Traffic capacity is limited in many regions of the United States due to the number of lanes of roads. For example, in the Greater Seattle area drivers experience long delays during peak traffic hours because the volume of traffic exceeds the designed capacity of the road networks. This is particularly pronounced on Interstates 5, 90, and 405, as well as State Route 520, the roads of particular interest for this problem.
Self-driving, cooperating cars have been proposed as a solution to increase capacity of highways without increasing number of lanes or roads. The behavior of these cars interacting with the existing traffic flow and each other is not well understood at this point.
The Governor of the state of Washington has asked for analysis of the effects of allowing self-driving, cooperating cars on the roads listed above in Thurston, Pierce, King, and Snohomish counties. (See the provided map and Excel spreadsheet). In particular, how do the effects change as the percentage of self-driving cars increases from 10% to 50% to 90%? Do equilibria exist? Is there a tipping point where performance changes markedly? Under what conditions, if any, should lanes be dedicated to these cars? Does your analysis of your model suggest any other policy changes?
Your answer should include a model of the effects on traffic flow of the number of lanes, peak and/or average traffic volume, and percentage of vehicles using self-driving, cooperating systems. Your model should address cooperation between self-driving cars as well as the interaction between selfdriving and non-self-driving vehicles. Your model should then be applied to the data for the roads of interest, provided in the attached Excel spreadsheet.
Your MCM submission should consist of a 1 page Summary Sheet, a 1-2 page letter to the Governor’s office, 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.
Some useful background information: On average, 8% of the daily traffic volume occurs during peak travel hours. The nominal speed limit for all these roads is 60 miles per hour. Mileposts are numbered from south to north, and west to east. Lane widths are the standard 12 feet. Highway 90 is classified as a state route until it intersects Interstate 5. In case of any conflict between the data provided in this problem and any other source, use the data provided in this problem.
Definitions: milepost: A marker on the road that measures distance in miles from either the start of the route or a state boundary. average daily traffic: The average number of cars per day driving on the road. interstate: A limited access highway, part of a national system. state route: A state highway that may or may not be limited access. route ID: The number of the highway. increasing direction: Northbound for N-S roads, Eastbound for E-W roads. decreasing direction: Southbound for N-S roads, Westbound for E-W roads.
C題中文翻譯：
問題C：“合作和導航”
由於道路的數量，美國許多地區的交通容量有限。
例如，在大西雅圖地區，司機在交通高峯時段遇到長時間的延誤
因爲交通量超過了道路網絡的設計容量。這是特別
在州際公路5號，90號和405號以及州道路520號，特別感興趣的道路上發佈
對於這個問題。
自動駕駛，合作車已被提出作爲增加公路容量的解決方案
而不增加車道或道路的數量。這些汽車的行爲與現有的交互
交通流和對方在這一點上還不太瞭解。
華盛頓州州長要求分析允許自駕的影響，
在Thurston，Pierce，King和Snohomish縣上列的道路上合作汽車。 （看到
提供的地圖和Excel電子表格）。特別是，效果如何改變
自駕車的百分比從10％增加到50％到90％？是否存在平衡？有沒有
性能變化明顯的傾翻點？在什麼條件下，如果有的話，應該有車道
專用於這些車？您對模型的分析是否表明有任何其他政策變化？
您的答案應包括對車道數量，峯值和/或車道數量的影響的模型
平均交通量，以及使用自動駕駛，合作系統的車輛的百分比。你的
模型應該解決自駕車之間的合作以及自驅動車之間的相互作用
和非自駕車輛。您的模型應該應用於的道路的數據
利息，在附加的Excel電子表格中提供。
您的MCM提交應包含1頁的摘要表，1 - 2頁的信
總督辦公室和您的解決方案（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。
一些有用的背景信息：
平均而言，每日交通量的8％發生在高峯旅行時間。
所有這些道路的名義速度限制爲每小時60英里。
里程數從南到北，從西到東。
車道寬度是標準的12英尺。
高速公路90被分類爲狀態路線，直到它與州際5相交。
如果此問題中提供的數據與任何其他來源之間存在衝突，請使用
這個問題提供的數據。
定義：
milepost：在路上測量距離，從路線的起點或a
狀態邊界。
平均每日交通量：在道路上行駛的平均每天的汽車數量。
州際公路：作爲國家系統的一部分的有限進出高速公路。
國家路線：可能受限或不受限制的國家公路。
路由ID：高速公路的編號。
增加方向：N-S道北行，E-W道東行。
下降方向：N-S道南行，E-W道西行。
附件見：
http://blog.sciencenet.cn/home.php?mod=attachment&filename=2017_MCM_Problem_C_Data.xlsx&id=94053
http://blog.sciencenet.cn/home.php?mod=attachment&filename=2017_MCM_Problem_C_Map.pdf&id=94054