Multi-agent and driving behavior based rear-end collision alarm modeling and simulating

Simulation Modelling Practice and Theory 18 (2010) 1092–1103

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Simulation Modelling Practice and Theory

journal homepage: www.elsevier .com/locate /s impat

Multi-agent and driving behavior based rear-end collision alarmmodeling and simulating

Liang Jun a,*, Chen Long b, Cheng Xian-yi a, Chen Xian-bo a

a School of Computer Science and Telecommunication Engineering, JiangSu University, Zhenjiang 212013, Chinab School of Automobile and Traffic Engineering, JiangSu University, Zhenjiang 212013, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 10 December 2008Received in revised form 8 January 2010Accepted 11 February 2010Available online 18 February 2010

Keywords:Multi-agentRear-end warning systemSimulation

1569-190X/$ - see front matter Crown Copyright �doi:10.1016/j.simpat.2010.02.006

* Corresponding author. Tel.: +86 0511 88790321E-mail addresses: [email protected] (J. Liang),

(X.-b. Chen).

Distance-between-vehicle-measurement is the only factor in traditional car rear-end alarmsystem. To address the above problem, this paper proposes an alarming model based onmulti-agent systems (MAS) and driving behavior. It consists of four different types ofagents that can either work alone or collaborate through a communications protocol onthe basis of the extended KQML. The rear-end alarming algorithm applies the Bayes deci-sion theory to calculate the probability of collision and prevent its occurrence real-time.The learning algorithm of driving behavior based on ensemble artificial neural network(ANN) and the decision procedure based on Bayes’ theory are also described in this paper.Both autonomy and reliability are enhanced in the proposed system. The effectiveness androbustness of the model have been confirmed by the simulated experiments.

Crown Copyright � 2010 Published by Elsevier B.V. All rights reserved.

1. Introduction

The past twenty years has seen a rise of the number of traffic jams and accidents [1]. According to the investigations andstatistics, of all the traffic accidents ever took place, about seventy-five percent were caused by the misjudgment or steermiss of the drivers (see Fig. 1), which, to a large extent, was due to the insufficiency of the drivers’ cognitive and informationprocessing abilities when steering more speedy and complicated vehicles. As a result, the driver-and-passenger centeredintelligent active safety system for automobile, along with its new driving sensors and controllers, has become a greater con-cern to the manufacturers and mass consumers of automobiles and affiliated products in America, Japan, Europe and coun-tries all over the world [2,3]. After attentive studying of different car rear-end warning models including mazda model onCW/CA system, honda model and an improved model by California Berklee College, the authors found out the disadvantagesof most of the current alarm systems. One is that the distance between vehicles is taken as the only determinant factor ofvehicle collision by current alarm systems, while the possible effects of the driver’s behavior of driving is not taken into ac-count [3–6]. The other is that the technology of measurement applied by most of the current alarm systems is active mea-surement which entails special hardwares such as radar, infrared ray and CCD camera, etc., which are, more often than not,expensive and there could be signal interference.

As the latest development of artificial intelligence, the multi-agent system [7] is one of the most important branches inthe studies of distributed artificial intelligence. This system is widely used in automatic control, distributed information pro-cessing system, meta-synthesis of complex system, intelligent expert system and so on. Also, it offers a new exciting way forthe coming out of the car rear-end warning system [4,8].

2010 Published by Elsevier B.V. All rights reserved.

[email protected] (L. Chen), [email protected] (X.-y. Cheng), [email protected]

http://dx.doi.org/10.1016/j.simpat.2010.02.006

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Fig. 1. Statistics of traffic accidents.

J. Liang et al. / Simulation Modelling Practice and Theory 18 (2010) 1092–1103 1093

The car rear-end warning system based on the multi-agent system is the new generation of the intelligent alarm supportsystem [9]. Technically based on the multi-agent system theory in the field of artificial intelligence and theoretically guidedby the meta-synthesis method from qualitative to quantitative, the subject alarm system is expected to have improved per-formance and superior functions. A multi-agent-based car rear-end warning system is supposed to have the followingfeatures:

(1) better adapt to the inconstant traffic and make real-time reactions to the changes of environment [6];(2) highly fault tolerant;(3) increased speed of alarm, improved efficiency and strengthened real-time performance;(4) a more reliable system with robust design and easy installation and maintenance;(5) better scalability, reusability, openness and compatibility;(6) enhanced interaction between the alarm system and the driver.

