A Myopic Aggregate-Decision Model for Reservation Systems in Amusement Parks

摘要

We address the problem of optimizing amusement park enjoyment through distributing QuickPasses (QP), reservation slips that ideally allow an individual to spend less time waiting in line. After realistically considering the lack of knowledge faced by individuals and assuming a rational utility-oriented human-decision model and normally-distributed ride preferences, we develop our Aggregate-Decision Model, a statistical model of waiting lines at an amusement park that is based entirely on the utility preferences of the aggregate. We identify in this model general methods in determining aggregate behavior and net aggregate utility and use these methods, along with complex but versatile QP accounting and allocation systems to develop the Aggregate-Decision QuickPass Model. We develop criteria for judging QP schemes based on a total utility measure and a fairness measure, both of which the Aggregate-Decision QuickPass Model is able to predict. Varying the levels of individual knowledge, the QP line-serving rates, the ability to cancel one's QP, and the QP allocation routines, we obtain a variety of different schemes and test them using real life data from Six Flags: Magic Mountain as a case study. We conclude that the scheme in which individuals are able to cancel their QPs, know the time for which a QP will be issued, and are allocated to the earliest QP spot available provides park-goers with the greatest total utility while keeping unfairness levels relatively low.