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Maths of Planet Earth | Limitless Applications

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Published on May 20th, 2014 | by Liam


A fairer way to queue for a cure

Whether we’re at a bus stop or in a line at a checkout, we all spend time waiting. To make sure the wait is fair, people often form a queue. In a Maths+Statsqueue, the person who has been waiting longest is the next person to be served. But in a hospital waiting room, some people can’t wait for their turn. So is there a fairer way to work out who gets treated first in a hospital?

One way of organising a waiting room is to always treat the most serious patient in the room. This system is very simple, so doctors and nurses don’t spend lots of time organising a queue. But it’s not perfect. Someone with a less serious problem, such as a cough, could be waiting for many hours while other minor injuries such as sprained ankles are seen straight away.

A team of scientists from Australia, New Zealand and Canada looked for a better queue system. They found a promising idea that was used for computer networks, and adapted it for hospital queues.

You can imagine a regular queue as a points based system. Each minute you wait, you get a point, and the person with the most points will be served next. The new ‘accumulating priority queue’ is similar, but people with more serious injuries get points more quickly. Someone with a cough might get one point per minute, while a sprained ankle might get two points, and a broken arm might get four points per minute. It may take a while, but eventually the coughing patient will have the most points, and will be treated.

The accumulating priority queue is more complicated than a simple queue. But computer simulations show that it is good at reducing long waiting times. These clever queues could soon be coming to a hospital near you!

More information

Reducing ER wait times for patients
A queue brainteaser
The maths of queues (more advanced)


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