# Nerdvana: The important maths of supermarket self-service checkout queue speed.

Nerdvana: The important maths of supermarket self-service queue speed.

My heart sank a touch on Tuesday at the potentially dire state of public maths. While queuing at the supermarket, there were two neighbouring banks of self-service tills each with six people queuing. The issue? One had four tills, the other two.

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It seems many people had avoided the simple maths, doable either by observable instinct or observation, that the first tranche of tills had an average 1.5 people queuing per till, while the second had three people.

When I tweeted and Facebooked this, many people came up with potential reasons for the queue disparity. In this case none were true, but they do bear examination.

• “They may have seen old or stupid people ahead.” While I’m not sure I accept the assertion that older people are any less capable, or that you can judge by looking at someone’s self-service checkout skills, I’ll ignore that for a second.If you were unlucky enough to be stuck behind a till-doofus, maths plays a part here too…

Bank of two tills: A doofus blocking it reduces the number of tills by 50%

Bank of four tills: A doofus blocking it reduces the number of tills by 25%.

Therefore it would need double the doofuses (or is it doofi?) to have the same impact with more tills. Thus, even with one potential doofus in the queue, the bank of four tills wins.

• “People may’ve been counting the items each person had.” These were basket-only queues. So the item range is, let’s say, from one to 20. Yet the time taken to check out does not vary in line with the number of items – it doesn’t take twice as long to check out two items as it does for one.

Much of self-service time is spent starting, sorting bags, paying and dealing with ‘unexpected items in the bagging area’. This substantially reduces the risk of this playing a huge factor, and with six people in the queue you’re likely to be moving towards a more normalised variance in each queue anyway.

• “Alcohol and dangerous goods.” This one is bang on, as they require a member of staff to sign the customer through, causing a delay. However, the impact follows on much the same lines as the doofus argument above.
• “The queue you join always moves more slowly after you’ve joined it.” Many feel they have empirical data to prove the truth of this (ie, it’s happened to us all). Even if we exclude memory bias (we remember the bad times more than the good) and accept it as a rock-solid certainty of Sod, it is irrelevant.

By definition, this rule applies regardless of the queue joined, therefore it’s ‘on both sides of the equation’ and thus can be cancelled out. In other words, if you’re going to be unlucky, you may as well be unlucky in the queue with the better chance of moving more quickly.

• “Some people may want to queue longer.” I must admit I hadn’t thought of the perverse motivation factor. I had assumed everyone would want to reduce queuing time to a minimum. However, I’m wrong. There are of course some strange fetishes out there, and self-service queuing could be one of them.

Surely though, this is only a relatively small proportion of our great island nation. Even for just one of the six people in the bad-maths queue, to be so en-fetished seems unlikely. However, let’s assume they were. Even so, that leaves two others who shouldn’t have been there.

• “People are too stressed or tired to work it out.”While for a geek like me it is counter-intuitive (I was massively busy and rushed, so therefore working out relative queue speed was a priority, not something to ignore), I accept the likelihood of this thesis.

Yet that does sort-of take me back to where I started.This is a very simple bit of what should be intuitive maths. I wonder whether the fact people feel too tired to do it is a result of poor applied mathematics skills? In truth, all you need do is look and see one block has more tills, but the queue is the same length.

As for the empirical result? I joined the queue of four tills as the seventh member, and exactly as the maths would predict, arrived at a till at almost exactly the same time as the person who was fourth in the other queue.