Traffic Flow And Safety Analysis On Cellular Automata Model

Traffic Flow & Safety Analysis For Designing Effective Rules

Author : Luo Jianlan, Gan Xu, Xiang Chao

Corresponding Address : Wuhan University of Technology, Hongshan District, Wuhan, China

SummaryTraffic rule is a key factor affecting traffic flow and safety. We develop our modelaiming at calculating traffic flow and evaluating safety conditions with varied trafficrules.

Based on the NasCh rules, a model of cellular automata traffic flow is proposed tocalculate traffic flow. And a linear regression model is built to evaluate safetycondition, with variables being posted speed limits, average speed and traffic flow.

We investigate four types of paths in a freeway, namely two straight lanes, threestraight lanes, ramps, and roundabouts. In studies of these four cases, traffic flow,“time-space” map and safety condition are obtained under light and heavy trafficrespectively. And then we compare the “Keep-Right-Except-To-Pass” rule with thefree rule in the two-straight-lane case.

The results demonstrate that “Keep-Right-Except-To-Pass” rule is not as effective asthe free rule in promoting traffic flow; however, this rule ensures safety for driversbetter than the free rule. Additionally, a new traffic rule, which sets different postedspeed limits for adjacent lanes, is proposed to promote better traffic flow with safetyrequirements satisfied.

For left driving norms, our solution could be simply carried over with the substitutionof two initial conditions, i.e. position for vehicles to depart and lane-changing rules.We establish an intelligent system ignoring the previous randomness of deceleratingand lane-changing, under which both traffic flow and safety condition get better.

Finally, model’s sensitivity analysis regarding to probability of decelerating andposted speed limits proves its stability.

Key words: Traffic Flow Cellular Automata Linear Regression

Contents1 Introduction......................................................................................................................................12 Conventions......................................................................................................................................23 Assumptions..................................................................................................................................... 24 Cellular Automata............................................................................................................................ 35 Model Review.................................................................................................................................. 3

5.1 Traffic Flow Model...............................................................................................................45.2 Safety Simulation Model...................................................................................................... 7

6 Case Studies..................................................................................................................................... 86.1 Two-Straight-Lane Case....................................................................................................... 9

1) Light Traffic Case...........................................................................................................92) Heavy Traffic Case....................................................................................................... 10

6.2 Three-Straight-Lane Case...................................................................................................121) Light Traffic Case.........................................................................................................122) Heavy Traffic Case....................................................................................................... 13

6.3 Ramp Case.......................................................................................................................... 141) Light Traffic Case.........................................................................................................152) Heavy Traffic Case....................................................................................................... 16

6.4 Roundabout Case................................................................................................................ 181) Light Traffic Case.........................................................................................................192) Heavy Traffic Case....................................................................................................... 20

7 Effective Rules and Alternatives....................................................................................................228 Left Driving Norms........................................................................................................................249 Intelligent System.......................................................................................................................... 2510 Result Analysis.............................................................................................................................26

10.1 Sensitivity Analysis...........................................................................................................2610.2 Strengths and Weaknesses................................................................................................ 28

11 References.................................................................................................................................... 29

Team#28559 Page 1 of 31

1 Introduction

We address the problem of generating an optimal situation for tradeoffs betweentraffic flow and safety according to the given rules. The optimal situation contains twoaspects, the maximum of traffic flow and the minimum of accidents. Considering theambiguous statements, we make our own definition of some aspects in the problem.We define the two-lane paths, three-lane paths, roundabout and ramps to eliminate thecomplexity of real condition of freeways. In the process, we establish an advancedmodel to cover all these conditions and lane-changing. Besides, we develop anaccurate model to quantify safety, which includes other factors like weather.

