ProblemB: City Crime and Safety

In some cases, the road simply loses a lane as it enters a less traveled section. In other cases, the road narrows because of construction or roadwork. When this happens on a fairly busy highway, it may be a recipe for road rage*.  

Assume we’re on a busy two-lane road reducing to a one-lane road. Once a driver sees a sign indicating the right lane is going to end, he or she has a choice: drive in the right lane or drive in the left lane. Often, many drivers move into the left lane fairly quickly. This causes the left lane to become congested and slow down. Some drivers remain in the right lane and are able to maintain their speed (and pass the vehicles in the left lane which are now moving slower).  

When a lane closure is approaching, there will be signs indicating the distance of the lane closure as it nears (e.g. 1 mile, ½ mile, 500 ft.). As the end of the right lane approaches, some of the right lane drivers merge into the left lane, while others continue heading toward the lane closure. It’s at this point that the probability of road rage rapidly increases. Horns blast and gestures are made. Some cars will pull half way into the right lane in an attempt to prevent any cars from passing only to have another vehicle swerve around them and continue toward the lane closure point. At times, a vehicle will stay in the right lane directly next to, and driving at the same speed as, a chosen vehicle in the left lane in an effort to make the travel toward the lane closure “fair.”

Some states have done research on this phenomenon, but there is no consensus around best practices. Your team is tasked to provide a fresh analysis of this issue or add value to any existing analysis. Teams should not simply mimic previous research.

Part I: Analyze the various driver actions and their implications in lane closure situations on a major highway.

Part II: From your analysis in Part I, address and support fair and efficient driver actions:

a)In the case of two lanes merging to one, what is the “fairest” way for drivers to behave as they approach a lane closure?  What is the most “efficient” way for drivers to behave as they approach a lane closure?  Is there a difference between “fair” and “efficient?”

b)Use your analysis to address and support what drivers should do if a three-lane highway is reducing to two lanes? How should driver behavior change, if at all, if the three-lane highway is reducing to one lane?

c)Discuss and support any differences in fair and efficient driver behavior for lane closures on a secondary road with a 35 mile per hour speed limit versus a highway with a 65 mile per hour speed limit.

Part III: Policies and Practices  

a)From your analysis in Parts I and II, develop guidelines for inclusion in the Department of Motor Vehicles driver education materials and signage used by the Department of Highway Safety to encourage appropriate driver actions when approaching a lane closure.

b)In addition to the HiMCM contest format, write a one-page cover letter in support of your guidelines and signage to the Director of the Department of Transportation, urging adoption of your recommendations.

* Road rage is aggressive or angry behavior by a driver of an automobile or other road vehicle. Such behavior might include rude gestures, verbal insults, deliberately driving in an unsafe or threatening manner, or making threats. Road rage can lead to altercations, assaults, and collisions that result in injuries and even deaths. It can be thought of as an extreme case of aggressive driving. (http://en.wikipedia.org/wiki/Road_rage)

A题

 路怒是一个汽车或其他道路车辆司机愤怒的行为。这种行为可能包括粗鲁的手势，辱骂，故意用一个不安全的或威胁的方式驾驶，或威胁。路怒症可引起口角纷争，殴打，和冲突乃至受伤甚至死亡。它可以被认为是一个极端的情况下，借故生端的驾驶。

 防止路怒症。你有没有在公路上行驶，当你看到一个或两个标志？

在某些情况下，这条路只会失去一个通道，因为它进入一个不太有旅行的部分。在其他情况下，道路变窄由于改造或施工。当这发生在一个相当繁忙的公路上，它可能是一个造成道路愤怒的因素。假设我们在一条繁忙的双车道减少到一个车道。当一个司机看到一个标志，表明正确的车道将结束，他或她有一个选择：在右车道或在左车道行驶。很多时候，很多司机很快就进入了左车道。这会导致左车道变得拥挤而慢下来。一些驾驶者留在右车道上，并能够保持他们的速度（并比在左车道的车辆移动速度快）。当一个车道临近关闭时，会有标志显示距离施工地约（如1英里，½英里，500英尺）。当右车道临近关闭时，一些右车道司机合并到左车道，而其他人继续朝着车道关闭的方向前进。这时，路怒的可能性迅速增加。狂按喇叭和做手势。有些车会开进右车道，为了防止汽车通过的只有一个车辆转弯及继续向车道关闭点右车道。有时，车辆将直接临近停留在右车道，并以相同的速度行驶，在左车道的一个选择的车辆，以使旅行向车道关闭“公平”一些国家已经做了这一现象的研究，但没有达成共识的最佳做法。您的团队负责提供一个关于这个问题全新的分析，或补充任何现有的分析。团队不应该简单地模仿以往的研究。

  第一部分：分析在一个主要公路道路封闭的情况下，各种司机的行为及其影响。

  第二部分：在你第一部分的分析，地址和支持公平高效的驱动作用

  ：a）至于两车道合并到一个车道，当司机接近车道封闭路段时，最合理的方法是什么？最有效的方式又是什么？“公平”与“效率”有什么区别？

  ：b）如果三车道公路减少到2车道，使用你的分析，来说明并论证司机应该做什么?如果三车道的高速公路减少到一个车道，司机的行为应该如何改变？

  ：c）讨论和论证在一个道路封闭的二级道路上，限速35英里每小时与限速65英里每小时，公平和有效的驾驶行为的任何差异。

  第三部分：政策和做法

  ：a）从你在第一二部分的分析中，制定指引，包括在汽车司机教育材料和标牌，公路安全部门使用这些来敦促当接近公路封闭时司机采取合理的行为。

 ：b）除himcm竞赛格式之外，另向交通部门的领导写一页的附函，来支持你的方针和指示牌，敦促采纳你的建议。（http://en.wikipedia.org/wiki/road_rage） 

更多美赛国赛资料见

数学建模与统计建模论坛

Mathematical Modelling and Statistical Modelling Forum

http://www.mathsccnu.com/forum.php