If a fun park wants to reduce ride waiting time, should the length of the rides be increased or decreased? At a recent trip to a fun park I was struck by the long waiting time for rides (eg roller coasters). So I was wondering: if you changed the duration of a ride (eg let a merry-go-round go around ten times instead of five times or let a roller coaster go around twice), would the ride queues get longer or shorter?


*

*My first guess was that to reduce the waiting times you should reduce the ride time because then the queues would move faster. But this is only taking one ride at a time into account.

*So then my second guess was that if you increased the ride time the waiting times would reduce. This is because at a (simplified) fun park people can only do one of three things: 1. be on a ride, 2. queue for a ride, 3. walk between rides. If you increase the time on a ride the time, would the time for queuing decrease?



Total time at park = Ride time + Queue time + Travel time

So if time on a ride is the only variable you change, should you increase it or decrease it to reduce ride waiting time?
 A: It is unclear how the traveling time works (will people stay for several rides or travel every time ?), so I absorb it in the waiting time.
Assume there are $n$ times more people than the coasters can accomodate. At any time, there are $n-1$ batches of people travelling/waiting and one batch riding. Thus on average people will be riding $1/n^{th}$ of the time and travelling/waiting $(n-1)/n^{th}$ of the time.
Whatever the ride duration. (What changes is the number of rides, but not the total time spent on or off the coasters. If there is a fixed travel time after a ride, the pure waiting time will indeed be shorter with shorter rides.)
A: My guess would be that the queue time will probably stay pretty much the same: Queueing for 20 minutes is worth it, queueing for 40 minutes is a drag, and no one likes to queue for an hour.  So, increasing the time of a particular ride will probably decrease the length of the queue in such a way that the queue time will remain pretty much what it was.
Also, I would say there are various other ways in which people spend their time, e.g eating some food, shopping at a gift shop, sitting somewhere on a bench, watch some exhibit, etc.  So, if there is any time gained or lost, people will mostly change how much time is spent on those 'other' things: spending 20 minutes more in the food court is a lot more enjoyable than spending 20 minutes more queueing.
A: Think of the queuing time as a cost or as the price of a ride. If the ride is shorter the benefit is presumably less so people will pay less for this and thus not be prepared to queue for so long. As they now have spare time they will distribute their time amongst the other rides in the park including the one in question by riding it twice. So the queue for this ride will get shorter.
A: The waiting times would be shorter if the rides were longer.
My argument:
The time it takes to buy tickets for a ride is unchanged by the duration
of the ride, thus if the rides were longer, the time it takes to buy tickets 
would impact the whole waiting time a lot less than if the rides were shorter.
For example it takes 2 minutes to sell tickets for a ride that's 5min long as well as a ride that's 15 min long.
Now this argument's validity depends on the way tickets are being sold at a park.
Now if we completely ignore this argument, reducing or increasing the duration of the rides would not impact the waiting times
as the queue time is proportional to the ride duration.
