless comment, but I couldn't stand the exclusion of graph theory.

How could I forget chaos theory and string theory.
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