MCM北美数学建模论文模版.doc
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1、Team # 4488 Page 9 of 9TitleAbstract: Key words: Contents1. Introduction.3 1.1 Why does toll way collects toll? .3 1.2 Toll modes3 1.3 Toll collection methods.3 1.4 Annoyance in toll plazas.31.5 The origin of the toll way problem.31.6 Queuing theory.42. The Description of Problem.5 2.1 How do we app
2、roximate the whole course of paying toll? .52.2 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 plaza6 2.2.3 Compromise.62.3 Overall optimization and local optimization.62.4 The differences in weights and sizes of vehicle
3、s.72.5 What if there is no data available? .73. Models.73.1 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.133.2 Improved Model.14 3.2.1 Extra Symbols.14 3.2.2
4、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.194. Conclusions.19 4.1 Conclusions of the problem.194.2 Methods used in our models.19 4.3 Application of our models.195. Future Work.19 5.1 Another mod
5、el19 5.2 Another layout of toll plaza.23 5.3 The newly- adopted charging methods.236. References.237. Appendix.23 Programs and codes.24I. IntroductionIn order to indicate the origin of the toll way problems, the following background is worth mentioning.1.1 1.2 1.3 1.4 1.5 1.6 II. The Description of
6、the Problem2.1 How do we approximate the whole course of paying toll?llll2.2 How do we define the optimal configuration? 1) From the perspective of motorist: 2) From the perspective of the toll plaza: 3) Compromise: 2.3 The local optimization and the overall optimizationlll Virtually: 2.4 The differ
7、ences in weights and sizes of vehicles 2.5 What if there is no data available?III. Models3.1 Basic Model3.1.1 Terms, Definitions and SymbolsThe signs and definitions are mostly generated from queuing theory. l l l l l 3.1.2 Assumptionsl l l l l3.1.3 The Foundation of Model1) The utility functionl Th
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