2023年12月21日发(作者：高职高考数学试卷练习)
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
Team # 29254 Page 2 of 12
Content
Content ............................................................................................................................................................ 2
1。 Introduction ........................................................................................................................................... 3
2。 Analysis of the problem ...................................................................................................................... 3
3. Assumption ................................................................................................................................................ 3
4。 Symbol Definition ................................................................................................................................. 3
5. Models ......................................................................................................................................................... 3
5.1 Building of the Cellular automaton model .......................................................................................... 3
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 .................................................... 8
5。2.2 Conclusion ............................................................................................................................ 8
5。3 Taking the an intelligent vehicle system into a account ................................................................... 8
5.3。1 Introduction of the Intelligent Vehicle Highway Systems ................................................ 9
5.3。2 Control problem .................................................................................................................. 9
5.3.3 Results 9
5。3.4 The comprehensive analysis of the result .......................................................................... 9
6。 Improvement of the model ............................................................................................................... 10
6。1 strength and weakness .................................................................................................................... 10
6。1.1 Strength .............................................................................................................................. 10
6。1.2 Weakness ............................................................................................................................ 10
6.2 Improvement of the model ................................................................................................................. 11
7. Reference ................................................................................................................................................. 12
Team # 29254 Page 3 of 12
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
xi(t)be the position of vehicle
iat time
t,
vi(t) be the speed of vehicle
iat time
t,
Team # 29254 Page 4 of 12
and R be the proportion of trucks and buses， the
pbe the random slowing down probability，distance between vehicle
i and the front vehicle at time
tis:
gapixi1(t)xi(t)1, if the front vehicle is a small vehicle。
gapixi1(t)xi(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 （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
vvcontrol，
gapif(t)min(vi(t)1,vmax)，
gapib(t)gapsafe, the vehicle will turn into the adjacent right lane， and the speed of the
vehicle after lane changing remains unchanged, where
vcontrol is the minimum speed of the
corresponding lane.
The application of the Nasch model evolution
Let
Pd 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）,
gapif(t)
indicates the distance between the vehicle and the nearest front vehicle,
gapib(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
Team # 29254 Page 5 of 12
one) [4］。
Fig。5。1。1 Control plan of overtaking process
（1） If vehicle on the first lane (passing lane） meets
gapif(t)min(vi(t)1,vmax) and
gapib(t)gapsafe, 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
asp(NCAR3Ntruck)/3L, whereNCAR indicates the number of small vehicles on the
driveway,Ntruck 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,QNT/T， where
NTis the number of vehicles observed in time
average speed
Va(1/NT)11vit，
vitis the speed of vehicle
i at time
t。 Take overtaking ratio
pfas the evaluation indicator of the safety of traffic flow， which is
Tithe 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
Team # 29254 Page 6 of 12
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。
(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 become difficult to overtake， so the overtaking ratio is almost 0。
(2) when the proportion of large vehicles is less than 0.5, the overtaking ratio will rise with
the increase of large vehicles; when the proportion of large vehicles is about 0。5, the
overtaking ratio will reach its peak value; when the proportion of large vehicles is larger than
0.5, the overtaking ratio will decrease with the increase of large vehicles， especially under
lane-based control condition s the decline is very clear.
Concrete impact of under different control rules on overtaking ratio
Fig。5。1.4
Fig。5.1。4
Relationships among vehicle density， proportion of large vehicles and overtaking ratio under
different control conditions。 (Figures in left-hand indicate the passing lane control, figures in right-hand indicate the
speed control。
Pf1 is the overtaking ratio of small vehicles over large vehicles,
Pf2 is the overtaking ratio of
Team # 29254 Page 7 of 12
small vehicles over small vehicles，
Pf3 is the overtaking ratio of large vehicles over small vehicles，
Pf4 is the
overtaking ratio of large vehicles over large vehicles.）。
It can be seen from Fig. 5。1。4：
（1） The overtaking ratio of small vehicles over large vehicles under passing lane control is
much higher than that under speed control condition, which is because， under passing lane
control condition, high-speed small vehicles have to surpass low-speed large vehicles by the
passing lane， while under speed control condition， small vehicles are designed to travel on
the high—speed lane， there is no low- speed vehicle in front， thus there is no need to
overtake。
Impact of different control rules on vehicle speed
Fig。 5。1.5
Relationships among vehicle density， proportion of large vehicles and average speed under
different control conditions. （Figures in left-hand indicates passing lane control, figures in right—hand indicates
speed control.
Xa is the average speed of all the vehicles，
Xa1 is the average speed of all the small vehicles，
Xa2 is the average speed of all the buses and trucks。）.