Hence, taking advantage of the flexibility, autonomy, interaction and intelligence of the multi-agent system and takinginto account both driving behavior and traditional alarm means of distance measurement, the paper intends to propose amodel of car rear-end warning based on MAS and behavior (MCRWMB), which utilizes the Bayes decision algorithm incar rear-end warning system to the calculation of collision probability in order to prevent the automobile accidents suchas tailgating or collision.

2. MCRWMB

2.1. Driver behavior

The history of driving behavior model can be traced back to the theory of field analysis of vehicles. The research of drivingbehavior did not gain much progress in 50 years although some work still has been done. But it became a hot research areasince 2000. After the comparison and analysis of the existing theory and model, Vaa [10] pointed out in 2001 that the cog-nition and emotion is good tools for prediction, avoidance and evaluation of dangerous situation. Then Salvucci, Krajzewiczand Delorme developed investigation on the cognitive structure of driving behavior and it turns out that the rapid develop-ment of cognition science and modeling methods are helpful to the research of driving behavior [4,7].

The model of driving behavior can be described as (E,H) abstractly, where E = (E1,E2, . . .,En) is used to express external sit-uation such as the road, weather and so on; H = (H1,H2, . . .,Hn) representing the driving behavior which refers to the oper-ation behavior on vehicles. It includes operations on steering wheel, accelerator (throttle), brake pedal, clutch pedal andrelated control unit like steering lamp, lighting lamp, windscreen wiper, etc. The driver usually follows his/her own habitsor preference of (E,H). The preference model of driver can be learned based on a lot of records of his/her driving behavior andcan be used to predict his/her future behavior Hi. If the risk evaluation function y(.) can be built simultaneously based on this,then the risk of the predicted behavior can be assessed. Both the learning algorithm of driving behavior based on ensembleartificial neural network (ANN) and the decision procedure based on Bayes’ theory are described in Section 4.

2.2. MCRWMB structure

The multi-agent system theory provided a new way for the research of decision support system [7,9]. Car rear-end warn-ing model based on multi-agent (see Fig. 2) have four kinds of agents. Each agent is autonomous, and the cooperation amongthe agents could improve the accuracy and the real-time performance of the alarm system. For this end, it is necessary that areasonable framework of multi-agent alarm system be designed with the ability of learning and dynamic coordination,which could give full play to its own superiorities and change the traditional routinization of the calculation mode so asto improve the warning efficiency and reinforce the driving security.

Fig. 2. MCRWMB.

1094 J. Liang et al. / Simulation Modelling Practice and Theory 18 (2010) 1092–1103

2.3. Agents’ structure

The interface-agent is the tie and bridge between the alarm system and the user. It can receive and complete the tasksassigned by the user, who is not supposed to know its complex internal structure and working principles in the first place.The interface-agent can also study and summarize the user’s driving preference during the process of driving [4]. So it en-sures improved precision of early warning, makes the interface of the whole system more user-friendly and adapt to differ-ent users in a dynamic way. As a result, the user could utilize the alarm system more easily and efficiently. What’s more, theinterface-agent can also receive the alarm given by the alarm-agent and then give alarm to the driver. In light of its func-tional characteristics, the authors designed the structure of the interface-agent (see Fig. 3).

The features-extraction-agent is used to extract main features from road images. Thanks to its initiative and the ability ofself-adaptation, the features-extraction-agent can choose a reasonable way to pick up the most remarkable characteristicsfrom the current circumstances based on different weather and road conditions [4]. In the light of the above mentioned func-tional characteristics, the authors designed the structure of the features-extraction-agent (see Fig. 4). In consideration of thecomplexity of feature extraction and object recognition, and in view of the fact that there are lots of related research findings,of which SIFT characteristic, Hough characteristic, spectrum characteristic and so on are the relatively mature ones, theauthors choose to apply the technique of SIFT characteristic to the features-extraction-agent. This paper does not go into par-ticulars about the technique of SIFT characteristic as it is proved to be one of the more feasible ones [11].

