The Tipping Point
Let's say a ride can handle 1,000 people per hour.
- If 10 pph show up one day, no line
- if 500 pph show up the next day, no line
- if 1,000 pph show up the next day, no line
- if 1,100 pph show up the next day -- just a 10% increase from the day before -- there will be a line
- in the first hour there will be 100 people in line
- in the second hour and extra 100 people can't be accommodated, and so, there will be 200 people in line
- by the 10th hour of the park, there will be 1,000 people in line
- if 2,000 pph show up the next day, the line grows by 1,000 people per hour, leading to 10,000 people in line at the end of the day
That's what happens when you pass a ride's maximum. Up until the maximum, there will be no line. Once you go past it, it starts building up.
And of course, at some point, people decide the line's too long to wait and so there's a slow down on the build-up of people waiting (unless it's FoP... 5 hours? OK!).