Suppose you are waiting in line for something. How would you expect the service provider to take people out of the line?
Unless you are at some place like an emergency room where different customers have clearly different needs and different levels of urgency, you might expect that customers are served in the order of their arrival — that is, a first-in, first-out discipline is used. That’s a natural and common assumption (at least in the US). It is also makes headlines like “Have we been queuing all wrong? Lines move faster if the person at the back is served first, study finds” (Daily Mail, Aug 14) or “Danish researchers have an enraging proposal to speed up queues: Serve the last person first” (Quartz, Sep 7) attention grabbing . Here is the crux of the Daily Mail article:
A group of Danish researchers have discovered a rather unexpected solution to the long lines of people that can appear ahead of new iPhone launches or to get into sporting events.
They say serving the person at the back of the queue first can actually make lines move faster – something which may horrify British and Americans who adhere to the strict etiquette of waiting your turn.
Instead it suggests people like the Italians, who often frustrate other tourists with their lack of regard for the order of a queue, may have been on to something after all.
The findings could put an end to traditions which have become almost British institutions such as queuing to get tickets for Wimbledon or the Proms.
So what is going on here? Is serving customer last-in, first-out really the answer to queuing woes?
The article is, in fact, based on a working paper by a pair of Danish economists and is part of a line of work showing that different ways of organizing queues can improve outcomes. (For another example along these lines, see here.) Unfortunately, the paper in question doesn’t really match up with the Daily Mail’s claims.
First, let’s think about what this paper does. It considers customers who are all seeking service from the same facility and all have the same value for that service. These customers need to choose when to show up over some horizon and their value for the service depends on two things — when they receive service and how long they have to wait for service. All else being equal, they prefer shorter waits and earlier service, i.e., given the choice between a five-minute wait and getting served at 11:00 AM or a five-minute wait and getting served at 1:00 PM, they all prefer service at 11:00 AM. The paper then considers how different ways of organizing the queue affects social welfare — or the utility customer receive from service less their waiting costs.
With this set up, you can see how first-in, first-out (FIFO) service is going to lead to bad outcomes; customers already have an incentive to come early because they value early service and FIFO just reinforces that. Last-in, first-out (LIFO) offers a counter weight to valuing early service. Arriving later lowers the value of the service, but offers a shorter wait if everyone else is showing up early.
With that background, we can now think about the claims in these articles. For one, nothing about this set up is going to make the queue move faster in an absolute sense. If the server can process one customer per minute, it is going to take on average five minutes to get five people through the system regardless of how they are pulled out of the line. Further, this research does not show (or claim to show) that using LIFO processing will minimize the waiting time customers experience. It’s focused on maximizing the value created; if customer valuation fall steeply over the horizon, that will be a dominant effect over the waiting costs.
It is also not clear that the model presented by the Danes actually fits the settings posited by the Daily Mail. The real challenge of queuing for tickets at Wimbledon is that you might wait forever but not get them. The Danes assume that everyone gets served eventually, that is, the firm never runs out of the goods. This is not to say that FIFO is necessarily the best system when it comes to goods that are in short supply. As we have noted before, firms as diverse as Apple and the Chicago Cubs have resorted to lotteries to reduce the incentive to queue early for a limited set of goods.