The Quest for the Quickest Queue

A few years ago, a paper was released, claiming that “according to maths” that the last person in a queue should be the first one served. Crazy right. Well according to this paper by two researchers from Denmark, that is correct.

First of all, let’s understand what they mean by a ‘good’ or ‘bad’ queue. A ‘good’ queue is one that people spend the least amount of time in it, while a ‘bad’ queue is the converse.

So, why is a last come first served queue a ‘good’ queue? To answer this, you need to understand that with a first in first out (FIFO) queue, getting in line early provides you with a reward; you get served earlier. But this system results in people getting to the queue really early and increasing their waiting time. This can be seen in an event like the release of a new iPhone, where queues can reach hundreds of meters long as eager fans wait to get their hands on the newest phone.

For a last come, first serve (LCFS) queue, there is no reward for coming early, but rather one to come at a time when other people wouldn’t be coming. This reduces the total wait time of everyone in the queue.

Image – wikimedia


As was alluded to before, this new system for queuing is “crazy”. And that is what is perceived by people participating in these queues. A study found that, while FIFO queues are slower, people found them to be fairer. The study also found that people regard the ‘fairness’ of a queue to be more influential than the waiting times. In other words, people don’t care if they must wait a little longer because FIFO queues are seen as fair.

What does this mean for queues of the future? Well, sadly this probably won’t change how everyone queues as the fairness of a queue is seen as more important, but it may change some of the ‘invisible queues’ that we enter (invisible queues are queues that you may not know you are in, i.e. a call centre). Another study suggested using a combination of LIFS and FIFO queues in a call centre where normally the last person to call up would get served first, but if someone was waiting for a really long time then they would be given preference and served next.

On a personal note, the maths behind queuing systems is a really diverse and interesting area that has a huge number of practical and theoretical applications. In saying that, I hope to explore and write about this and other interesting mathematical issues in the future, so get in line, or maybe not.