It can be seen from Fig。 5。1。5:
(1） The average speed will reduce with the increase of vehicle density and proportion of
large vehicles.
(2) When vehicle density is less than 0.15,Xa，Xa1andXa2are almost the same under both
control conditions。
Effect of different control conditions on traffic flow
Team # 29254 Page 8 of 12
Fig。5.1。6
Fig. 5.1.6 Relationships among vehicle density, proportion of large vehicles and traffic flow under different
control conditions. （Figure a1 indicates passing lane control, figure a2 indicates speed control, and figure b
indicates the traffic flow difference between the two conditions.
It can be seen from Fig. 5。1.6：
（1) When vehicle density is lower than 0.15 and the proportion of large vehicles is from 0。4 to 1, the traffic flow of the two control conditions are basically the same。
(2) Except that, the traffic flow under passing lane control condition is slightly larger than
that of speed control condition。
5。1。3 Conclusion
In this paper， we have established three-lane model of different control conditions， studied
the overtaking ratio, speed and traffic flow under different control conditions， vehicle density
and proportion of large vehicles.
5.2 The solving of second question
5.2.1 The building of the stochastic multi-lane traffic model
5。2。2 Conclusion
On one hand， from the analysis of the model, in the case the stress is positive， we also
consider the jam situation while making the decision. More specifically， if a driver is in a jam
situation， applying
B(2,PR(x)) results with a tendency of moving to the right lane for this
driver. However in reality， drivers tend to find an emptier lane in a jam situation. For this
reason, we apply a Bernoulli process
B(2,0.7) where the probability of moving to the right is
0.7and to the left otherwise， and the conclusion is under the rule of keep left except to pass,
So， the fundamental reason is the formation of the driving habit。
5.3 Taking the an intelligent vehicle system into a account
For the third question， if vehicle transportation on the same roadway was fully under the
control of an intelligent system， we make some improvements for the solution proposed by us
Team # 29254 Page 9 of 12
to perfect the performance of the freeway by lots of analysis.
5。3。1 Introduction of the Intelligent Vehicle Highway Systems
We will use the microscopic traffic simulator model for traffic simulation purposes. The
MPC traffic controller that is implemented in the Matlab needs a traffic model to predict the
states when the speed limits are applied in Fig.5。3。1. We implement a METANET model for
prediction purpose[14］。
5。3。2 Control problem
As a constraint, the dynamic speed limits are given a maximum and minimum allowed value.
The upper bound for the speed limits is 120 km/h, and the lower bound value is 40 km/h. For
the calculation of the optimal control values, all speed limits are constrained to this range。
When the optimal values are found, they are rounded to a multiplicity of 10 km/h， since this is
more clear for human drivers, and also technically feasible without large investments。
5。3。3 Results and analysis
When the density is high， it is more difficult to control the traffic， since the mean speed
might already be below the control speed。 Therefore， simulations are done using densities at
which the shock wave can dissolve without using control， and at densities where the shock
wave remains. For each scenario， five simulations for three different cases are done, each with
a duration of one hour. The results of the simulations are reported in Table 5。1, 5。2, 5.3。
Table。5。1 measured results for the unenforced speed limit scenario
qdem
case
no shock
wave
no
controlled
controlled
no shock
wave
＃1
494。73
520.42
513。45
#2
＃3 ＃4
#5
428。30
539。58
TTS:mean（std）
TPN
445.21（6.9%）
5:41
517。92（4.9％）
6:36
4700
4700
4700
4700
452.15 435.98 414.88
517。48
536.13
475。98
488.43 521.35 479.75 486.50
500.75（4.0％） 6：24
521。10
489。43
493.96(3.5％）
604.84(5.3％)
6:03
7:24
493.90 472.60 492.78
584。92
654.12
643。72
589。77
4700 uncontrolled 635.10
4700 controlled
575。30
571.85 588.63
572。15
586。46
597。84（6。 4％）
7:19
Enforced speed limits
Intelligent speed adaptation
For the ISA scenario, the desired free-flow speed is about 100％ of the speed limit. The
desired free-flow speed is modeled as a Gaussian distribution, with a mean value of 100％ of
the speed limit, and a standard deviation of 5％ of the speed limit。 Based on this percentage，
the influence of the dynamic speed limits is expected to be good［19］.
5.3。4 The comprehensive analysis of the result
Team # 29254 Page 10 of 12
From the analysis above, we indicate that adopting the intelligent speed control system can
effectively decrease the travel times under the control of an intelligent system， in other
words， the measures of dynamic speed control can improve the traffic flow.
