1、Abstract:Key words:TitleTeam # 4488Page 12 of 10Contents1. Introduction31.1 Why does toll way collects toll? .31.2 Toll modes 31.3 Toll collection methods . -31.4 Annoyance in tollplazas 31.5 The origin of the toll way problem . 3.1.6 Queuing theory . 4-.2. The Description of Problem-52.1 How do we

2、approximate the whole course of pay ing toll?52.2 How do we define the optimal configuration?: .52.2.1 From the perspective of motorist .52.2.2 From the perspective of the toll plaza 62.2.3 Compromise . . 6.2.3 Overall optimization and local optimization . 62.4 The differences in weights and sizes o

3、f vehicles . 72.5 What if there is no data available?73. Models 73.1 Basic Model73.1.1 Symbols and Definitions . 7.3.1.2 Assumptions . 8 .3.1.3 The Foun dati on of Model 93.1.4 Soluti on and Result 1.13.1.5 Analysis of the Result .11 .3.1.6 Strength and Weakness . -33.2 Improved Model143.2.1 Extra S

4、ymbols . 143.2.2 Additi onal Assumptions . 1.43.2.3 The Foun datio n of Model .143.2.4 Soluti on and Result- 15.3.2.5 Analysis of the Result 18 -.3.2.6 Strength and Weakness .194. Conclusions194.1 Conclusions of the problem . .194.2 Methods used in our models . .194.3 Application of our models . .19

5、 .5. Future Work195.1 Ano ther model 195.2 Another layout of toll plaza . 235.3 The newly- adopted charging methods . 236. References237. Appendix23Programs and codes .24I. I ntroductionIn order to indicate the origin of the toll way problems, the following background is worth men ti oning.1.11.21.3

6、1.41.51.6II. The Description of the Problem2.1 How do we approximate the whole course of paying toll?2.2 How do we define theoptimalconfiguration?1) From the perspective of motorist:2) From the perspective of the toll plaza:3) Compromise:2.3 The local optimization and the overall optimizationVirtual

7、ly:2.4 The differences in weights and sizes of vehicles2.5 What if there is no data available?III. Models3.1 Basic Model3.1.1 Terms, Definitions and SymbolsThe sig ns and defi niti ons are mostly gen erated fronqueu ing theory3.1.2 Assumptions3.1.3 The Foundation of Model1) The utility functionThe c

8、ost of toll plaza:The loss of motorist:The weight of each aspect:Compromise:2) The integer programmingAccord ing to queu ing theory, we can calculate the statistical properties as follows.3) The overall optimization and the local optimizationThe overall optimization:The local optimization:The optima

9、l number of tollbooths:3.1.4 Solution and Result1) The solution of the integer programming:2) Results:3.1.5 Analysis of the ResultLocal optimization and overalloptimization:Sensitivity:The result is quite sensitive to the change of ththree parametersTrend:Comparison:3.1.6 Strength and WeaknessStreng

10、th: In despite of this, the model has provecthat . Moreover, we have draw n some useful con clusi on sibout. The model is fit for, such asWeakness:This model just appliesto. As we have stated, . That sjust what we should do in the improved model.3.2 Improved Model3.2.1 Extra SymbolsSigns and defi ni

11、ti ons in dicated above are still valid. Here are some extra sig ns and defi niti ons.3.2.2 Additional AssumptionsAssumpti ons concerning the an terior 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 con cluded from the Basic

12、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 simulatio n.3) Solution3.2.5 Analysis of the Result3.2.6 Stre

13、ngth and WeaknessStrength: The Improved Model aims to make up forthe n eglect of.The result seems to declare that this model is more reas on able tha n the Basic Model and much more effective thanthe existi ng desig n.Weakness:. Thus the model is still an approximate on a large scale. Thishas doomed to limit the applications of it.IV. Conclusions4.1 Conclusions of the problem4.2 Methods used in our models4.3 Applicatio