Recently, different models of traffic flow in terms of the theory cellular automata (CA)have been proposed. Nagel and Schreckenberg proposed a model under four rules fortraffic flow of a single lane in 1992. Simultaneously, the NaSch model laid thefoundation of modeling in traffic flow. However, the traffic flow in our daily life isgenerally composed of various types of vehicles with different desired speeds andmoving in more than one lane. Then the models of two lanes and three lanes arepublished allowing the simulation of lane change. From then on, the study of the flowof the multi-lane traffic starts. Multi-lane models are currently studied in depthbecause these are closer to what happens to the flow of traffic in our daily life. In ourtraffic flow model, we take two-lane and three-lane for example to discuss theproblem respectively, which can be deduced to the general cases. [1] [2] [3] [4]

Hence, we develop the primary traffic flow model on the NaSch’s and make differentrules of changing lanes for two-lane ,three-lane, ramps and roundabout. Case study onthese conditions is of great significance for finding the tradeoffs between traffic flowand safety. Given the factors of safety, we establish the next model to guarantee theminimum number of accidents. Then we are required to discuss the effectiveness ofthis rule in promoting traffic flow and suggest alternative factors. Lastly, we aresupposed to generalize the discussion of former rule to the opposite rule and applyearlier analysis to the intelligent system. In the process, we solve the problem byimproving the existing algorithm to simulate the lane-changing, and it can prove outthe rationality of our results.

We approach the problem by first mathematically analyzing the two major factors,traffic flow and safety, in lane-changing, and establish two major models to quantifythese two factors and make tradeoffs between them. Then we examine theperformance of the Keep-Right-Except-To-Pass rule, including in conditions underlight or heavy traffic and promoting traffic flow.


We also develop a computer simulation which model the traffic flow process whileaccounting for various freeway conditions and the safety factors. In addition, weapply our method of simulation to obtaining the desired conditions and test our results.Finally, we analyze the sensitivity of our results and discuss the strengths andweaknesses of our models.

2 Conventions

This section defines the basic terms used in this paper. The following definitions andvariables will be used in our discussion of the problem.

L is the number of cells in a 1-dimensinal array.

nd stands for the distance between the n th vehicle and its front one. And we

use ,n fd for the distance between the n th vehicle and its front one in adjacent

lanes, ,n bd for the distance between the n th vehicle and its rear one in adjacent

lanes.

nC stands for the lane which the n th vehicle is in.

K is a key parameter to measure safety condition, which records total numbers of

such situations

vS is a speed variable coefficient to measure posted speed limits. We use an

equation in the safety simulation model to calculate it.

is a variable parameter in terms of VS .It is classified in relation to the different

values of VS .

F refers to the accident rate in the equation of safety simulation model.

3 Assumptions

We make the following assumptions about the problem to simplify analysis.

The physical quantities in our simulation correspond to that in real traffic for an

exact proportion. This is a vital assumption in our process of simulation and

guarantees the validity of our simulation.

The micro-level dynamics can reflect that in macro-level. Thus, the

micro-interactions are of great significance and typical in modeling.

We assume that the majority drivers are willing to the maximum speed, and the

others choose the cruise control system. It leads to randomness in the problem.

The freeways we discussed are flat. We ignored the rugged condition of freeways.


We assume that the psychological factors of drivers have little influence on our

model and we ignore these.

4 Cellular Automata

Cellular automata (CA) were first proposed by Von Neumann in 1950s. And it was notuntil the 1970s and Conway’s Game of Life, a two-dimensional cellular automaton,that interest in the subject expanded beyond academia. [5] As a discrete model, CAhas been widely applied in many fields of science, especially in traffic flow problem.CA models are conceptually simple, thus we can use a set of simple CA rules toproduce complex behavior. Besides, CA models have the distinction of being able tocapture micro-level dynamics and relate these to macro-level traffic flow behavior.This is in contrast with existing models, which are either aggregate in their treatmentof traffic flow (macroscopic models) or detailed and limited in scope (microscopicmodels). Hence, CA models gain the advantage of capturing the complexity of thereal traffic adequately. [6]

A cellular automaton consists of a regular grid of cells. Each is in one of a finitenumber of states, such as on and off, which are in contrast to a coupled map lattice.And the grid can be in any finite number of dimensions. For each cell, a set of cellscalled its neighborhood is defined relative to the specified one. An initial state isselected by assigning a state for each cell and a new generation is created according tosome fixed rule. The rule determines the new state of each cell in terms of the currentstate and its neighborhood. Simultaneously, the updating rule is applied to the wholegrid and would not change over time.

