an winning summary in MCM

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应朋友之邀把我们在美国数学建模竞赛中获奖论文的summary贴在这儿
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Summary

The magic QuickPass System (QPS) is designed to avoid long queue waiting by relocating the peak crowds in time and in space, which enables the QuickPass Customers (QPC) to pass quickly during their designated returning time period and meanwhile produces negligible negative influence upon regular queuers. Our model aims at improving the existed QPS by optimizing factors that may affect returning time of QPC and managing all queues in certain ride as a whole.

We initiate our model by studying the waiting time in regular lines and QuickPass lines. Proper Classic Distribution laws are introduced to simulate the arriving time situation of all customers and the special QPC, upon which the approximate beginning time of the returning period is calculated. Modifications about the returning time period are made after considering probability of Bad Chance and the former statistics regularity. Then optimization of the model with proper parameters is achieved by considering the interaction between regular queues and QuickPass lines. Finally an easy and effective model is obtained, tested and proved.

An alterative model is also proposed by focusing on the returning time distribution of QPC, on the basis of which the probability for some QPC to turn up at concentrated time period can be obtained. Then a computer program designed to simulate all factors of QPS is employed to find from varieties of random data a proper time period that would limit the probability of over-queue to some tolerable extent, finally resulting a practical model.

In all, both of our two models can be applied to handle the QPS in hot rides even when the average number of visitors reaches 1,000 per hour, with the former functioning better in less QPC rides and the latter dealing better with situations in which QPC take the majority, providing an average of 30% better service than where there is not a QPS. Meanwhile after a computer-based sensitivity and error analysis, our model proves to be stable even in range of 7,000 customers.