中考数学大题数学建模美赛题目及翻译

2020年11月19日发(作者：慎守礼)
PROBLEM A: The Keep-Right-Except-To-Pass Rule

In countries where driving automobiles on the right is the rule
(that is, USA, China and most other countries except for Great
Britain, Australia, and some former British colonies), multi-lane
freeways often employ
a rule that requires drivers to drive in
the right-most lane unless they are passing another vehicle,
in which case they move one lane to the left, pass, and return
to their former travel lane.


Build and analyze a mathematical model to analyze the
performance of this rule in light and heavy traffic. You may wish
to examine tradeoffs between traffic flow and safety, the role of
under- or over-posted speed limits (that is, speed limits that are
too low or too high), and/or other factors that may not be
explicitly called out in this problem statement. Is this rule
effective in promoting better traffic flow? If not, suggest and
analyze alternatives (to include possibly no rule of this kind at all)
that might promote greater traffic flow, safety, and/or other
factors that you deem important.

In countries where driving automobiles on the left is the norm,
argue whether or not your solution can be carried over with a
simple change of orientation, or would additional requirements
be needed.

Lastly, the rule as stated above relies upon human judgment for
compliance. If vehicle transportation on the same roadway was
fully under the control of an intelligent system – either part of
the road network or imbedded in the design of all vehicles using
the roadway – to what extent would this change the results of
your earlier analysis?

问题A：除非超车否则靠右行驶的交通规则

在一些汽 车靠右行驶的国家（比如美国，中国等等），多车道的高速公
路常常遵循以下原则：司机必须在最右侧驾 驶，除非他们正在超车，超
车时必须先移到左侧车道在超车后再返回。


建 立数学模型来分析这条规则在低负荷和高负荷状态下的交通路况的
表现。你不妨考察一下流量和安全的权 衡问题,车速过高过低的限制，或
者这个问题陈述中可能出现的其他因素。这条规则在提升车流量的方面
是否有效？如果不是，提出能够提升车流量、安全系数或其他因素的替
代品（包括完全没有这种 规律）并加以分析。


在一些国家，汽车靠左形式是常态，探讨你的解决方案是否 稍作修改
即可适用，或者需要一些额外的需要。最后，以上规则依赖于人的判断，
如果相同规则 的交通运输完全在智能系统的控制下，无论是部分网络还
是嵌入使用的车辆的设计，在何种程度上会修改 你前面的结果？