2020美赛数学建模 校级培训——Week_3_problem_c_data_wordle.xlsx

引言：

博主在今年寒假参加了学校组织的美国大学生数学建模竞赛培训， 在此，用博客来记录这段培训时光。

本篇博客将记录第三轮培训（1.14——1.19）的相关培训内容：

Day 11: 2020.1.14

第三轮模拟题：2017MCM_C

1. Problem

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 self- driving 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.

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 oth