2017美国数学建模MCM B题（离散型）翻译 收费后的车流合并问题

2017美国建模MCM B（离散型）翻译 收费后的车流合并问题 2017美国数学建模MCM B题(离散型)翻译 收费后的车流合 并问题 Problem B: Merge After Toll问题B:收费后的车流合并问题 Multi-lane divided limited-access toll highways use “ramp tolls” and “barrier tolls” to colle ct tolls from motorists. 高速路使用的是多车道划分的封闭式收费系统，收费站通过“匝道收费”和“过卡收费”两种方 式来收取驾驶员的高速费。 A ramp toll is a collection mechanism at an entrance or exit ramp to the highway and these do not concern us here. 匝道收费是一种在入口和出口的匝道处设立的收费站，我们不讨论这个问题。 A barrier toll is a row of tollbooths placed across the highway, perpendicular to the direction of traffic flow. 过卡收费是在垂直高速路行驶方向，设立一排收费窗口。 There are usually (always) more tollbooths than there are incoming lanes of traffic (see former 2005 MCM Problem B). 而这些收费窗口通常都会比车道条数要多(详情参见2005年MCM的B问题)。 So when exiting the tollbooths in a barrier toll, vehicles must “fan in” from the larger nu mber of tollbooth egress lanes to the smaller number of regular travel lanes. 因此，当汽车驶出收费站之后，车流必须从较宽的收费站出口呈扇形快速并入车道较少的常 规机动车道。 A toll plaza is the area of the highway needed to facilitate the barrier toll, consisting of the fan-out area before the barrier toll, the toll barrier itself, and the fan-in area after the toll barrier. 收费广场是为改善过卡之后的拥堵状况建立的，包括收费站之前多车道区域，收费站本身以 及经过收费站之后的扇入区域。 For example, a three-lane highway (one direction) may use 8 tollbooths in a barrier toll. After paying toll, the vehicles continue on their journey on a highway having the same number of lanes as had entered the toll plaza (three, in this example). 举个例子，一条单向的三车道高速路需要8个收费窗口，在支付过桥费后，驾驶员可以继续 保持与自己进收费广场之前的车道数目(三条车道)继续前行。 Consider a toll highway having L lanes of travel in each direction and a barrier toll containing B tollbooths (B > L) in each direction. 试考虑一个收费高速公路上两个方向都有L条车道，每个方向上有B个收费站(B>L)， Determine the shape, size, and merging pattern of the area following the toll barrier in which vehicles fan in from B tollbooth egress lanes down to L lanes of traffic. 请确定你的收费区域的形状，大小以及当汽车从驶出B时如何将车道进行合并至L条 车道。 Important considerations to incorporate in your model include accident prevention, throughput (number of vehicles per hour passing the point where the end of the plaza joins the L outgoing traffic lanes), and cost (land and road construction are expensive). 在你的设计中请注明一些重要事项如事故预防，吞吐量(即每小时有多少车辆从收费广场驶 出，驶入L条车道)和成本(土地和公路建设的费用很昂贵) In particular, this problem does not ask for merely a performance analysis of any particular toll plaza design that may already be implemented. 重点在于并非只是对现有的收费广场进行性能分析， The point is to determine if there are better solutions (shape, size, and merging pattern) than any in common use. 请试着探索是否有比现今采用的更好的收费解决(包括形状，大小以及收费方式)。 Determine the performance of your solution in light and heavy traffic. 请确定你的解决方案在小车流量和大车流量下的性能现。 How does your solution change as more autonomous (self-driving) vehicles are added to the traffic mix? 随着更多的私家(自驾)车进入其中，你的解决方案会有什么改变呢? How is your solution affected by the proportions of conventional (human-staffed) tollbooths, exact-change (automated) tollbooths, and electronic toll collection booths (such as electronic toll collection via a transponder in the vehicle)?你的解决方案会如何影响常规收 费站(需要人员进行收费)，不找零(自动化的)收费站以及电子收费站(比如通过车内的发射器 应答器来收取费用)? Your MCM submission should consist of a 1 page Summary Sheet, a 1-2 page letter to the New Jersey Turnpike Authority, and your solution (not to exceed 20 pages) for a maximum of 23 pages. Note: The appendix and references do not count toward the 23 page limit. 你提交的MCM文章应包括1页摘要表，1-2页提交给新泽西州收费公路管理局的信件，以 及您设计的解决方案(不超过20页)，最多23页。注:附录和参考文献不计入23页之内。