2017美赛数学建模M奖论文

For office use only

T1 ________________

T2 ________________

T3 ________________

T4 ________________

Team Control Number

For office use only

F1 ________________

F2 ________________

70028

Problem Chosen

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F4 ________________

B

2017

MCM/ICM

Summary Sheet

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Type a summary of your results on this page. Do not include the name of your school, advisor, or team members on this page.

Summary

The performance of highway toll plaza directly affects the capacity of the

highway, so the design of road toll plaza is imperative.

In this paper, we conduct performance analysis for a specific toll plaza in New

Jersey, USA, including accident prevention, throughput and cost. First of all, we use

grey model to predict the future output of the toll plaza, and compared with the real

data, the average value of the residual value is 0.429. Then we can draw a conclusion

that the throughput performance of the toll plaza is secondary. Next, we use queuing

theory to get the service index of the toll plaza in the light and heavy traffic, and the

cellular automaton model is used to consider the changing circumstances of service

level, uses regression model to establish a function relation between traffic accident

and four factors. Then, we find that the rate of change has the greatest influence on

it and the pavement performance has the least influence . In terms of cost, we

consider the toll plaza land and road construction. And the cost of road construction

is divided into the labor cost and material cost.

Next, according to the influence of road geometry on the traffic performance of

Toll Plaza, we select the transition curve trajectory model to improve the toll plaza

transition, which can also have an improvement on the size and shape of the toll plaza

and merge mode.

Finally, we do a series of performance studies for our improved toll plaza. First

of all, the improvement in the square flow and car flow under the condition of service

level are determined respectively through simulation .Next, we draw a conclusion that

the service performance of the toll plaza is not obvious in small car flow, but there is a

marked increase in large flow. Then, due to the fact that the unmanned vehicle could

deal with a variety of road conditions, it undoubtedly expands our improved optional

scheme. Eventually, we obtain the throughput of toll before and after the improvement

under the different proportion of mixed charge mode and find that the improved

throughput in the toll plaza has been increased on the performance.

contents

1 Introduction: ............................................................................................................ 1

1.1 Problem background: ................................................................................... 1

1.2 Steps: ............................................................................................................ 1

1.3 Our work: ..................................................................................................... 1

2 Assumptions ............................................................................................................ 2

3 Nomenclature .......................................................................................................... 2

4 Throughput analysis of grey 3

5 error analysis ........................................................................................................... 4

6 Service level of toll station ..................................................................................... 5

7 Vehicle lane changing rules based on Cellular Automata ....................................... 6

8 Security analysis based on multivariate statistical regression mode ...................... 8

8.1 Study on the rate of change of Toll Plaza ..................................................... 8

8.2 Study on the longitudinal slope of entrance section of Toll Plaza ............... 9

8.3 Research on service level of toll station ..................................................... 10

8.4 Study on pavement performance of toll station .......................................... 10

9 Safety performance evaluation model of toll station ............................................ 11

10 Cost analysis model of toll station .................................................................... 11

11 Analysis of the influence of lane geometry parameters on its capacity ............ 12

11.1 Determination of lane changing rate .......................................................... 12

11.2 Influence of geometric parameters on the flow of the car lane .................. 14

11.3 Energy consumption analysis based on cellular automata model .............. 15

Definition of energy consumption: ................................................................ 16

Numerical simulation and analysis of the results: ......................................... 17

Influence of curvature radius on energy consumption ................................... 17

Influence of arc length on energy consumption ............................................. 18

12 The effect of traffic flow on service performance based on improved queuing

theory 19

13 The influence of unmanned vehicles on the improved model of Toll Plaza .. 21

14 The influence of charging method on improving model of Toll Plaza .......... 21

15 Strengths and Weaknesses ............................................................................. 22

15.1 Strengths: .................................................................................................... 22

15.2 Weaknesses: ................................................................................................ 22

15.3 Future Model Development: ...................................................................... 22

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Comprehensive improvement strategy of toll

plaza

1

Introduction:

1.1 Problem background:

Highway toll and toll plaza is to ensure traffic safety and unimpeded, however

because of lack of unified design specification, toll station and its square construction

exists many problems. Such as: low value because of the technical indicators to make

square construction scale too small and cause the toll plaza opened only few years as

the traffic bottleneck, and use the high value on the one hand, because of the

technical indicators and make the toll station construction scale is too large, waste a

lot of money and resources. Due to incorrect linear indicators, or too short, the

gradual square square length is insufficient, square road centerline offset, etc., it is

too difficult to use after the completion of the establishing the toll gates

and the toll plaza design norms, as soon as possible, has the very vital significance in

standardizing the construction of the toll station, ensuring the smooth general

characteristic of toll plaza and traffic safety, improving the charging efficiency and

management level, reducing the land acquisition and controlling investment and so

on .

1.2 Steps:

·A performance analysis of any particular toll plaza design that may already be

implemented through the following three factors: accident prevention, throughput

and cost .

·Determine if there are better solutions (shape, size, and merging pattern) than any

in common use.

·Consider the performance of your solution in light and heavy traffic.

·Consider the situation where more autonomous (self-driving) vehicles are added

and how the solution is affected by the proportions of conventional (human-staffed)

tollbooths, exact-change (automated) tollbooths, and electronic toll collection

booths (such as electronic toll collection via a transponder in the vehicle)

1.3 Our work:

·Based on the available data ,we make a performance analysis of any particular

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toll plaza design that may already be implemented .

·According to the problem from the performance analysis ,we make out a

better solutions (shape, size, and merging pattern) than any in common use.

·Determine the performance of the solution in light and heavy traffic ,how the

solution change as more autonomous (self-driving) vehicles are added to the traffic

mix and how the solution is affected by the proportions of conventional

(human-staffed) tollbooths, exact-change (automated) tollbooths, and electronic toll

collection booths.

2

Assumptions

To simplify the problem and make it convenient for us to simulate real-life

conditions, we make the following basic assumptions.

1. Each section of roads is one-way traffic

es in the retention period of toll station can be neglected

any hour of the vehicle arrival rate is proportional to the length of time

probability of any vehicle arrival in one hour of time is not affected by the

previous history .

5. The vehicles arrive in line with the Poisson distribution, namely the headway

is negative exponential distribution

3

Nomenclature