The uncertain roads and obstacles against complex background should be recognized before the alarm system makes cor-rect decision. Based on the features extracted by the features-extraction-agent and the established database of the objects,the recognition-agent carry out the target recognition of such objects as road, pedestrians, vehicles and road signs. The ob-jects can be classified into mobile ones and immobile ones. Immobile objects are nonmoving objects relative to the road,while mobile objects are relatively moving objects. As far as a mobile object is concerned, the recognition-agent shouldbe able to identify its motion features including speed, acceleration and moving direction, etc. Accordingly, the authors de-signed the structure of the recognition-agent (see Fig. 5). Typical pattern recognition algorithms such as statistical identifi-cation and support vector machine (SVM) [12] can both be used as recognition algorithm for the recognition-agent.

Fig. 6 illustrates the structure of the alarm-agent. When the recognition-agent has recognized the various objects andtheir attributes, the alarm-agent calculates the probability of rear-end collision based on both the results from the recogni-tion-agent and the behavior database provided by the interface-agent. If the probability is too high, the alarm-agent will givewarning to the interface-agent [13]. The danger degree is divided into 5 classes: quite safe (class A), safe (class B), mild dan-gerous (class C), fairly dangerous (class D), extremely dangerous (class E). When the degree of danger reaches or exceedsclass D, the alarm-agent will report to the interface-agent.

3. Multi-agent communications based on extended KQML

Knowledge query and manipulation language (KQML) is a kind of most generally used agent communication language[7,9,14], which could function as a coordinator or cooperator to help realize the real-time information share among agents

Fig. 3. The structure of interface agent.

Fig. 4. The structure of feature extraction agent.

Fig. 5. The structure of recognition agent.


through information change. Moreover, KQML have the characteristics of openness, expandability, readability, convenienceand platform independence. Therefore, on the foundation of original reserved words in KQML, we defined several new ones,such as <Announce>, <Precaution>, <Accept>, etc (see Table 1) so as to realize real-time communication in our multi-agentsystem.

Fig. 6. The structure of precaution agent.

Table 1The semantics of extended KQML.

Name Weather reserved words Meaning

Release N Interface-agent send the driving message to allConfigure Y Alarm-agent need to be initialized before drivingAnnounce N Interface-agent send messages about road and driving habit to other agents, and hope

to get the message backPrecaution N Alarm-agent send the result of alarm in ‘‘content” to interface-agentAccept N Interface-agent accept the alarm message and begin to give an alarm to driver


3.1. Interface initialization

First, the interface-agent need to release a detailed information concerning driver circumstances before driving,

(Release: sender interface-agent: receiver all: reply-with interface-agent – release: content (driver’s information: sex, age, driving age, driving license level, character; environment information: weather,

road degree, vehicle type, place of departure, destination, etc.): language KQML: ontology KQML – ontology).

3.2. Pre-setting

It initializes other agents in the system. For example, the alarm-agent needs to be pre-set before driving.

(Configure: sender alarm-agent: receiver interface-agent: in-reply-to interface-agent – release: content (offer related information about alarm such as speed, acceleration, curve acceleration, steering wheel, pedals,

levers, switches, knobs, other feedback, onboard information terminal displays, onboard measurement equipment dis-plays, warning lights, audio information in traditional early-warning system; and the danger degree of driving behaviorin our framework)

: language KQML: ontology KQML – ontology).

3.3. Driving

The interface-agent sends message to the other agents. A case in point is the alarm-agent which comes out with the infor-mation about relative velocity, distance to the car afront, driving preferences, etc.

(Announce: sender interface-agent: receiver alarm-agent: reply-with interface-agent – Announce: content (vehicle information, obstacle position, close object information, type of vehicle, weather, speed, relative velocity,

driving preferences, etc.): language KQML: ontology KQML – ontology).


3.4. Alarm

Upon receiving the messages sent from the interface-agent, other agents evaluate them based on their own knowledgeand set up their own reaction plan. A case in point is the alarm-agent which is to send the result of alarm in ‘‘content” tothe interface-agent.

(Precaution: sender alarm-agent: receiver interface-agent: reply-with alarm-agent-precaution: in-reply-to interface-agent-alarm-agent – announce: content (the danger degree report combining traditional early-warning means and driving behavior evaluation): language KQML: ontology KQML – ontology).

3.5. Alarm acceptance

When receiving the alarm message, the interface-agent begin to give an alarm to driver through voice, light andelectricity.

(Accept: sender interface-agent: receiver alarm-agent: content (accept alarm and begin to give an alarm to driver): language KQML: ontology KQML – ontology).

4. Bayes decision with driving behavior

In this section we need to model the relationship between environment, driving behavior and danger which we abbre-viate to env, beh and dang respectively.

