Airport Queues Explained

There’s a simple equation that explains all queues, including the customs check-in ones. And the amazing thing is that the equation shows that there is massive sensitivity in the system, so that a small reduction in staff makes the queues become massive. Here is why….
The equation says that if the utilisation of a resource (number of customers arriving divided by the number you can cope with) is called U, then the average queue length will be U(1-U). Don’t panic, I will explain!
Clearly if the utilisation is greater than 100% (more people arriving than you can cope with) the queues will just grow and grow. But the interesting thing is when the utilisation is just less than 100% – let’s say 95%.

So if you have 1000 people per hour arriving at the immigration desk and because of cost cutting you’ve got rid of all spare staff, leaving you with enough staff to deal with 1050, so you are 95% utilised – a very tight ‘safety margin’ but should be OK, you are thinking. But no!  You are already going to get queues, due to random fluctuation of arrivals (several planes at once, varying numbers per plane, etc ) so the formula predicts an average queue length at customs of 95/(100-5) = 95/5 = 19 people. This was probably about the situation when the airport was running more or less OK a few years ago.
Now let’s say that this would take 35 staff – the actual number doesn’t matter, it’s just an example. What if you get rid of just one person, so you have 34 instead of 35 people and now you can only handle 1020 people per hour – “should still be OK”, you think. Just less waste, less fat in the system. Sounds good! (I’ve just made up the number of people to illustrate that a small change in the numbers of people has a huge effect on the queues) – from the formula, what will the queue length be now…?
Q = U/1-U, and U is now 1000/1020 = 98%, so Q = 50. The queue has more than doubled and all you did was get rid of one person out of 35! And you should still have been OK!
And suppose you got rid of two people and you now can only cope with 1005/hour – although you think you’re still OK the utilisation is now 1000/1005 = 99.5% and so the average queue rises to 200 people!
That’s probably where we’re at now.
This formula is a statistical law which can be shown with dice or a random spreadsheet (see https://docs.google.com/open?id=0B6BLBzKogj_iOWZlMzIyNzUtNWI1Mi00YmZlLTkxMWMtNzI2ZTY2MGUwODRi ) so there’s no point in trying to beat the system – it is what WILL happen. The answer is to accept the fact that you need at least 10% spare capacity, preferably 20%, and to pay the accompanying extra cost, if you want to get a decent service. And be very careful about small cuts when you’re already near the edge….