2009年美国数学建模 A 题

MCM PROBLEMS

PROBLEM A: Designing a Traffic Circle 问题A：设计一个道路的圆形交叉路口

Many cities and communities have traffic circles—from large ones with many lanes in the circle (such as at the Arc de Triomphe in Paris and the Victory Monument in Bangkok) to small ones with one or two lanes in the circle. Some of these traffic circles position a stop sign or a yield sign on every incoming road that gives priority to traffic already in the circle; some position a yield sign in the circle at each incoming road to give priority to incoming traffic; and some position a traffic light on each incoming road (with no right turn allowed on a red light). Other designs may also be possible.

很多城市和社区有一些道路的圆形交叉路口----大的有很多路口（例如巴黎的Arc de Triomphe和Bangkok的Victory Monument），小的有一两个路口。一些圆形交叉路口在每个进口处设置停止或让路标识，使已经在环形交叉路口的车辆拥有优先权；有的在进口处只设置停止标识（在红灯时不允许右转）。 许多城市和社区有环形交叉口。大的环形交叉口有许多小路，比如说巴黎的凯旋门和曼谷的胜利纪念碑。小的环形交叉口只有一或者两条小道。一些环形交叉口在每个来路上作为停止或让路标记，给在环形内的车辆以优先进入权。一些在来路上只作为让路标记，给来往车辆以优先权。一些在来路上作为交通灯的作用(红灯不能右转)也有一些其他的设计作用。

The goal of this problem is to use a model to determine how best to control traffic flow in, around, and out of a circle. State clearly the objective(s)

you use in your model for making the optimal choice as well as the factors that affect this choice. Include a Technical Summary of not more than two double-spaced pages that explains to a Traffic Engineer how to use your model to help choose the appropriate flow-control method for any specific traffic circle. That is, summarize the conditions under which each type of traffic-control method should be used. When traffic lights are recommended, explain a method for determining how many seconds each light should remain green (which may vary according to the time of day and other factors). Illustrate how your model works with specific examples.

这个题目的要求是用模型决定环形交叉口内外的交通流动。清晰的说明你设计的模型中最理想的选择和影响这一选择的原因。包括一份技术摘要。用来向工程师解释如何使用你的模型来选择能适用于任何精确环形交叉口的交通流动的控制方案。总结各种交通控制方案的条件。当使用交通灯时，解释每个交通灯需要保持绿灯的秒数（由每天的时间和其他因素的变化而变化）阐述你的模型如何应用于特定的例子。字数要求：2页，双倍行距