4.1. The model of environment and danger

Considering the complexity of alarm environment, we introduce the fuzzy thought [12]. The dang is the measurement ofcriticality, which is a number in [0,1], and 0 means having no danger and 1 means the severest danger. The env is also a num-ber between 0 and 1, 0 shows that the environment is very good, such as clear whether, hollowness on road, no foot pas-sengers and no vehicles, and 1 means that the environment is very abominable (the complex road, many roadblocks andthe bad weather). According to the linear model as follows, we can evaluate the environment.

env ¼Xn

i¼1

aixi ð1Þ

In formula (1), xi is the factor to evaluate, such as weather condition, road grade and the number of roadblock in certainrange; ai is relative weight of influencing factors, which need to be appointed by the man who has great experience; beh isnamed as behavior tolerance, which, as mentioned earlier, is the result of risk evaluation y(Hi) of driving behavior, lowerbehavior beh means the rear-end accident has low probability to happen. We call P(env) as prior probabilities which expressoccurrence probability of different environment, and regard it as uniform distribution when we have no prior information.Pðenv; behjdangÞ expresses the occurrence probability of special environment and behavior conditioned on the danger hap-pened, and it needs to be represented by a probability model such as GAUSS model [13]. PðbehjenvÞ is the probability ofadopting beh behavior under the current environment. PðdangjenvÞ is the tolerance of danger degree toward this currentenvironment. In this paper, PðbehjenvÞmodel and PðdangjenvÞmodel are all built by GAUSS model, which can be showed by:

beh ¼ a�env þ edang ¼ b�env þ e0

�ð2Þ

where a,b is called counter-change parameter, e and e0 is noise data. Two cases in the experiment can be seen in Figs. 7 and8. Pðdangjenv; behÞ is the probability of the danger of dang occurring under the current environment and driving behavior.When the value of Pðdangjenv; behÞ is larger than the presented threshold, interface-agent will adopt many kinds of formssuch as sound, photo electricity to send the danger’s degree to driver.

Fig. 7. Distribution of dang when env equal 0.5.

Fig. 8. Distribution of beh when env equal 0.5.


4.2. Learning of driving behavior based on ensemble ANN

Now we focus on the relationship between driving behavior and environment as follows. The structure of our ensembleANN is illustrated in Fig. 9. It is composed of three layers: the input layer, the middle layer and the output layer. It is themiddle layer which differs it from traditional ANN. In traditional ANN, the middle layer consists of the neural which mapesby using a simple function like sigmoid function. But in our ANN, the middle layer (hidden layer) constitutes multiple indi-vidual neural networks referred as sub-NN which is used to learn each behavior such as accelerator (throttle), brake pedal.The output of sub-NN is the probability that behavior happens and they are trained by traditional learning algorithm, etc. BP.The output of sub-NN is collected in the output layer based on decision theory. Here PðbehiÞ represents the probability thatbehavior happens and wi is the combination factor which affects the weight of each behavior. Now our goal is to learn bothhidden neurons and factor w. According to the classical decision theory, the behavior leading to the largest wiPðbehiÞ will bechosen as the output finally. This can be expressed as follows:

behi ¼ arg maxi

wiPðbehiÞPjwjPðbehjÞ ð3Þ

Usually, PðbehiÞ has a parametric form which can be written down explicitly as PiðaiÞ and then, the above expression canbe rewritten as:

Fig. 9. The structure of ensemble ANN.


behi ¼ arg maxi

wiPiðaiÞPjwjPiðajÞ ð4Þ

In other words, the finally behavior is selected according to the largest wiPiðaiÞ,ri. We consider a behavior classificationproblem with K different behaviors, with a 1-of-K binary coding scheme for the target t, which means ti is 1 if the ith behav-ior is chosen while the other tj is 0 ðj – iÞ. Then we can construct a sum-of-squares function:

Eðw;aÞ ¼X

n

ktðnÞ � rðnÞk2 ð5Þ

while n indicates the nth samples.On the basis of (5), we can use training samples to learn both the parameters ai and wi simultaneously through optimi-

zation method such as conjunct graduation descent.Having learned the unknown parameters, we can obtain the relationship between environment and driving behavior

through the first-half of the ensemble ANN (Fig. 9).

