2015 HiMCM A题特等奖学生论文下载6117

2015 HiMCM A题特等奖学生论文下载6117

 

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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.)
Team Control Number: 6117
Problem Chosen: A

Lane closures are one of the most common sources of traffic congestion, which can lead to dramatically increased driver anger and slower commute times for everyone. In order to improve this situation, our team analyzed the possible outcomes of a lane closure scenario and determined optimal strategies, both on the individual and systemic level, to improve traffic flow and prevent road rage. We applied Monte Carlo and fluid dynamic methodologies to create a robust simulation and experimented with countless different scenarios. Through our model, we have determined a series of guidelines that one individual can follow to improve his commute time and overall traffic flow, as well as guidelines, that if implemented on a larger scale, could result in much less traffic congestion for everyone.

When creating our model, we sought to make it realistic and able to test the multitude of scenarios that one may encounter, and determine best practices for each. Our model was primarily a Java simulation, comprising the given road with a lane closure, and populated with car objects. As in real life, different cars may have different driving styles, but our test driver was programmed to follow specific strategies and determine whether they were effective. Since the problem gave a very generalized situation, we found it more tractable to work with additional specificity, testing all possible scenarios that composed the general case. In this manner, our model became very robust and could test situations or strategies that were unexpected or unintuitive. We applied Monte Carlo principles of testing all possible scenarios to determine the optimal strategy.

We also looked toward fluid dynamic principles for insight. The Darcy-Weisbach equation, which models the outflow of laminar fluid towards an opening, was modified for our purposes to accurately model the analogous outflow of non-laminar cars towards an opening -- the unblocked lane. Instead of finding the pressure of the fluid at various points in the tube, we could calculate congestion, the parallel to pressure for our modified equation, at those points, and our test driver would act accordingly to reduce congestion in the system. In this way, we determined not only generalizable guidelines for optimal actions in any scenario, but also scenarios or strategies that would reduce congestion as a whole.

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