2016 HiMCM A题特等奖学生论文下载6770

2016 HiMCM A题特等奖学生论文下载6770

 

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论文摘要如下：

Team Control Number: #6770

Problem Chosen: A

 

In order to best organize a triathlon with a 1500m swim, a 40K bike, and a 10K run, we calculated the average time in seconds it took for different divisions of participants based on age, gender, and skill level to complete each segment of a triathlon using data from a previous event. By compiling this data, we were able to develop a model that minimized congestion and had road blockage time below 5.5 hours using incremented waves of participants with similar completion times.

 

The first part of our process was to divide the participants into different divisions in order to group and split them into various wave starts. All skill levels were grouped into two divisions based on gender, with further age classification for the large “Open” registrators. Using the times given by the Mayor to complete a previous triathlon of the same length, we calculated the average time in seconds it took for each of the 24 divisions to complete the swimming, cycling, and running segments, along with the two transition times in between. Then, the data was used to split large divisions and group smaller divisions with similar completion times together in order to create waves with a consistent number of contestants.

 

The second part of our process was to develop a model in order to appropriately sequence and separate wave starts with the goal of minimizing congestion as much as possible. Using a distance-time graph, we used the Q1, mean, and Q3 values of the average completion times for the participants in each wave start to create functions in order to illustrate the estimated range (Q1-Q3) of speeds that contestants in a certain wave start would have. Lastly, we developed a refined model of the wave starts during the triathlon by using a logarithmic function to represent the “slowing down” of the participant during the swimming segment, a linear function to represent the constant speed of the contestant during the bike, and an exponential function to show the increase in speed of runners in the last segment, accommodating for the transitions during the race. To evaluate the effectiveness of our refined model, we proposed a cost function to calculate the cost of congestion and cost of time. Our goal is to reduce the cost as much as possible. In this cost function, time is considered least expensive as long as it fits within the 5.5 hours and congestions are usually more expensive because we think it is more important for participants to have a better experience with less congestions. To calculate the total cost, we used a combination of programming and integrals as demonstrated in 3.2.

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