5 Model Review

In order to eliminate the complexity of real traffic of freeways, we take four types ofpaths into consideration, i.e. two-lane paths, three-lane paths, ramps and roundabout.We wish to simulate traffic flow and accident rate (which we regard as an indicatorreflecting safety condition) respectively using our models. Hence, we develop twotypes of models to solve this problem: for the one to simulate traffic flow, we setdifferent traffic rules to obtain flow data and time-space evolution tracking curve foreach vehicle; while we apply multiple regression analysis to fit accident rate underdifferent circumstances in the other one.


5.1 Traffic Flow Model

This model basically consists of two components, i.e. following and passing. CA hasbeen widely applied in traffic flow researches, and has laid solid fundamental in thisarea [7]. And NasCh model is a well-reputed one among those traffic flow models;however, it is defined on a 1-dimensional array, which is so simplified that can notcover most situations. Hence, we proposed an advanced model based on the existingNasCh one.

Primary procedures in our model could be executed in orders below:

1: 2 : " "

STEP Using advanced NasCh model to update position of each vehicle in its own laneSTEP Using certain passing rules like the given keep it right rule to move vehicles

from one lane to othersSTE 3 : 1P Back to step

Updating vehicles’ positions

We consider a 1-dimensinal array of L cells, and each cell represents 7.5m in realworld. And each cell could be empty or occupied by a vehicle, each vehicle posses avelocity that ranges from 0 to 8 (216 / )km h . A “gap function” is determined asequation (1):

1( ) 1i iGap i x x （1）

Where ix stands for the i th position of a vehicle in a certain lane, the “gapfunction” hence clearly calculates the number of empty cells between adjacentvehicles in a lane.Four steps are taken to update each vehicle’s position in our advanced NasCh model:

1: Deterministic AccelerationSTEPmin max( 1, )ji jiv v v 2 : Deterministic DecelerationSTEP

min= [ , ( ) ]ji ji jv v Gap i 3 : Random DecelerationSTEP

minji pv v 4 : Position UpdatingSTEP

'ji ji jix x v

Where jiv represents the velocity of i th position vehicle in lane j ; maxv standsfor the maximum velocity a vehicle can reach; ( ) jGap i for the value that function

( )Gap i applied on the j th lane; minpv for the posted minimum speed in a

freeway; jix and 'jix for i th position of a vehicle on j th lane before and

after updating positions respectively.


Lane-Changing Principles

Clearly, it is the principle for vehicles of changing lanes that really matters amongdifferent paths. We propose that a driver would like to change his lane to becomefaster for two reasons: one is that he had been blocked in current lane while the otherthat his safety could been guaranteed. After thoroughly viewing those requirements,we set corresponding principles under “Keep-Right-Except-To-Pass” rule and others.

Two-Lane-Changing Principle

Equation (2) presents the definition of a flag parameter deciding whether changinglanes or not:

' maxmin , ,{ 1, }, ,

Others

1 n

n n n sn f n bn

n

d v v d d d dCCC

（2）

Where nd stands for the distance between the n th vehicle and its front one;

,n fd for the distance between the n th vehicle and its front one in adjacent lanes;

,n bd for the distance between the n th vehicle and its rear one in adjacent lanes;

sd for the required safety distance of lane changing, and sd is set as maxv here;besides, nC and '

nC for the lane which the n th vehicle is in respectively.

According to equation (2), min max{ 1, }n nd v v describes a situation that the n thvehicle is blocked in its current lane; , ,,n f n n b sd d d d describes that this blockedvehicle could get faster in its adjacent lane without any safety threats.

Driving faster by changing lanes is not what decent driving actually means, drivingfaster with less safety threats is what we really care about. Hence, we introduce a keyparameter K to measure safety condition. This parameter records total numbers ofsuch situations: ,n b sd d , i.e. this car is seriously close to its rear one when lane ischanged.

