2006MCMB题

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交流美赛经验、共同进步

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此贴为又为青年提供交流平台

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加油加油加油哦

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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

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