Informatica 42 (2018) 117–125 117
Microscopic Evaluation of Extended Car-following Model in Multi-lane Roads
Hajar Lazar, Khadija Rhoulami and Moulay Driss Rahmani
LRIT-CNRST (URAC No. 29)
Faculty of Sciences, Mohammed V University in Rabat, Rabat 10000, Morocco
E-mail: hajar.lazar@gmail.com
Keywords: car following models, velocity separation difference model, lane changes model
Received: February 4, 2017
This paper describes a micro-simulation model which combined car following with lane change model. For
that, we proposed a new car-following model which is an extended of velocity-separation difference model
(VSDM) by introducing a new optimal velocity function, named a modified velocity-separation difference
model (MVSDM) which react better in braking case. The problems of collision in urgent braking case
existing in the previous models were solved. Furthermore, the simulation results show that (MVSDM) can
exactly describe the driver’s behavior under braking case, where no collision occurs.
Povzetek: Članek opisuje mikrosimulacijski model avtonomne vožnje, ki kombinira sledenje avta z za-
menjavo voznega pasu.
1 Introduction
The accelerated growth of the urban population and the ex-
tension of cities, the intensification of economic exchanges
have made road traffic and its management one of the major
challenges of sustainable development. Recently, there has
been a strong focus on improving the efficiency and safety
of transportation and this has led to the development of the
Intelligent Transportation Systems (ITS) (1). Among the
most notable urban transport problems:
– Traffic congestion occurs when, at a specific point in
time and in a specific section, there is an imbalance
between transport demand and supply .
– Environmental impacts includes the pollution and
noise problems generated by circulation.
– Accidents and safety problems due to growing traffic
in urban areas with a growing number of accidents and
fatalities.
In this context, traffic flow modeling and simulation has be-
come a famous area of research in recent years, and consti-
tute efficient tools to evaluate different tasks such as traffic
prediction, traffic control and forecasting, the repercussion
of the construction of new infrastructure onto the global be-
havior of the traffic flow. For studying the traffic problem,
traffic flow are classified into two different types of ap-
proaches, namely, macroscopic and microscopic ones (2).
Macroscopic models describe traffic flow as a continuous
fluid, which describe entities and their activities and inte-
ractions at a relatively low level of detail and established
relationships between speed, flow and density. In contrast,
microscopic model attempts to model the motion of indi-
vidual vehicles and their interaction at a high level of de-
tail and describe the reaction of every driver (accelerating,
braking, lane changing, etc) depending on the surrounding
traffic. Microscopic models are better adapted to the des-
cription of more punctual elements of the network, while
macroscopic models are adapted to the representation of
networks of large sizes. On the other hand, mesoscopic
models characterized by the high level of aggregation, low
level of detail, and typically based on a gas-kinetic ana-
logy in which driver behavior is explicitly considered (3).
Figure 1 presented the different simulation approaches of
traffic flow. In this context, we are mainly interested with
the microscopic approach which road traffic is modeled by
individual motion of each vehicle. In this model, the speed
of a vehicle is directly according to the distance that sepa-
rates it from the leading vehicle, modulo a delay time. This
delay time is generally assimilated to the reaction time of
the driver in order to take into account the variations in be-
havior of his leading vehicle. This is a car-following pro-
cess also known as longitudinal driving behavior. The mo-
deling of traffic in the broader sense proposes to describe
more finely the flow of vehicles on a road. For that, it is
necessary to understand two behavioral sub-models which
are responsible for vehicle movement inside the network:
Car Following (CF) and Lane Changing (LC) models. Car-
following process were developed to model the manner in
which individual vehicles follow one another in the same
lane where the driver adjusts his or her acceleration accor-
ding to the conditions in front and following each other on a
single lane without any overtaking (2). The purpose of this
paper is to propose a extended car-following model taking
into account the effects of lane changing behavior. The
work presented in this paper is devoted to overcome the
shortcomings such as the unrealistic deceleration and the
collisions in braking cases of many existing car-following
models. However, we implemented the proposed approach
using the open source simulator for traffic flow (4), in order
118 Informatica 42 (2018) 117–125 H. Lazar et al.
Figure 1: Traffic flow approaches
to improve the efficiency of a proposed approach compared
with the existing ones.
The paper is organized as follows. The state-of-the art of
car-following and lane changing models will be introduced
in Section 2. The proposed approach will be presented in
Section 3. In section 4, the simulation results are carried
out. At last, the conclusion is given in Section 5.
2 Related work
2.1 Car-following models
The most widely known class of microscopic traffic flow
models is so-called the family of car-following or follow-
the-leader models. Car-following theories describe the way
in which each vehicle follow another in the same lane. The
most car-following models have a significant impact on the
ability of traffic micro-simulations to replicate real-world
traffic behavior (5). Various models were formulated to re-
present how a driver reacts to the changes in the relative
positions of the vehicle ahead. Figure 2 describes the vehi-
cular traffic sketch. We denote as i the car whose behavior
is currently under investigation, at instant t, such vehicle
is at a position xi(t), and travels with a speed vi(t), that
means its instantaneous acceleration can be expressed as
ai(t). Index i−1 identify the front vehicles with respect to
i , which are located at xi−1(t) and travel at speed vi−1(t)
at time t. The front bumper to back bumper distance bet-
ween i and i− 1 is identified as S(t) = 4xi = xi−1 − xi.