Evidently, under the intelligent speed control system， the effect of the dynamic speed
control measure is better than that under the lane speed control mentioned in the first problem.
Because of the application of the intelligent speed control system， it can provide the optimal
speed limit in time。 In addition, it can guarantee the safe condition with all kinds of detection
device and the sensor under the intelligent speed system.
On the whole， taking all the analysis from the first problem to the end into a account, when
it is in light traffic, we can neglect the factor of safe with the help of the intelligent speed
control system。
Thus， under the state of the light traffic, we propose a new conclusion different from that in
the first problem: the rule of keep right except to pass is more effective than that of lane speed
control.
And when it is in the heavy traffic， for sparing no effort to improve the operation efficiency
of the freeway， we combine the dynamical speed control measure with the rule of keep right
except to pass, drawing a conclusion that the application of the dynamical speed control can
improve the performance of the freeway.
What we should highlight is that we can make some different speed limit as for different
section of road or different size of vehicle with the application of the Intelligent Vehicle
Highway Systems。
In fact, that how the freeway traffic operate is extremely complex， thereby， with the
application of the Intelligent Vehicle Highway Systems， by adjusting our solution originally，
we make it still effective to freeway traffic.
6。 Improvement of the model
6。1 strength and weakness
6。1。1 Strength
it is easy for computer simulating and can be modified flexibly to consider actual traffic
conditions ，moreover a large number of images make the model more visual。
The result is effectively achieved all of the goals we set initially, meantime
the conclusion is
more persuasive because of we used the Bernoulli equation。
We can get more accurate result as we apply Matlab.
6。1。2 Weakness
The relationship between traffic flow and safety is not comprehensively analysis.
Due to there are many traffic factors, we are only studied some of the factors， thus our
model need further improved。
Team # 29254 Page 11 of 12
6。2 Improvement of the model
While we compare models under two kinds of traffic rules， thereby we come to the
efficiency of driving on the right to improve traffic flow in some circumstance。 Due to the
rules of comparing is too less， the conclusion is inadequate. In order to improve the accuracy，
We further put forward a kinds of traffic rules: speed limit on different type of cars。
The possibility of happening traffic accident for some vehicles is larger, and it also brings
hidden safe troubles。 So we need to consider separately about different or specific vehicle
types from the angle of the speed limiting in order to reduce the occurrence of traffic
accidents， the highway speed limit signs is in Fig。6.1。
Fig。6.1
Advantages of the improving model are that it is useful to improve the running condition
safety of specific type of vehicle while considering the difference of different types of vehicles.
However, we found that the rules may be reduce the road traffic flow through the analysis。 In
the implementation it should be at the
V85speed of each model as the main reference basis. In
recent years, the
V85of some researchers for the typical countries from Table 6.1［ 21]：
Table 6。1 Operating speed prediction mode
Author
Ottesen and
Krammes2000
Country
America
Model
V85102.441.57DC0.012LC0.01DCLC
V8598.25(2795/R)(894/Ra)7.486DC9.308LT
[]Andueza2000 Venezuela
Jessen2001
Donnell2001
America
America
V85100.69(3032/R)27.819LT[]
V8572.100.432VP0.00212ADT[NLSD]
V8586.800.279VP0.614G10.00239ADT[LSD]
V85(2)78.40.0140R1.40G20.00724LT2
V85(3)75.10.0176R1.48G20.008369LT2
Team # 29254 Page 12 of 12
V85(4)74.50.0176R1.69G20.00810LT2
V85(5)83.12.08G20.00934LT2
BucchiA。BiasuzziK。
And
SimoneA。2005
Fitzpatrick
Italy
V8566.1640.124DC
V8555.3663.46E0.4DCV8565.7450.119DC1.35E0.5DC2
America
V85111.07175.98
KMeanwhile, there are other vehicles driving rules such as speed limit in adverse weather
conditions. This rule can improve the safety factor of the vehicle to some extent. At the same
time， it limits the speed at the different levels.
7。 Reference
［1] M。 Rickert， K. Nagel， M. Schreckenberg， A。 Latour， Two lane traffic simulations
using cellular automata， Physica A 231 (1996) 534–550.
［20］ J.T. Fokkema, Lakshmi Dhevi, Tamil Nadu Traffic Management and Control in
Intelligent Vehicle Highway Systems，18（2009)。
［21] Yang Li, New Variable Speed Control Approach for Freeway. (2011） 1-66
更多推荐
高职,高考,数学试卷,练习,作者
发布评论