Improving on the queue

Speaking of social science technologies...

I grew up in Los Angeles, so I went to Disneyland a lot.  By now I've seen everything a hundred times, so the experience is not so enjoyable.  But when I was a kid, the problem was that I couldn't get enough of the rides, because the lines were so long.

When I was 11, Disneyland introduced the Fastpass system.  At the front of each major ride there were these magical boxes.  You'd put your park ticket in, and you'd get out a Fastpass which had a time printed on it.  The time is calculated based on how many other people have gotten Fastpasses so far that day.  At the printed time, you could get in a special line at the ride which moved much faster than the normal line.  The drawback was that you could only have a single fast pass per park ticket.

The fastpass sure was gratifying, because we'd get to zoom past lines that would normally take over an hour.  But the rides can only serve a certain number of people per unit time, so it couldn't possibly benefit everyone, could it?  Was the benefit of the Fastpass all an illusion, or was there more to it?

My hypothesis is that there is a real benefit, and it has to do with game theory.  Normal queues are a prisoner's dilemma, and the Fastpass system mitigates the problem.

The swimming pool analogy

Imagine, for instance, that we're in a swimming pool, and the diving board is so popular that there's always a line for it.  We all prefer staying in the swimming pool, but we're also willing to stand out of the water for a while in order to try the diving board.  The shorter the line is, the more people willing to get into it, which makes the line longer again.  So the length of the line reaches a sort of Nash equilibrium.

However, the equilibrium line length is not the best line length.  The best line length would be zero.  Instead of everyone lining up, people could stay in the pool.  Then people would voluntarily go up to the diving board at a steady pace, always maintaining a line length of zero.  In this scenario, just as many people get to use the diving board, and no one has to stand for long outside of the pool.  To get in line is to take the defecting strategy in a prisoner's dilemma.

And unfortunately, this is a prisoner's dilemma that involves many people (as many as there are in the swimming pool).  So it's virtual certainty that everyone will defect.  Tragedy of the commons.

You could imagine queueing systems that attempt to defeat the prisoner's dilemma.  For example, you could have people write their names on a list (on a waterproof board?), while one person calls people to the diving board at the appropriate times.  You'd have to restrict the number of times people can sign their name to prevent people from just signing over and over with virtually no cost to themselves.  This new system would allow everyone to stay in the swimming pool.  Unfortunately, since the cost of diving is lower, the "line" would be much longer, consisting of many people who only marginally enjoy diving.

The Fastpass

The Disney Fastpass system is similar to the queuing system I proposed for the swimming pool.  Rather than having everyone wait in line, they get Fastpasses, which is just like signing your name on a board.  The time on the Fastpass is the time when the ride calls you up.  The Fastpass system doesn't allow more people to enjoy the ride, but it does allow people to spend less time in line overall.

What do people do with that extra time?  If you really like this one ride, you might just get in the normal line over and over again.  But if that's your behavior, then it's unlikely that the Fastpass system benefits you.  The Fastpass line makes the normal line slower.*  So even though you're getting the benefits of the Fastpass line every few hours, on average you're doing no better, or possibly worse.

*There's also an equilibriating response--fewer people are willing to line up in a slow line.  The wait is the product of the speed of the line and the number of people in it.  Despite the equilibriating response, the total wait will be longer.

A more beneficial way to spend the time is to watch shows or go on other less popular rides.  These attractions would normally operate at less than full capacity.  But because of the Fastpass system, more people may have time to take these rides and watch these shows.

Another alternative (one which I suspect is Disneyland's favorite) is to use the extra time to patronize shops and restaurants.

That's my hypothesis.  But what does Disneyland think are the advantages of Fastpass?  Take a look at the Fastpass patent:

Not only is the customer frustrated at not being able to access more attractions, but the amusement park itself suffers from having underutilized attractions because the customers are waiting in line for other attractions. Instead of waiting in line for a single attraction, a customer could be riding other attractions, eating food, shopping at stores, playing games, or other activities.

Yep.  I got it right.  It's a brilliant idea IMO.