1、数学中国国际赛论文参考模版分解第三届“认证杯”数学中国数学建模国际赛承 诺 书我们仔细阅读了第三届“认证杯”数学中国数学建模国际赛的竞赛规则。我们完全明白，在竞赛开始后参赛队员不能以任何方式（包括电话、电子邮件、网上咨询等）与队外的任何人（包括指导教师）研究、讨论与赛题有关的问题。我们知道，抄袭别人的成果是违反竞赛规则的, 如果引用别人的成果或其他公开的资料（包括网上查到的资料），必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出。我们郑重承诺，严格遵守竞赛规则，以保证竞赛的公正、公平性。如有违反竞赛规则的行为，我们将受到严肃处理。我们允许数学中国网站()公布论文，以供网友之间学
2、习交流，数学中国网站以非商业目的的论文交流不需要提前取得我们的同意。 我们的参赛队号为：1402我们选择的题目是： B 参赛队员 (签名) ： 队员1： 队员2：队员3： 参赛队教练员 (签名)： 无第三届“认证杯”数学中国数学建模国际赛编 号 专 用 页参赛队伍的参赛队号：（请各个参赛队提前填写好）：1402竞赛统一编号（由竞赛组委会送至评委团前编号）：竞赛评阅编号（由竞赛评委团评阅前进行编号）：TITLEAbstract: Key words: Contents1. Introduction.3 1.1 Why does toll way collects toll? .3 1.2 Tol
3、l 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 approximate the whole course of ? .52.2 How do we define the optimal configuration? .5 2.2.1 From the perspective of .5 2.2.2
4、 From the perspective of the 6 2.2.3 Compromise.62.3 Overall optimization and local optimization.62.4 The differences in weights and sizes of .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
5、.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 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. Conclu
6、sions.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 model19 5.2 Another layout of .23 5.3 The newly- adopted methods.236. References.237. Appendix.23 Programs and codes.24I. IntroductionIn order to indicate the ori
7、gin of problems, the following background is worth mentioning.1.1 1.2 1.3 1.4 1.5 1.6 II. The Description of the Problem2.1 How do we approximate the whole course of ? 2.2 How do we define the optimal configuration? 1) From the perspective of : 2) From the perspective of the : 3) Compromise: 2.3 The
8、 local optimization and the overall optimization Virtually: 2.4 The differences in weights and sizes of 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. 3.1.2 Assumptions 3.1.3 The
9、 Foundation of Model1) The utility function The cost of : The loss of : The weight of each aspect: Compromise: 2) The integer programmingAccording to theory, we can calculate the statistical properties as follows.3) The overall optimization and the local optimization The overall optimization: The lo
10、cal optimization: The optimal number of : 3.1.4 Solution and Result1) The solution of the integer programming:2) Results: 3.1.5 Analysis of the Result Local optimization and overall optimization: Sensitivity: The result is quite sensitive to the change of the three parameters Trend: Comparison: 3.1.
11、6 Strength and Weakness Strength: In despite of this, the model has proved that . Moreover, we have drawn some useful conclusions about . The model is fit for, such as Weakness: This model just applies to . As we have stated, . Thats just what we should do in the improved model.3.2 Improved Model3.2
12、.1 Extra SymbolsSigns and definitions indicated above are still valid. Here are some extra signs and definitions. 3.2.2 Additional Assumptions Assumptions concerning the process are the same as the Basic Model.3.2.3 The Foundation of Model1) How do we determine the optimal number?As we have conclude
13、d from the Basic Model, 3.2.4 Solution and Result1) Simulation algorithmBased on the analysis above, we design our simulation arithmetic as follows. Step1: Step2: Step3: Step4: Step5: Step6: Step7: Step8: Step9: 2) Flow chartThe figure below is the flow chart of the simulation.3) Solution3.2.5 Analy
14、sis of the Result3.2.6 Strength and Weakness Strength: The Improved Model aims to make up for the neglect of . The result seems to declare that this model is more reasonable than the Basic Model and much more effective than the existing design. Weakness: . Thus the model is still an approximate on a
15、 large scale. This has doomed to limit the applications of it. IV. Conclusions4.1 Conclusions of the problem 4.2 Methods used in our models 4.3 Applications of our models V. Future Work5.1 Another model5.1.1 The limitations of queuing theory5.1.2 5.1.3 5.1.4 1) 2) 3) 4) 5.2 Another layout of 5.3 The newly- adopted charging methodsVI. References1 2 3 4 VII. Appendix