Figure 1 shows the exact situation when lane-changing is possible, and satisfyconstrains what equation 2 presents:


nd

,n fd ,n bdmaxmin , ,{ 1, }, ,n n n sn f n bd v v d d d d

Figure 1 Two-Lane-Changing Diagram

Multiple Lanes Changing Principles

Pedersen’s work [8] has pointed out a basic three-lane-changing principle, weestablish our own based on that. We mark lanes with 1,2, , lN from right to leftaccordingly, and vehicles will change their lanes with following principles.

max(1) : ( ) , ( ) ( ), ( ) ( 1) 1, ( ) ( 1).

r rn n n n n

n n

Consider its right lane if d t v d t d t then new l t lane telse new l t lane t

max min max(2) : ( ) [ ( ) ( ( ) 1, ) ( ) 0]

( ) ( ) ( ) ( ) ( ) ( 1) 1

ln n n n

l r ln n n n

n n

Consider its left lane if d t v and d t v t v or v t

and d t d t and d t d tthen new l t lane t(3) : ( ) ( ) (1 ).

.n n ignoreLane changing Let lane t new l t with probability p

Apply this rule from right lane to left accordingly in case of collisions

Where ( )xynd t stands for the total number of empty cells between vehicle n and

adjacent ones in its current lane, left lane and right lane at time t , x could be ,l ror none; l represents left lane while r right lane, and empty value for current lane.y could be or : for front vehicle while for vehicle in the back.

( )nlane t shows which lane the n th vehicle is in at time t . ( )nnew l t stands forthe potential lane that the n th vehicle may enter.

Rule (1) shows that vehicles preferred changing to their right lanes if their drivingcondition will not be bothered. Rule (2) shows that vehicles change to their left lanesonly when left ones are better than their current lanes and right lanes. Besides,

( ) 0nv t ensures that vehicle will not get stuck in traffic jam if they wish to changetheir current lanes. Rule (3) introduce a probability ignorep to describe a situation thatdrivers will not change their lanes even lane-changing requirements are satisfied.


5.2 Safety Simulation Model

By safety evaluation, we mainly use accident rate to measure it. In our consideration,posted speed limit is a major factor influencing safety condition in freeways. Hu’swork [9] indicates that accident rate is related to traffic flow, average speed andposted speed limits, and it could be predicted by linear regression. However, Hu’smodel is complicated in its form, we simplify it into solving this problem.

We introduce a speed variable coefficient vS to measure posted speed limits.Equation (3) gives the calculation of vS .

vv

a

SV

（3）

Here, aV average speed during a period

V Standard deviation of V during a given time t

t Time period we pick up

Clearly, in this equation, vS is in terms of V and aV , which are strongly related toposted speed limits. In other words, higher posted speed limits ensure a higheraverage speed; moreover, it also encourages more vehicles to change lanes to obtainhigher velocity. Hence, V and aV vary with the posted speed limits respectively,thus causing VS vary with the posted speed limits.

We set a variable parameter in terms of VS , Table 1 gives the classification ofdifferent values of VS .

Table 1 Value of

Variable Parameter Level Value Classification StandardLow 0 0.12VS

Medium 1 0.12 0.2VS

High 2 0.2VS

We have equation (4) to estimate accident rate:

6 3 20 1 2 3ln( ) ln( 7 10 0.0151 9.9289 2355.9) ln aF a a Q Q Q a V a

（4）

Here, F Accident rate, 0,1, 2,3ia i Undetermined coefficient

Q Traffic flow during given time t

aV Average speed during given time t


Value of corresponding vS , see table 1

Before solving this equation, we have to do some simple transformation.Let ln( )y F , 6 3 2

1 ln( 7 10 0.0151 9.9289 2355.9)x Q Q Q , 2 ln ax V , thusturning equation (4) into a pure linear regression form like equation (5).

0 1 1 2 2 3y a a x a x a （5）

Equation (5) is the multiple linear regression equation to be solved in case studies.

6 Case Studies

In this section, we will present our results regard with traffic flow and accident rate.

