2015 HiMCM A题特等奖学生论文下载6080

2015 HiMCM A题特等奖学生论文下载6080

 

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论文摘要如下：

To address the problem of roadway congestion, our team adopted an interdisciplinary approach combining theoretical mathematics, statistics, physics, computational science, and philosophy to perform a fresh analysis of driver actions and their implications in lane closure situations. Beginning with a simple model of road crossing grounded in Newtonian physics, we characterized the relationship between cars on a roadway in quantitative terms. Improving upon this physical analysis, we built computational simulations using NetLogo agent-based modeling to determine the effects of each road crossing strategy across a major highway. Using metrics of fairness and efficiency grounded in mathematical philosophy, including Rawlsian logic and rule utilitarianism, the viabilities of various strategies of road crossing and placements of lane closure were analyzed. We concluded that encouraging cars to merge out of the closing lane as soon as possible and placing the lane closure sign 1 mile away from the closure maximized both fairness and efficiency. We then performed sensitivity analyses on our recommendations to ensure their robustness. To supplement our computational simulations, we created probability density functions to estimate the distributions of cars on a roadway in lane closure situations to create an algorithm usable by policymakers to determine optimal sign placement for a major highway with n lanes and o open lanes, so that our model is easily customizable for public use. When applied to the sample situation of a three-lane highway, the model indicates that cars on the highway with n=3 and o=1 should begin to merge sooner than the cars on the highway with n=3 and o=2, so signs indicating a lane closure should be placed further from the lane closure to decrease congestion.

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