2014 HiMCM A题特等奖学生论文下载5086

2014 HiMCM A题特等奖学生论文下载5086

 

下载方式见文末

 

论文摘要如下：

Summary Sheet

Train stations have always been a hub for commuters, but this hub becomes a nightmare once congestion prevents people from leaving the station and getting to work. In certain train stations, the placement and size of staircases is often a limiting factor that prevents the continuous flow of movement from the train platform to the street level exit. Our models seek to minimize the time it takes to leave the train, move across the platform, and go up the stairs based on the given variables: platform length (p), number of stairs (q), train car length (d), and the number of train cars (n). Each train is at least 10 cars long, with each car having three seats on one side and two on the other. The current staircase can only hold two columns of people.

In approaching this problem, we focused on the overall time it takes to leave the station. This time was broken into three components: the time taken to unload a train and walk to the stairs, the time spent in the queue waiting to walk up the stairs, and the time needed to ascend the stairs. Our goal was to minimize the time it takes to clear the train station, meaning the time it takes the last passenger to reach street level.

 

We created both a mathematical and a computational model to accomplish this goal. Our mathematical model used flow rate differential equations and Euler’s method estimates in an Excel spreadsheet to determine how long it takes to get through the stairway waiting queue. These time values incorporate the time to unload a train, walk to the stairs, and walk up the stairs. The computational model was a NetLogo program that modelled the time taken to completely empty a train station. For almost all of our calculations, the mathematically and computationally calculated times to empty the station were similar or equal.

Using these tools, we then modified the values of our variables to adjust the timeframe. Modifying the variables represents changing the conditions in the station platform. As we initially expected, the width of the stairwell is the most significant factor that impacts the time; allowing at least 6 people to walk up the stairs at one time halves the amount of time it takes to clear the train station. The placement of stairs, number of staircases, and even the arrangement of train cars does not have as great an influence.

2014 HiMCM特等奖论文完整版 下载链接