For traffic flow, we would like to present our results with a “time-space” map besidesregular statistics of traffic flow at each lane. By “time-space” map, we mean that amap records each vehicle’s position in terms of time. We create a 3-dimentionalarray , , (0 599,0 399,0 2)i j kA i j k , and the first column of it is used forstoring positions of each vehicle; the second column for storing time; the third columnfor storing RGB color. Once this array is accomplished, we load it into a BMP filethat we have created before, thus making those tracks of vehicles visible.

For accident rate, we use equation (5) in 6.2 to calculate. Since there are 4 parametersin equation (5) to be solved, at least 4 sets of ( )F Q W，， data are required. In fact,we get far more sets of ( )F Q W，， data than we need. After ignoring someusefulness data sets, we plug some data sets into equation (5) to do linear regression.

Here follows an authentic example we calculate, and our results about accident rateare all gained by this method unless specially acknowledged.

In one calculation, we plug data sets into equation (5), and we get values ofparameters as follows:

0 1 2 3{ , , , } {23.2473,2.7679,3.3096, 0.1523}a a a a （6）

Before we plug these into equation (4), we have to check its regression parameters.Table 2 shows those parameters.

Table 2 Regression Parameters

CorrelationCoefficient

Statistic of F Probability withStatistic of F

Standard Error

0.9819 18.0533 0.1709 0.0090

By checking these parameters in related statistical tables, we are confirmed that theregression makes sense; hence, we could plug equation (6) into equation (4), and weobtain an analytic expression of F .


( 0.1523 23.2473) 3.3096 6 3 2 2.7679( 7 10 0.0151 9.9289 2355.9)VSF e V Q Q Q （7）

According to this analytic expression, we could plot the graphic of F in terms withV andQ , and it is very convenient to see the trend of accident rate when V and Qvary.

6.1 Two-Straight-Lane Case

In this case study, we apply equation (2) as lane-changing rules for vehicles, andequation (1) as updating rules for each lane respectively. Liu’s work [8] [10] haspointed out that vehicles are nearly Poisson distributed when traffic is light whilebinomial distributed when traffic is heavy. And we have set a “button” in our Matlabcode to distinguish “light traffic” and “heavy traffic”; hence, our results will bepresented under these circumstances.

1) Light Traffic Case

Figure 2 is a time-space graphic which reflects each vehicle’s position in terms oftime. Figure 3 describes accident rate under different value of , i.e. differentposted speed limits.

Figure 2 Time-space graphic in two-straight-lane under light traffic


Figure 3 Prediction of accident rate in terms with traffic flow and average speed

2) Heavy Traffic Case

Figure 4 and Figure 5 share the same meaning with Figure 2 and Figure 3 except theheavy-traffic condition.

Figure 4 Time-space graphic in two-straight-lane under heavy traffic



Figure 6 compares arrival flow under these two traffic loads.

Figure 6 Comparison of arrival flow under two traffic loads


6.2 Three-Straight-Lane Case

Like the way section 7.1 presents, we present our results in three-straight-lane case asfollows.


Figure 7 is a time-space graphic which reflects each vehicle’s position in terms oftime. Figure 8 describes accident rate under different value of , i.e. differentposted speed limits.





Figure 9 and Figure 10 share the same meaning with Figure 9 and Figure 10 exceptthe heavy-traffic condition.






6.3 Ramp Case

Ramps are common paths in most freeways, Figure 12 shows how it works.

,n bd ,n fd C

D

Figure 12 Ramps Diagram

E

In this figure, vehicles enter lane A from ramp B, and leave the freeway from ramp C.Our models can not directly applied in ramps, however, we can regard the process thatvehicles entering lane A from ramp B as a simple lane-changing process with only one

B

A


direction to choose from. Hence, equation (2) could be applied here. And we assume aprobability exitp to leave lane A from ramp C for vehicles passing through thisexiting ramp. Besides, lane-changing rule between A and E is in agreement with ourprevious model, i.e. equation (2).


Figure 13 shows time-space relationship for each vehicle in lane A and lane E. Figure14 shows traffic flow in ramp B and ramp C while Figure 15 demonstrates traffic flowin lane A and lane E.


