4 ms·

Isn't this essentially equivalent to having a single queue though... except now you have a kind of cache at each register holding a small number of customers?

gujk 15y ago
Yes, and it is how real stores work, which is the point.
- alsocasey 15y ago
  Right. I wonder what would happen if we try to include a measure of perceived fairness from the customer's point of view into this type of analysis. I always feel I'm picking the wrong queue at stores... single queues going to whatever cash is open seem fairer, if that makes sense.
  - Someone 15y ago
    Perceived fairness is very hard to quantify objectively. Is it fair if there are queues for people buying less than X items? If there are queues for people not paying cash? For frequent flyers? That you, by sheer misfortune, end up in the slow queue three times in a row? Should pensioners wait for people having work to do? Should fit people make room for the elderly? To what extent? Etc. Instead, I think you should do the math; it will teach you that the probability that a given queue is slow is smaller than the probability that, given a person in a queue, that person is in a slow queue. So, you spend more time in slow queues than in fast ones. Once you know that, train yourself to accept it.
  - bostonvaulter2 15y ago
    That's because if there are 4 lines there is generally a 75% chance that one of the other lines was faster.
- nlawalker 15y ago
  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 predictions don't show up when your model is based on distributions. The register queues are not independent, but they are not related as simply as you say.
  - dxbydt 15y ago
    >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 )
    - nlawalker 15y ago
      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?
      - 15y ago

gujk 15y ago

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

alsocasey 15y ago
Right. I wonder what would happen if we try to include a measure of perceived fairness from the customer's point of view into this type of analysis. I always feel I'm picking the wrong queue at stores... single queues going to whatever cash is open seem fairer, if that makes sense.
- Someone 15y ago
  Perceived fairness is very hard to quantify objectively. Is it fair if there are queues for people buying less than X items? If there are queues for people not paying cash? For frequent flyers? That you, by sheer misfortune, end up in the slow queue three times in a row? Should pensioners wait for people having work to do? Should fit people make room for the elderly? To what extent? Etc. Instead, I think you should do the math; it will teach you that the probability that a given queue is slow is smaller than the probability that, given a person in a queue, that person is in a slow queue. So, you spend more time in slow queues than in fast ones. Once you know that, train yourself to accept it.
- bostonvaulter2 15y ago
  That's because if there are 4 lines there is generally a 75% chance that one of the other lines was faster.
nlawalker 15y ago
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 predictions don't show up when your model is based on distributions. The register queues are not independent, but they are not related as simply as you say.
- dxbydt 15y ago
  >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 )
  - nlawalker 15y ago
    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?
    - 15y ago