关于美国高铁的数学建模(全英文)

28号交流的时间10:00----10:10 How should the national rail system be built?what the nation high speed rail will bring to American?

Summary

First of all, we select the top 20 states through the rankings of the total GDP of the U.S. states divided into seven economic zones in each economic region between First select total GDP and GDP per capita, the top row and a total population of more citiesdesign of high-speed rail line. After we are through the high-speed rail line to connect each economic zone, and eventually form a complete high-speed rail network. In the design of high-speed rail line, we use the prim algorithm. By constructing a minimum spanning tree to determine the railway between which two points is the best.

The construction of high-speed rail manufacturing relationship with the economy, tourism, Select economically developed regions reasons.First, according to the economic divide block, we get seven economic blocks through the analysis of GDP of 20 states, and then consolidated the top of the urban population and 50 selected priority to the construction of high-speed rail city, and finally we decided the 31 cities priority the construction of high-speed rail.The second year the main purpose is to connect some of the blocks, integrated urban population in 100 cities elected before connecting the city and some of the more populous city, and finally selected 26 new high-speed rail city.The third and fourth years of the connection of the eastern and western regions of the central region.The first five years the construction of the difficulty of some larger and some minor high-speed rail construction.

The impact of the aircraft on the high-speed railway, we assume that its effect is linear.800 miles ago, the choice of high-speed rail and aircraft are fixed, the number of aircraft in the 800 miles increased linearly select number of high-speed rail will decrease linearly.

Key words

The prim algorithm, Economic zones Linear effects

Contents

1. Introduction (3)

1.1 Why does toll way collects toll? (3)

1.2 Toll modes (3)

1.3 Toll collection methods (3)

1.4 Annoyance in toll plazas (3)

1.5 The origin of the toll way problem (3)

1.6 Queuing theory (4)

2. The Description of Problem (5)

2.1 How do we approximate the whole course of paying toll? (5)

2.2 How do we define the optimal configuration? (5)

2.2.1 From the perspective of motorist (5)

2.2.2 From the perspective of the toll plaza (6)

2.2.3 Compromise (6)

2.3 Overall optimization and local optimization (6)

2.4 The differences in weights and sizes of vehicles (7)

2.5 What if there is no data available? (7)

3. Models (7)

3.1 Basic Model (7)

3.1.1 Symbols and Definitions (7)

3.1.2 Assumptions (8)

3.1.3 The Foundation of Model (9)

3.1.4 Solution and Result (11)

3.1.5 Analysis of the Result (11)

3.1.6 Strength and Weakness (13)

3.2 Improved Model (14)

3.2.1 Extra Symbols (14)

3.2.2 Additional Assumptions (14)

3.2.3 The Foundation of Model (14)

3.2.4 Solution and Result (15)

3.2.5 Analysis of the Result (18)

3.2.6 Strength and Weakness (19)

4. Conclusions (19)

4.1 Conclusions of the problem (19)

4.2 Methods used in our models (19)

4.3 Application of our models (19)

5. Future Work (19)

5.1 Another model (19)

5.2 Another layout of toll plaza (23)

5.3 The newly- adopted charging methods (23)

6.References (23)

7.Appendix (23)

Programs and codes (24)