2014 HiMCM A题特等奖学生论文下载4813

2014 HiMCM A题特等奖学生论文下载4813

 

下载方式见文末

论文摘要如下：

17th Annual High School Mathematical Contest in Modeling (HiMCM) Summary Sheet
(Please attach a copy of this page to your Solution Paper.)
Team Control Number: 4813
Problem Chosen: A
Please type a summary of your results on this page. Please remember not to include the
name of your school, advisor, or team members on this page.

The goal of our model is to show the amount of time it would take people in a crowded train station to leave their trains, make their way to the stairway, and exit the station.

First, we mapped out the problem and identified constants: for some elements of the station, such as platform width and seat width, we assigned values that are similar to the average values of standard trains and that follow certain train specification and standard transportation guidelines. The number of people that can be on the stairway at a certain time is limited; thus, we realized that a queue would build up around the bottom of the stairs. We soon realized that the queue is a central element of the entire model because of the magnitude of the effect it has on time required to leave the station. To simulate this effect, we allowed a person waiting in the queue to take up about 4 sq ft of space and calculated a new reduced walking speed for people standing in the queue. We made the queue a rectangular shape to accurately simulate human behavior and made the width of the rectangle the platform width of 29.5 ft., which is the average platform width of a regular railway station. People enter the stairs, join the queue, and walk at three different constant rates. The rate is set by the capacity of the stairs to take up new people every second, so we were able to precisely determine the speed at which people in the queue would walk in a real-world situation.

Second, we developed a mathematical model to optimize for time. We began by obtaining the rate at which people arrive at the queue by finding the amount of time it takes the average passenger to leave the train car. Then, we calculated the distance traveled in the queue and the distance traveled on the platform. Using all of this information, we calculated the amount of time all of the passengers spent in the queue and on the platform.

2014 HiMCM特等奖论文完整版 下载链接