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.

B題中文翻譯：

問題B：收費後合併

多車道有限接入收費公路使用“坡道收費”和“障礙收費”來收取駕駛員的收費。斜坡收費是在高速公路的入口或出口匝道處的收集機構，並且這些不關心我們在這裡。障礙收費是一排跨過高速公路的收費站，垂直於交通流的方向。通常（總是）更多的收費站比交通車道（見前2005年MCM問題B）。因此，當駛出收費站時，車輛必須從較大數量的收費站出口車道“扇入”到較少數量的常規行駛車道。收費廣場是高速公路需要用於促進障礙收費的區域，包括在障礙收費之前的扇出區域，收費路徑本身以及收費路徑之後的扇入區域。例如，三車道高速公路（一個方向）可以在障礙通行費中使用8個收費站。在支付了費用之後，車輛在具有與進入收費廣場相同數量的車道（在該示例中為三個）的高速公路上繼續行駛。

考慮在每個方向上具有L個行駛車道的收費高速公路和在每個方向上包含B個收費站（B> L）的障礙通行費。確定跟隨收費障礙的區域的形狀，尺寸和合並模式，其中車輛從B過街出口車道下行到L個車道。在您的模型中納入的重要注意事項包括事故預防，吞吐量（每小時通過廣場末端加入L外出車道的車輛數量）和成本（土地和道路建設昂貴）。特別地，該問題不僅僅要求可能已經實現的任何特定收費廣場設計的效能分析。重點是確定是否有比任何常用的更好的解決方案（形狀，大小和合並模式）。

確定您的解決方案在輕和重的流量的效能。隨著更多自主（自駕）車輛新增到交通組合中，您的解決方案如何改變？您的解決方案如何影響常規（人員配備）收費站，精確更換（自動）收費站和電子收費站（例如通過車輛中的應答器收集電子費用）的比例？

您的MCM提交應包括1頁摘要表，1-2頁給新澤西州收費公路管理局的信件，以及您的解決方案（不超過20頁），最多23頁。注意：附錄和參考文獻不計入23頁的限制。

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