Problem B: Merge After Toll
Multi-lane divided limited-access toll highways use “ramp tolls” and “barrier tolls” to collect tolls from motorists. A ramp toll is a collection mechanism at an
entrance or exit ramp to the highway and these do not concern us here. A barrier toll is a row of tollbooths placed across the highway, perpendicular to the
direction of traffic flow. There are usually (always) more tollbooths than there are incoming lanes of traffic (see former 2005 MCM Problem B). So when exiting the tollbooths in a barrier toll, vehicles must “fan in” from the larger number of tollbooth egress lanes to the smaller number of regular travel lanes. 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. 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).
Consider a toll highway having L lanes of travel in each direction and a barrier toll containing B tollbooths (B > L) in each direction. 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. 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). In particular, this problem does not ask for merely a performance analysis of any particular toll plaza design that may already be implemented. The point is to determine if there are better solutions (shape, size, and merging pattern) than any in common use.
Determine the performance of your solution in light and heavy traffic. How does your solution change as more autonomous (self-driving) vehicles are added to the traffic mix? 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)?
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.
多车道有限接入收费公路使用“坡道收费”和“障碍收费” 收取驾驶人士的收费。斜坡收费是一个收集机制
入口或出口匝道到高速公路，这些不关心我们在这里。障碍 收费是一排收费站横跨高速公路，垂直于 交通方向。通常（总是）更多的收费站比 （见2005年前MCM问题B）。所以退出时 收费站在通行费，车辆必须“扇入”从大量
收费站出口车道到较少数量的常规旅行车道。收费广场 是高速公路所需的便利通行费的区域，包括
障碍物前的扇出区域，收费口障本身以及后面的扇入区域 收费屏障。例如，三车道公路（一个方向）可以使用8 收费站。在支付费用后，车辆继续他们的旅程
在具有与进入收费广场相同数量的车道的高速公路上 （在本示例中为三个）。
考虑在每个方向上具有L个行驶车道的收费高速公路和障碍收费 （B> L）。确定形状，大小和
合并模式的区域跟随收费障碍车辆扇入
B收费站出口线下至L车道的交通。重要注意事项 包括在您的模型包括事故预防，吞吐量（ 车辆每小时通过广场的末端加入L的点 出行车道）和成本（土地和道路建设昂贵）。在 特别的，这个问题不要求任何的性能分析
特定的收费广场设计可能已经实施。关键是要
确定是否有更好的解决方案（形状，大小和合并模式） 任何常见的使用。
确定您的解决方案在轻和重的流量的性能。如何 您的解决方案随着更多自主（自驾）车辆添加而改变 交通混合？你的解决方案如何影响常规的比例 （人员）收费站，精确更换（自动）收费站和电子 收费亭（例如通过转发器在电子收费站收集 车辆）？
您的MCM提交应包含1页的摘要表，1-2页
给新泽西州收费公路局的信，以及您的解决方案（不超过20 页面），最多23页。注意：附录和参考文献没有 计数到23页的限制。
2017年建模美赛B题带翻译
