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2021年2月10日发(作者：沈阳市实验学校)

The Keep-Right-Except-To-Pass Rule

Summary

As for the first question, it provides a traffic rule of keep right except to

pass, requiring us to verify its effectiveness. Firstly, we define one kind of

traffic

rule

different

from

the

rule

of

the

keep

right

in

order

to

solve

the

problem

clearly;

then,

we

build

a

Cellular

automaton

model

and

a

Nasch

model

by

collecting

massive data; next, we make full use of the numerical simulation according to

several

influence

factors

of

traffic

flow;

At

last,

by

lots

of

analysis

of

graph

we

obtain,

we

indicate

a

conclusion

as

follow:

when

vehicle

density

is

lower

than

0.15, the rule of lane speed control is more effective in terms of the factor

of safe in the light traffic; when vehicle density is greater than 0.15, so the

rule of keep right except passing is more effective In the heavy traffic.

As

for

the

second

question,

it

requires

us

to

testify

that

whether

the

conclusion

we obtain in the first question is the same apply to the keep left rule. First

of all, we build a stochastic multi-lane traffic model; from the view of the

vehicle flow stress, we propose that the probability of moving to the right is

0.7and to the left otherwise by making full use of the Bernoulli process from

the

view

of

the

ping-pong

effect,

the

conclusion

is

that

the

choice

of

the

changing

lane is random. On the whole, the fundamental reason is the formation of the

driving habit, so the conclusion is effective under the rule of keep left.

As for the third question, it requires us to demonstrate the effectiveness of

the result advised in the first question under the intelligent vehicle control

system.

Firstly,

taking

the

speed

limits

into

consideration,

we

build

a

microscopic traffic simulator model for traffic simulation purposes. Then, we

implement a METANET model for prediction state with the use of the MPC traffic

controller. Afterwards, we certify that the dynamic speed control measure can

improve the traffic flow .

Lastly neglecting the safe factor, combining the rule of keep right with the

rule of dynamical speed control is the best solution to accelerate the traffic

flow overall.

Key

words

：

Cellular

automaton

model Bernoulli

process Microscopic

traffic

simulator model The MPC traffic control

Content

Content

......... .................................................. ...................

2

1. Introduction

. .................................................. ...................

3

2. Analysis of the problem

< /p>

........................................ ...................

3

3. Assumption

... .................................................. ...................

3

4. Symbol Definition

.............................................. ...................

3

5. Models

....... .................................................. ...................

4

5.1 Building of the Cellular automaton model

.....................................

4

5.1.1 Verify the effectiveness of the keep right except to pass rule

.........

4

5.1.2 Numerical simulation results and discussion

............................

5

5.1.3 Conclusion

................. ............................................

8

5.2 The solving of second question

..............................................

8

5.2.1 The building of the stochastic multi-lane traffic model

................

9

5.2.2 Conclusion

................. ............................................

9

5.3 Taking the an intelligent vehicle system into a account

......................

9

5.3.1 Introduction of the Intelligent Vehicle Highway Systems

................

9

5.3.2 Control problem

.................... ....................................

9

5.3.3 Results and analysis

............... ....................................

9

5.3.4 The comprehensive analysis of the result

..............................

10

6. Improvement of the model

............... ..........................................

11

6.1 strength and weakness

............... .......................................

11

6.1.1 Strength

................... ...........................................

11

6.1.2 Weakness

................... ...........................................

11

6.2 Improvement of the model

.............. .....................................

11

7. Reference

.................. .................................................. ....

13

1. Introduction

As

is

known

to

all,

it

’

s

essential

for

us

to

drive

automobiles,

thus

the

driving

rules is crucial important. In many countries like USA, China, drivers obey the

rules

which

called

“

The

Keep-Right- Except-To-Pass

(that

is,

when

driving

automobiles, the rule requires drivers to drive in the right-most unless they

are passing another vehicle)

”

.

2. Analysis of the problem

For

the

first

question,

we

decide

to

use

the

Cellular

automaton

to

build

models,

then analyze the performance of this rule in light and heavy traffic. Firstly,

we mainly use the vehicle density to distinguish the light and heavy traffic;

secondly, we consider the traffic flow and safe as the represent variable which

denotes the light or heavy traffic; thirdly, we build and analyze a Cellular

automaton

model;

finally,

we

judge

the

rule

through

two

different

driving

rules,

and then draw conclusions.

3. Assumption

In order to streamline our model we have made several key assumptions



The highway of double row three lanes that we study can represent

multi-lane freeways.



The

data

that

we

refer

to

has

certain

representativeness

and

descriptive



Operation condition of the highway not be influenced by blizzard

or

accidental factors



Ignore the driver's own abnormal factors, such as drunk driving and

fatigue driving



The operation form of highway intelligent system that our analysis can

reflect

intelligent system



In the intelligent vehicle system, the result of the sampling data has

high accuracy.

4. Symbol Definition

i

The number of vehicles

t

The time

5. Models

By analyzing the problem, we decided to propose a solution with building a

cellular automaton model.