Figure 14 Traffic flow in ramp B and ramp C




Figure 16, 17 and 18 have the same expressions as Figure 13, 14 and 15 respectively,except the heavy-traffic condition.




Figure 18 Traffic flow in ramp B and ramp C




6.4 Roundabout Case

A roundabout is also named “traffic island” which functions as guiding vehicles atdifferent steering. Figure 20 demonstrates how a roundabout works.

A

B

C D

E

F

GH

Central Island

Figure 20 Roundabout

In this roundabout, vehicles could drive into it through B, D, F and H; and they could


leave it through A, G, E, and C.

We set 4 basic rules for every vehicle in this roundabout:

1 Each vehicle may drive into this roundabout in one of four entrances of it withprobability 0.25ep

2 Each vehicle may leave this roundabout in one of four exits of it with probability0.25op

3 Central Island could not be passed through

4 Every vehicle should circle around this roundabout counterclockwise, and it mayleave at any of the four exits

We build our algorithm based on these rules; brief procedures of our algorithm arelisted as follows:

Step I: Check each entrance whether there is a chance to generate a vehicle (i.e.enough safe space)

Step II: Update new vehicles with certain probability in each entrance, count thetotal number of vehicles input

Step III: Analyze every vehicle’s speed and position; let those leave thisroundabout with certain probability when they drive near any exit; and count thetotal number of vehicle output

Step IV: For those vehicles in the ring road of this roundabout, use our previousmodel to update their speed and position.


Figure 21 shows time-space relationship for each vehicle in internal lane and externallane of ring road near the center island. Figure 22 describes accident rate underdifferent value of , i.e. different posted speed limits.


Figure 21 Time-space graphic under light traffic



Figure 23, 24 have the same expressions as Figure 21, 22 respectively, except theheavy-traffic condition.


Figure 23 Time-space graphic under heavy traffic





7 Effective Rules and Alternatives

In order to check whether this “Keep-Right-Except-To-Pass” rule is effective inpromoting traffic flow, we carry on several simulations with and without this rulerespectively. We choose two-straight-lane as our simulation environment. One groupof simulations is carried under this rule, while the other is free of rules.Figure 26 demonstrates that the “Keep-Right-Except-To-Pass” rule could not promotetraffic flow as much as the free rules.

Figure 26 Flow comparison


Figure 27 shows that, however, this “Keep-Right-Except-To-Pass” rule is relativelysafer than free rules.

Figure 27 Accident rate comparisonsThe alternative we proposed is limiting the speed of different lanes. We take two-lanefreeway for example to state it. The lowest speed of the quick lane should bedetermined over the highest speed of slow lane. Thus, the vehicles must slow downwhen returning to the slow lane. And this solution can reduce the lane-changingbehaviors. Besides, making divisions in speed among different vehicles can reducethe accident rate and enhance the safety of traffic.We use the following three figures to show the comparisons under our alternatives.Figure 28 shows the comparison between the left and right lane of time-space graphicunder our alternative.Figure 29 shows the prediction of accident rate in terms with alternative.Figure 30 demonstrates that alternative could promote traffic flow as well as thesafety factor.

Figure 28 Time-space graphic under alternative


Figure 29 Prediction of accident rate under alternative

Figure 30 Flow comparisons under alternative

8 Left Driving Norms

Since our algorithm is flexible, we could simply change our initial conditions toobtain results of left driving norms. We choose a two-straight-lane to demonstrate this.In our algorithm, we only have to do a symmetry transformation of initial conditions.In other words, vehicles depart on the right lane while on the left lane if left drivingrule is employed; and equation (2) only has to do a symmetry transformation to ensurevehicles passing from right lanes. We obtain our results as Figure 31.


Figure 31 Comparison between two rules in terms with traffic flow

9 Intelligent System

In intelligent system, we ignore the random factors, such as the emotions andbehaviors of drivers. Thus, we can’t apply the initial model for intelligent system.

We put off the random factors to cover this condition and simulate under rigorouslogic.

The following changes are applied in our simulation.

Ignore the procedure of random slowing down in initial algorithm.

