PROBLEM C:“Cooperate and navigate”

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，司機在交通高峰時段遇到長時間的延誤

因為交通量超過了道路網路的設計容量。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釋出

對於這個問題。

自動駕駛，合作車已被提出作為增加公路容量的解決方案

而不增加車道或道路的數量。這些汽車的行為與現有的互動

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

效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，峰值和/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資料

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。

一些有用的背景資訊：

平均而言，每日交通量的8％發生在高峰旅行時間。

所有這些道路的名義速度限制為每小時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被分類為狀態路線，直到它與州際5相交。

如果此問題中提供的資料與任何其他來源之間存在衝突，請使用

這個問題提供的資料。

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：作為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

2017_MCM_Problem_C_Data.xlsx

2017_MCM_Problem_C_Map.pdf

C題重要提示：

The 2016 MCM introduces a new modeling challenge – Problem C - that is best described asData Insights. Problem C is intended to focus on and amplify specific elements of mathematicalmodeling challenges associated with data. In this sense, techniques stemming from statistics andpattern classification will play a larger role in creating a mathematical model on this problem than in previous contests.

While not a ‘big data’ challenge in the sense of teams needing to develop specialized computerscience-based data handling algorithms and analysis techniques or have access to highperformance computing platforms, the problem will provide teams with an opportunity toencounter real-world, challenging data that have interesting characteristics. Naturally occurringcomplicating factors such as data set size (but not big data), blend of data types, breadth ofrepresentation in data elements, cross-discipline sources, time series dependencies, censored ormissing data, and others could present themselves depending on the specifics of the modelingproblem.

MCM Problem C: Data Insights

Teams will be given access to database files that will be made available from a publicwebsite.

The database files will be compressed for size but the file size could still be 100mbs ormore and teams should take this into consideration prior to choosing Problem C.

Each zipped file may include the database files along with the data dictionary, datamapping file, and program code to create value labels.

The database will be made available in multiple formats SAS, SPSS, STATA and CSV.

Software such as Statistica, JMP, SAS, SPSS, Excel, R, Matlab or other applications maybe used to aid in your solution but no one particular piece of software is endorsed orrequired. If specialized software or custom code is used to support the contest effort,teams should take care to clearly communicate an understanding of the mathematics andassumptions applied via tools and algorithms in the software.

When submitting your final electronic solution you are NOT required to submit back thedatabase file or any data for that matter. The only thing that should be submitted is yourelectronic (word or PDF) solution.

© 2017 COMAP, The Consortium for Mathematics and Its Applications
May be reproduced for academic/research purposes
For More information on COMAP and this project visit http://www.comap.com

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