4.3. Bayes’ formula

Bayes’ formula is an extremely useful rule for combining two probability distributions. Its mathematical derivation issimple, although scientific applications of Bayes’ formula can be fairly complicated. Bayes’ formula follows from the defini-tion of conditional probability. P(a) is the probability that event a will occur. Then PðajbÞ is the probability of event a con-ditional on event b, i.e., the probability that event a will occur given that event b has occurred. The mathematical definition ofconditional probability is

PðajbÞ ¼ PðabÞ=PðbÞ ð6Þ

where P(ab) is the probability that events a and b will both occur. Bayes’ formula is

PðajbÞ ¼ PðbjaÞPðaÞ=PðbÞ ð7Þ

It follows from the definitions of the conditional probabilities PðajbÞ and PðbjaÞ. From the definition of

PðbjaÞ; PðabÞ ¼ PðbjaÞPðaÞ ð8Þ

Substitute Eq. (8) into Eq. (6) to obtain Eq. (7).And, let the event of interest a happens under any of hypotheses ai with a known (conditional) probability PðbjaiÞ: As-

sume, in addition, that the probabilities of hypotheses a1; a2; . . . ; an are known (prior probabilities). Then the conditional(posterior) probability of the hypothesis is ai; i ¼ 1;2; . . . ;n, given that event b happened, is

PðaijbÞ ¼ PðbjaiÞPðaiÞ=PðbÞ; ð9Þ

where PðbÞ ¼ Pðbja1ÞPða1Þ þ Pðbja2ÞPða2Þ þ � � � þ PðbjamÞPðamÞ.


We call formula (9) as conditional probability. PðaiÞ is called as prior probabilities, which was gained by the analyzed data,and PðaijbÞ is posterior probability, which is the renewed modificatory probability. In all, bayes’ formula of conditional prob-ability is the MCRWMB’s theory basis.

4.4. MCRWMB algorithm

Combining the information of the risk assessment function of yðHiÞ and the grade of alarm sent by alarm-agent, we canobtain the result by bayes’ formula of conditional probability

Pðdangjenv ; behÞ¼ Pðenv ; behjdangÞPðdangÞ=ð

Pdang

Pðenv ; behjdangÞPðdangÞÞ

/ Pðenv ; behjdangÞPðdangÞ¼ Pðbeh;dangjenvÞPðenvÞ¼ PðbehjenvÞPðdangjenvÞPðenvÞ

ð10Þ

Each item of the last line of (10) has been studied in the previous sections, which are now combined to infer the finalprobability of danger with regard to special environment and driving behavior.

5. Simulation experiment and analysis

In this paper, the authors venture to design a simplified experiment of virtual-single-lane and double-vehicles-followingin order to obtain relevant data needed in MCRWMB model. In the experiment, we translated the 3D virtual models of vehi-cles and roads built by 3DMAX into 3DS format, and then input them into the virtual reality software Eon Studio. The posi-tion coordinates of those vehicles and roads were obtained from the ‘‘Property Bar” in Eon Studio. The main data recorded bythis experiment was driver’s reactions while facing the acceleration and decelerating of the vehicle afront in the virtual vehi-cle flow, mainly including the records of the accelerator and the brake. The multi-group data were also obtained by measur-ing and recording the following distance and speed difference of the opposite vehicles.

Experiment 1: verifying the effectiveness of MCRWMB.When we input the speed difference ðDvÞ and the following distance ðDsÞ measured previously into the model, we ob-

tained the output, i.e., the collision time ðDt ¼ Ds=DvÞ and the change process of the risk degree, which is illustrated inFig. 10. It is shown in Fig. 10 that the interface-agent gave alarm twice during the driving process. The alarm degree forthe first time is relatively higher than that of the second time, which is in accordance with the experiment design. Hencethe effectiveness of this model could be verified.

Comparing two curves in Fig. 10, we found that MCRWMB model gave right alarm when the degree of the dangerous cir-cumstances reached class C or above. and the above degree. whereas, at about 1000 sample point, the output of the modelwas class C while the collision time curve showed only a minor degree of danger at this time, which means deviation existsin the estimation of the model. However, it could just be explained that MCRWMB model adopt quite cautious ‘‘attitude”towards danger.

In the experiment, when the alarm-agent gave the first alarm, the following car’s driver braked urgently, and then turnedinto another kind of normal driving state. According to the above analysis, we can see that MCRWMB model not only can tellthe driver’s driving preference and give effective alarm, but also has good robustness at noise data caused by the driver’sunsuitable operation in urgent conditions.