5.1 Building of the Cellular automaton model

Thanks to its simple rules and convenience for computer simulation, cellular

automaton

model

has

been

widely

used

in

the

study

of

traffic

flow

in

recent

years.

Let

< p>
x

i

(

t

)

be the position of vehicle

i

at time

t

,

v

i< /p>

(

t

)

be the speed of vehicle

i

at time

t

,

p

be the random slowing down probability, and R be the proportion

of

trucks

and

buses,

the

distance

between

vehicle

i

and

the

front

vehicle

at

time

t

is:

g ap

i



x

i



1

(

t

)



x

i

(

t

)



1

, if the front vehicle is a small vehicle.

gap

i



x

i



1

(

t

)

< br>

x

i

(

t

)



3

, if the front vehicle is a truck or bus.

5.1.1 Verify the effectiveness of the keep right except to pass rule

In addition, according to the keep right except to pass rule, we define a new

rule called:

Control rules based on lane speed. The concrete explanation of the

new rule as follow:

There is no special passing lane under this rule. The speed of the first lane

(the

far

left

lane)

is

120

–

100km/h

(including

100

km/h)

；

the

speed

of

the

second

lane

(the

middle

lane)

is

100

–

80km8/h

< p>
(including80km/h)

；

the

speed

of

the

third

lane (the far right lane) is below 80km/ h. The speeds of lanes decrease from

left to right.



Lane changing rules based lane speed control

If vehicle on the high-speed lane meets

v



v

con trol

,

gap

i

f

(

t

)



min(

v

i

< br>(

t

)



1

,

v

max

)

,

gap

i

b

(

t

)



gap

safe

,

the

vehicle

will

turn

into

the

adjacent

right

lane,

and

the

speed

of

the

vehicle

after

lane

changing

remains

unchanged,

where

v

control

is

the

minimum

speed of the corresponding lane.



The application of the Nasch model evolution

Let

P

d

be

the

lane

changing

probability

(taking

into

account

the

actual

situation that some drivers like driving in a certain lane, and will not take

the initiative to change lanes),

gap

i

f

(

t

)

indicates the distance between the

vehicle

and

the

nearest

front

vehicle,

gap

i

b

(

t

)

indicates

the

distance

between

the

vehicle and the nearest following vehicle. In this article, we assume that the

minimum safe distance gap safe of lane changing equals to the maximum speed of

the following vehicle in the adjacent lanes.



Lane changing rules based on keeping right except to pass

In general, traffic flow going through a passing zone (

Fig.

5.1.1) involves

three processes: the diverging process (one traffic flow diverging into two

flows), interacting process (interacting between the two flows), and merging

process (the two flows merging into one) [4].

Fig.5.1.1

Control plan of overtaking process

(1)

If

vehicle

on

the

first

lane

(passing

lane)

meets

gap

i

f

(

t

)



min(

v

i

< br>(

t

)



1

,

v

max

)

and

gap

i

b

(

t

)



gap

safe

,

the vehicle

will turn into the second lane, the speed of

the

vehicle after lane changing remains unchanged.

5.1.2 Numerical simulation results and discussion

In

order

to

facilitate

the

subsequent

discussions,

we

define

the

space

occupation rate as

p



(

N

CAR



3



N

truck

)

/

3



L

, where

N

CAR

indicates the number of

small

vehicles

on

the

driveway,

N

truck

indicates

the

number

of

trucks

and

buses

on

the

driveway,

and

L

indicates

the

total

length

of

the

road.

The

vehicle

flow

volume

Q

is

the

number

of

vehicles

passing

a

fixed

point

per

unit

time,

Q



N

T

< p>
/

T

,

where

N

T

is the number of vehicles observed in time duration

T

.The average speed

V

a



(

1

/

N



T

)



1



1

v

i

< br>t

,

v

i

t

is the speed of vehicle

i

at time

t

. Take overtaking

ratio

p

f

as

the

evaluation

indicator

of

the

safety

of

traffic

flow,

which

is

the

ratio

of

the

total

number

of

overtaking

and

the

number

of

vehicles

observed.

After

20,000

evolution

steps,

and

averaging

the

last

2000

steps

based

on

time,

we

have

obtained the following experimental results. In order to eliminate the effect

of randomicity, we take the systemic average of 20 samples [5].



Overtaking ratio of different control rule conditions

Because

different

control

conditions

of

road

will

produce

different

overtaking

ratio, so we first observe relationships among vehicle density, proportion of

large vehicles and overtaking ratio under different control conditions.

T

i

(a) Based on passing lane control (b) Based on speed control

Fig.

5.1.3

Fig.

5.1.3

Relationships

among

vehicle

density,

proportion

of

large

vehicles

and

overtaking

ratio

under

different control conditions.

It can be seen from

Fig.

5.1.3:

(1) when the vehicle density is less than 0.05, the overtaking ratio will

continue to rise with the increase of vehicle density; when the vehicle density

is larger than 0.05, the overtaking ratio will decrease with the increase of

vehicle

density;

when

density

is

greater than

0.12,

due

to

the

crowding,

it

will

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