Theme park cast member stories: Doing the math behind theme park wait times
Written by Robert Niles
Theme park lines are heaven to a math geek like me.Tweet
No, I don't like waiting in them more than anyone else does. But I find the math behind theme park queues fascinating.
Crowds queue for Harry Potter and the Forbidden Journey at Universal's Islands of Adventure theme park
It seems simple, at first. If more people during any given hour get in line for an attraction than that attraction can handle in that hour, some of those people are going to have to wait.
And if you know how many people get in that line, as well as how many riders that attraction can handle per hour, you can do the math to figure out the average wait time.
[Math geek stuff: The average wait time for a theme park attraction equals the number of people who get in line during an hour minus the attraction's hourly capacity. Take that number and divide it by the hourly capacity. Then multiply that result by 60 - for minutes in the hour. The result is your average wait time during that hour. See, I told you it was simple! :^) ]
But experience theme park operators know that the physical shape and orientation of a attraction's queue can affect wait times, as well. I thought about these issues after reading a piece by John Seabrook in the New Yorker last week, about the dangers of waiting crowds.
Seabrook details some of the disasters that happened when organizers failed to plan properly how to queue waiting crowds: One dead at a Walt-Mart in New York, nine at a concert in Denmark, 95 people at a football match in England.
As a former theme park employee, I find it unconscionable that anyone would organize an event sure to draw a large crowd, and not plan for how those people will get into the event. Whether you create a physical queue or a virtual one (such as Disney's FastPass system, or advance reservations for restaurants or museum exhibits), organizers simply must have a plan for handling people while they wait their turn.
Experienced theme park operators have become masters of crowd control, and anyone planning a major event - from a rock concert to an after-Thanksgiving sale, would do well to learn from them.
First, you must create a space in which people can wait. Ideally, the space will be designed in such a way that the people who arrive first are admitted first. First come, first served.
The simplest way to do this is with what we call a serpentine queue. That's because it looks like a long snake, with people lines up single file, in queues that go up and down long parallel rows.
That queue works great if you are going to load people onto an attraction one at a time. But what happens when you need to load an entire theater of theme park guests? Filling a 500-seat theater by pulling people one at a time out of a serpentine queue would take 15-20 minutes, time enough to run one extra performance for most theme park shows. Remember, hourly capacity is everything in reducing wait times. If you're giving up half your performances every hour because you need that time to load the theater, you've cut your capacity in half, doubling everyone's wait time.
That's why theme park shows have pre-show waiting areas. It's just not to entertain you while you wait. It's so that operators can group you into a single mass, the size and shape of the theater, so that the crowd can slide from the pre-show area into the theater in less than five minutes.
Saving that 10-15 minutes every show cycle allows the park to run more performances per hour, reducing wait times and allowing park guests to enjoy more shows each day. But that wouldn't happen without efficient pre-show queue design. (And a fondness for doing the math!)
I encountered this challenge while working as lead on the Tom Sawyer's Island rafts. Our hourly counts were horrible at the beginning of that summer. Part of the problem was the amount of time it was taking us to load the rafts.
Guests would wait for rafts in fenced waiting areas. There was a gap in the fence through which people would walk onto the dock and then onto the raft. The trouble was, people would crowd around that gap, creating a much smaller version of that crushing effect that Seabrook detailed in his New Yorker article.
No one's health was a risk with such relatively small crowds. But it did slow down the flow of guests onto the raft, enough to cause us to take closer to 10 minutes for each round-trip cycle, instead of the five minutes we could do with more efficient loading.
So, with the help of a few of the raft drivers, we redesigned the waiting areas, moving benches around to narrow the area right in front of the raft to the width of the gap in the fence. Each raft's capacity was 55 people, so we moved enough benches in place to define a space that would hold about that many people. This way we could slide that group of 55 from the wait area and onto the raft like a pre-show crowd into a theater. Behind them, the size of the wait area opened up. But by keeping the "pinch point" behind the next group of riders, the crowding around it didn't slow the loading of the rafts, allowing us to move more rafts per hour and reduce the overall average wait time for everyone.
Anyone experienced working with crowds comes to learn that, in a large group, people become liquid. You know how a fire hose can pour a lot more water than a little garden hose? Theme park queues are that way, too. A wide queue, such as at Disney World's Pirates of the Caribbean, can handle a lot more volume through it that a single-file queue, such as Big Thunder Mountain.
But eventually, we'd need the crowd to narrow to single file as we assigned them into specific rows on the boat. Ever notice how on some wide Disney queues, such as Disneyland's Haunted Mansion and the left queue at Disney World's Pirates, there's a U-turn just before you arrive at the loading area? That U-turn functions as a funnel, narrowing the flow of guests to a single file and making life much easier for the cast or team member at the loading position.
Overlook at last detail, and multiple parties will crowd the loader at once, each appealing to go before the others, forcing the load operator to calm everyone down and, literally, straighten things out.
Which, of course, slows the flow of guests onto the ride, reducing the hourly capacity and increasing everyone's wait time.
The math behind this stuff can get heavy duty. In college, I took a math class at Northwestern's Kellogg Graduate School of Management that included a section on queuing problems as part of a discussion of what the instructor called "mechanism design theory." (The instructor went on to win a Nobel Prize for this stuff. Like I said, heavy duty.)
But you don't need to be a Nobel laureate, or even a math geek, to appreciate how a theme park can move thousands of people through dozens of queues every hour of every operating day of the year. Just get in line, keep up with the folks in front of you, and please, be nice to the folks around you as you wait your turn.
You can read more of Robert's stories about working at Walt Disney World at themeparkinsider.com/stories.
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