Experiment 2: use simulative brake sample data as a case to verify MCRWMB ’s safety.

Fig. 10. The change process of normal state to collision and the degree of danger.

Fig. 11. The error function decreased after several hundreds of iterations.


The training process is illustrated in Fig. 11. The optimized method is conjunct graduation descent, we can see after sev-eral hundreds iterations the error reached its minimal meanwhile we get the unknown parameters which will be used in thenext step.

Here accelerator pedal motion time refers to the moment that the driver’s feet begin to move from the acceleration pedaland the start point at which the driver judges whether braking is needed. It is expressed in the data that the opening of accel-erate pedal change from an opposite and stable degree to 0 abruptly (see Fig. 12). It is an important guideline to scale thedriver’s driving habits. With the neural network training and simulation, the change procedure of accelerator pedal and theresult of simulation was shown in Fig. 12. Obviously, we may notice: (1) Sample data and simulation results’ trend is highlyaccordant; (2) compared with sample data and simulation results, they all lie in rather safe area, so the time of applying thebrake is brought forward and the distance of applying the brake is increased. It is not easy to obtain a global understanding ofthe procedure of accelerator pedal and the result of simulation. In fact, it is observed that several different characteristicsexist during the progress. However, it is enough to verify MCRWMB’s safety. It is worth of pointing out that sample dataand simulation results are fitting better in [0.91,0.94] and [0.78,0.83] section, which is marked A, but in section B there isstated warp. This calls for our further studies.

Experiment 3: compared with other typical models.According to the settings of ANFIS model and calculation model [15], the authors did 1500 experiments to MCRWMB

model, recorded the results and did the analysis and comparison adequately (see Tables 2–4). Table 2 shows that MCRWMBmodel has the longest safety-critical-distance and the least probability of rear-end collision when the speed is between 50and 120 km/h. Table 3 shows that combining driver’ driving preference, MCRWMB model has longer safety distance thanother model within the same length of braking time. And Table 4 shows that the forward misdiagnosis rate of MCRWMB,

Fig. 12. The change procedure of accelerator pedal and the result of simulation.

Table 2The critical safety distance under different speed (km h�1).

Speed/km h�1 50 60 70 80 90 100 110 120

ANFIS/m 40.6 50.6 65.4 79.2 98.1 115.3 142.2 168.4Calculation/m 39.6 51.1 64.2 78.8 95.5 112.8 132.8 152.6MCRWMB/m 40.9 50.7 65.5 79.5 98.1 116.1 143.6 171.3

Table 3The critical safety distance under different brake response time (s).

Brake time/s 0.2 0.5 0.8 1.1 1.5 1.8 2.1 2.2

ANFIS/m 16.4 26.4 34.1 43.2 52.5 61.5 69.4 74.5Calculation/m 15.6 25.8 33.2 41.3 49.9 55.8 60.5 65.1MCRWMB/m 16.6 26.9 35.8 44.4 53.8 62.6 70.1 76.9

Table 4The rate of forward misjudgment under different early warning times.

Average alarm times ANFIS Calculation MCRWMB

5 0.033 0.045 0.02810 0.035 0.046 0.02720 0.031 0.045 0.02930 0.036 0.042 0.03040 0.035 0.043 0.02550 0.037 0.044 0.02760 0.036 0.043 0.02870 0.034 0.045 0.026


i.e., the ratio of the alarms which should but not be given to all the alarms that should be given, is the lowest among thesemodels.

6. Conclusion

To sum up, the multi-agent-based car rear-end warning model has great value in reducing the number of traffic accidentsand in raising the utilization ratio of roads. With the factors of driving behavior added in, this model’s predominance ismainly embodied in the coordination and cooperation among agents, thus improving the reliability, correctness and auton-omy of the alarm system to a large extent. Furthermore, MCRWMB model incarnate that driver have the leading position indriver–vehicle–road closed-loop system. In the meantime, the effectiveness and robustness of MCRWMB model has beenverified by the simulated experiment, which is of great theoretical significance and practical value in the study of intelligenttransportation system.

Acknowledgements

This research is supported by National Natural Science Foundation of China (No. 50875112, 60841003, 60702056 and No.70972048). This study was presented at Asia Simulation Conference 2008/the 7th International Conference on System Sim-ulation and Scientific Computing (ICSC’2008), Beijing, October 10–14, 2008.

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Multi-agent and driving behavior based rear-end collision alarm modeling and simulating