Cutting the Queue
The phenomenon to be modeled is that high school students wait for their food in one long, disorganized line/clump. We are modeling the amount of time that each student takes to receive her food. The goal of this is to minimize the number of students in line at any given time. We will assume that each student takes up roughly an equal amount of space. To this effect, a side goal is to minimize the space that students take up as they wait for food. We can model how long it takes to receive each food group (i.e. a main course, then a side item, then a dessert, then a drink, etc.) We will also presume that the number of students does not change, even though increased efficiency in the process might motivate more students to buy hot lunch because they will not have to wait as long for it. One of our constraints is that all students eat at roughly 11:27am; we cannot divide the lunch period into two different times. Another constraint is the number of students who have to be fed; we cannot notably reduce the number of students in each grade who are ordering hot lunch. Another constraint is that we are limited in the amount of technology we can ask the district to purchase. We will code a simulation that will use Monte Carlo processes to model student time in the queue. This will require us to feed parameters to the method, including the number of total students ordering hot lunch. It is important to note that we will need to be collecting data by ourselves. The impact on the community is clear – high school students will be able to more conveniently obtain their food, which might improve their emotional states during a long school day.