# Background

Research of line optimization through queuing theory has spanned across a variety of fields all of which have one thing in common: lines. Examples include warehouses, banks, and hospitals. One paper that is particularly similar in scope to our project is titled “Managing Capacity and Flow at Theme Parks.” This paper does a similar analysis on theme park optimization as they focus on managing the flow throughout Six Flags Magic Mountain in Valencia, California. However, they look more into scheduling and timing of other attractions in order to detract from roller coaster lines at peak times. Our project approaches this problem by working with the major resources we have in the park, the four main roller coasters, without looking at any other attractions in the park. We are using this model to create a type of fastpass system to redistribute peak wait times, a different approach than the one they used in their report.

A great deal of quantitative information is available on this subject matter. Websites such as rollercoasterdatabase.com are easily accessible for any person to readily obtain information about rides including: capacity (maximum number of riders per house), duration of the ride, number of drops, speed of the ride, height of verticle drops, physical length of the ride, number of inversions, number of trains, how many cars per train, how many riders per car, and cost of manufacturing.

However, qualitative data is much more difficult to obtain. Through our discussion with Mark Rose, VP of Engineering at Busch Gardens Tampa, we know that 95% of entering guests go in the direction of the closest main attraction, Cheetah Hunt, and the remaining 5% go in the opposite direction of a further roller coaster, Sheikra. However, rider behavior is still not an exact science. Information such as popularity of a ride or about how many people visit each ride during certain hours is more difficult to obtain. As a result, knowing how close rides get to their capacity on any given trial is difficult to say. On one run, a roller coaster may reach nearly 100% capacity, while on another run it may only reach 70% due to groups of three wanting to sit together in a row for four. It should be noted that through running our simulation several times, we decided running the roller coasters at 80% efficiency was the most accurate for a real life simulation. Another unknown is human behavior in regards to fastpasses. Because human behavior is so difficult to predict, we had to determine an estimate of how many park guests will follow our fastpass system. How we came to these numbers is discussed further in the results section of the report.

The significance of this problem is twofold. For theme park guests, we are hoping to maximize their park experience. One of the largest complaints for theme park guests is the amount of time they spend waiting in line. No one wants to spend two hours baking in the sun for a 2.5 minute roller coaster. By minimizing wait times for everyone we are certain to have happier guests, which brings us to our second reason, park revenue. From the park’s perspective, an overall more positive experience from park guests encourages them to come for a second visit or even purchase a season pass. Plus, less time that guests spend in a line is more time they will be spending money in the park purchasing food from concession stands or playing games.

Theme park optimization is just one example of the overarching issue of efficiency that affects countless businesses. This type of optimization is sought after in any place that gives its guests a variety of choices upon entering. Grocery stores, for example, can be optimized by their layout. As mentioned above, banks, hospitals, and warehouses have also been studied. While it’s much easier to rearrange a grocery store or a warehouse in comparison to a theme park, bank, or hospital, the issue remains the same: creating an optimal flow of guests.