In our former model, we set an exact probability for divers to change lanes whenthey meet the requirements of lane-changing. In intelligent system, we ignore theprobability and drivers can determine whether to return to the primary lane afterlane-changing.

Figure 32 shows the intelligent system for opposite traffic flow conditions, the leftone represents the heavy traffic and the right one for the light traffic.

Figure 33 shows the accident rate under intelligence system for the heavy and lighttraffic.


Figure 32 Heavy (left) and light (right) traffic under intelligent system

Figure 33 Accident rate of heavy (left) and light (right) traffic

10 Result Analysis

10.1 Sensitivity Analysis

Considering the vital factors in our models and its’ sensitivities, we mainly discuss the

changing of following two aspects to conduct sensitivity analysis.

Changing the Maximum of Speed Limit

We change the maximum of speed limit and take these typical speeds 5, 8 and 11.The

accident rates are varying along the time respectively. It can be clearly drawn from

Figure 34. In addition, the traffic flows are varying with density in Figure 35.


Figure 34 Accident rate under different speed limit

Figure 35 Flow comparisons under different speed limit

Changing the probability of Slowing Down

We change the probability of slowing down to examine the accident rate and trafficflow. The given three probabilities, that is 0.1, 0.2 and 0.3, have different accidentrates as well as traffic flow. It can be clearly drawn from Figure 36 and 37.


Figure 36 The accident rate under different probability

Figure 37 Flow comparisons under different probability

10.2 Strengths andWeaknesses

Strengths:

The safety model we establish combines various relative safety factors and canquantify these factors either.

The traffic flow model can apply to various cases as well as the rules forlane-changing.

Weaknesses:

Our models are lack of emotional factors analysis. Those emotional factors lead to


some unreasonable phenomenon which we would never find in the real world.

Simulation Model has fewer restraints on arguments. However, there are morerestraints to consider in our model, and most of them are of no significance inimpacting the whole traffic model.

11 References

[1] K.Nagel, M.Schreckenberg. A Cellular Automata Model for Freeway Traffic,J.Phys.I. France 2, December 1992, Pages 2221-2229.[2] R. Mu, T. Yamamoto. An Analysis on Mixed Traffic Flow of ConventionalPassenger Cars and Micro Cars Using a Cellular Automata Model, Procedia-socialand Behavioral Sciences, Volume 43, 2012, Pages 457-465.[3] S.C.Lo, C.H.Hsu. Cellular Automata Simulation for Mixed Manual andAutomated Control Traffic, Mathematical and Computer Modeling, Volume 51, Issues7-8, April 2010, Pages 1000-1007.[4] B. Luna-Benoso, J.C. Martines-Perales, R. Flores-Carapia. Modeling Traffic Flowfor Two and Three Lanes through Cellular Automata, International MathematicalForum, Volume 8, 2013, No. 22, Pages 1091-1101.[5] Bialynicki-Birula, Bialynicka-Birula. Modeling Reality: How Computers MirrorLife. Oxford: Oxford University Press, 2004.[6] Saifallah Benjaafar, Kevin Dooley, Wibowo Setyawan. Cellular Automata forTraffic Flow Modeling, Department of Mechanical Engineering University ofMinnesota, 1997.[7] Guo Jian, Yang Yong, Zhang Lixun. Study on the NS Model and Improved NSModel of Mixed Traffic Flow with Periodic Boundary Condition, InternationalConference on Intelligence Computer Technology and Automation, 2010.[8] Liu Junde, Xu Bing, Liang Yong dong, Ma Rongguo. Traffic Safety Assessment ofExpressway in the Accident, Journal of Chang’an University (Natural ScienceEdition), Volume.32, No.6, November 2012, Pages 78-82.[9] Hu Gonghong, Research on Safety Evaluation and Improvement Strategies ofFreeway Traffic Flow, Chongqing Jiaotong University, March 30, 2008.[10] Jia Bin, Gao Ziyou, Li Keping, Li Xingang. Models and Simulations of TrafficSystem Based on the Theory of Cellular Automaton. Beijing: Science Press, October2007.

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Traffic Flow And Safety Analysis On Cellular Automata Model

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