2015 HiMCM A题特等奖学生论文下载6057

2015 HiMCM A题特等奖学生论文下载6057

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论文摘要如下：

18th Annual High School Mathematical Contest in Modeling(HiMCM) Summary Sheet
(Please attach a copy of this page to your Solution Paper.)
Merits of the Later Zipper Merge
Team Control Number: 6057
Problem Chosen: A
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Merits of the Later Zipper Merge

Summary

Lane merge could induce potential road danger to our smooth and happy trips. How can we get through of the merge as soon as possible? How can we direct busy drivers to drive fairly? This is a very exciting and challenging topic to our mad math group. There are several different scenarios in lane merge: a) 2 lanes merge into 1; b) 3 lanes merge into 2 or 1; c) different speed limit. We crack the 3 scenarios with mathematic models one by one.

To address the 2-to-1 lane merge problem, we develop a “late zipper merge” strategy. By common practice, drivers merge into the left (main) lane as soon as they see the “lane closed” sign. Cars form a long queue in this lane and leave the right (merging) lane empty. Sometimes a “sneaky” driver drives in the empty lane and squishes in at the lane closure, making the “good and lawful” early mergers feel offended, since the through traffic has right-of-way. This may create delay, road rage, or accident.

In comparison to the “early merge” strategy, our “later zipper merge” is not only efficient but also fair, according to our math model. We recommend that drivers drive in both lanes until they’re 300 feet ahead of the closure, then merge in alternating order. In the first scenario, we use two models to compare these practices. Model 1 is a simplified and extreme case. Model 2 is a detailed and complex case. Both models yield the same conclusion that our “later zipper merge” has an advantage compared with “early merge.”

In the second scenario, we analyze 3-to-2 and 3-to-1 lane merge cases. After sincere and hard attacks to the current practice (merge into left lane whenever possible), we come up with a perfectly calculated model. However, this ideal model is very hard to implement in real life since our drivers are not robots and are not likely to carry out exact orders. So we have to forfeit our attempt of perfection. The common practice is actually not as bad as it seems. Our only plea is to the highway designer: “Please, please do not design a highway where 3 lanes merge into 1 all at once. At least not in my hometown.”