Smart queues, dumb queues and Metro queues

A shop - contains checkout queues
I've done a fair amount of work on queuing in my time, which is why I was very doubtful to see a Metro headline 'Why you're better queuing behind one person with a full trolley than people with baskets.' And I had good reason to be doubtful, because the argument was, well, total rubbish.

'Do you queue behind the person with a trolley filled to the brim, or do you wait behind the line of people in the "10 items or fewer" queue?' the article asked. Then it introduced Dan Meyer 'a former high school maths teacher' (a queuing expert, then), whose research tells us that transactions have a fixed time of 41 seconds, plus 3 seconds per item scanned.

'This means,' says the article, 'that queuing behind a line of people who have fewer things will take longer than a couple of people with full trolleys'. Again, I'm afraid, this is total garbage.

The article points out that one person buying 100 items will take 5 minutes 41 seconds, while four people with 20 items each will take 6 minutes 44 seconds to go through the till. This is true but irrelevant.

There are two big problems with this argument. Because of that 41 second overhead time, you can get through more items in the same time from a single trolley than lots of baskets. But I have never been in a basket queue with more than three or four people in front of me. And clearly they aren't going to have '20 items each', if it's a 10 items or fewer queue. Doh! Those four people with 10 items each (in practice some will have fewer than 10) will, according to Meyer's own numbers, only take 4 minutes 44 seconds to get through - so queue behind them, not the bloke with the full trolley.

The other problem with Meyer's analysis is that I can't think when I last went into a supermarket without self-checkout for baskets. These operate on the much more sophisticated single queue, multiple server system. So there may be five or six people in front of me in the queue - but we are waiting for 6 or 20 checkouts at my nearest supermarket (6 one end of the store, 20 the other*). Which means in practice you will be unlikely to have to wait for more than a few seconds to start scanning.

Three lessons then. The media, even the Metro, should think more about a maths or science based story before they publish it. Secondly, just because someone's an ex-maths teacher doesn't make him a queuing guru. And finally don't queue behind people with big trolleyfulls unless there's something seriously wrong with the basket checkouts.

* This is a much more interesting problem of which end to go to, as it is often quicker to go through the 6 checkout end, as far fewer people use it.