Since the 1990s, car following models have not only
been of great importance in an autonomous cruise control
system, but also as important evaluation tools for intelli-
gent transportation system strategies (6). The car-following
models have been designed for single-lane roads, based
essentially on the following ordinary differential equation
Figure 2: Car following process notation
(ODE):
ai(t) =
vi−1(t)− vi(t)
T
(1)
This model is based on the idea that the acceleration
ai(t) of the vehicle i at time t depends on the relative speed
of the vehicle i and its leader i−1 by means of a certain re-
laxation time T . However the previous equation describes
a phenomenon is not stable enough in the case of road traf-
fic. Hence the appearance of several variants of this model
includes:
– Safe-distance models or collision avoidance models
try to describe simply the dynamics of the only vehi-
cle in relation with his predecessor, so as to respect a
certain safe distance.
– Stimulus-response models based on the assumption
that the driver of the following vehicle perceives and
reacts appropriately to the spacing and the speed dif-
ference between the following and the lead vehicles
(7).
– Optimal velocity models are another approach gene-
rally based on the difference between the driver’s de-
sired velocity and the current velocity of the vehicle
as a stimulus for the driver’s actions.
In this paper, we focused on optimal velocity models and
we give here a state of art of the famous ones. For more
detailed information with respect to microscopic models,
particularly, car-following models can be found in the over-
view of (5) (8) (9)(10)(11) (12)(13)(14)(15). The optimal
velocity models attempt to modify the acceleration mecha-
nism, such that a vehicle’s desired speed is selected on the
basis of its space headway, instead of only considering the
speed of the leading vehicle (16). The first model defined
the optimal velocity function using an equilibrium relation
for the desired speed as a function of its space headway is
(17). The acceleration of Newell model is determined by
the following equation:
ai(t) = Vopt(xi−1(t)− xi(t)) (2)
Microscopic Evaluation of Extended Car- following Model in. . . Informatica 42 (2018) 117–125 119
Bando et al. later improved this model, by introducing
the notion of desired velocity, chosen as a function of re-
lative spacing or headway (18). They distinguished two
major types of theories for car-following regulations. The
first type called follow-the leader theory which was used by
(17), based on the idea that each vehicle must maintain the
legal safe distance of the preceding vehicle, which depends
on the relative velocity of these two successive vehicles.
The other type for regulation is that each vehicle has the le-
gal velocity, which depends on the following distance from
the preceding vehicle. Based on the latter assumption, the
authors (18) investigated the equation of traffic dynamics
and found a realistic model of traffic flow, resulting in the
following equation that describes a vehicle’s acceleration
behavior:
ai(t) = k ∗ [Vopt((S(t))− vi(t)] (3)
In which Vopt(S(t)) is the optimal velocity function
which depends on the headway S(t) to the car in the front.
The stimulus here was a function of the relative spacing
and the sensitivity k was a constant. The optimal velocity
function, generally, must satisfy the following properties: it
is a monotonically increasing function and it has an upper
bound (maximal velocity). The optimal velocity adopted
here calibrated by using actual measurement data proposed
by (19) as follows :
Vopt(S(t)) = V1 + V2 tanh[C1(S(t)− l)− C2] (4)
With V1, V2, C1, C2 parameters calibrated and l is the
length of the car. Unfortunately, the model produces many
problems of high acceleration, unrealistic deceleration and
is not always free of collisions. For this reason, Helbing
and Tilch proposed an extended model considering the he-
adway and the velocity of the following car and the relative
velocity between the preceding vehicle and the following
vehicle when the following vehicle was faster than the pre-
ceding vehicle (19). To solve the OVM problems, they ad-
ded a new term which represents the impact of the negative
difference in velocity on condition that the velocity of the
front vehicle is lower than that of the follower. The GFM
formula is:
ai(t) = k ∗ [Vopt((S(t))− vi(t)] + λH(− ˙S(t)) ˙S(t) (5)
Where H(.) is the Heaviside function, λ is another sen-
sitivity coefficient, and ˙S(t) = vi−1(t) − vi(t) means
the velocity difference between the current vehicle and the
vehicle ahead. The main drawback of GFM doesn’t take
the effect of positive velocity difference on traffic dyna-
mics into account and only considers the case where the
velocity of the following vehicle is larger than that of the
leading vehicle (15). The basis of GFM and taking the po-
sitive factor ˙S(t) into account. In 2001, the authors (20)
obtained a more systematic model called Full Velocity Dif-
ference Model (FVDM), one whose dynamics equation is
as:
ai(t) = k ∗ [Vopt((S(t))− vi(t)] + λ ˙S(t) (6)
In 2005, the authors in ref (21) introduced a weighting
factor which makes the OV model more reactive to bra-
king . They extended the OVM by incorporating the new
optimal velocity function obtained by the combination of
optimal velocity function Eq (8) with the weighting factor.
The modified optimal velocity function expressed as:
V newopt (S, Ṡ) = Vopt(S(t)) ∗W (S(t), ˙S(t)) (7)
Where the weighting factor is as follows:
W (S(t), ˙S(t)) =
1
2
+
1
2
tanhB(
Ṡ(t)
S(t)
+ C) (8)
In which B and C are the calibrated parameters. The
dynamic equation of the system is obtained as:
a(t) = κ(V newopt (S(t),
˙S(t))− vi(t)) (9)
In 2006, (6) conducted a detailed analysis of FVDM and
found out that second term in the right side of Eq (6) makes
no allowance of the effect of the inter-car spacing indepen-
dently of the relative velocity. For that, they proposed a
velocity-difference-separation model (VDSM) which takes
the separation between cars into account and the dynamics
equation becomes:
ai(t) = κ(Vopt(S(t))− vi(t)) (10)
+ λH( ˙S(t)) ˙S(t)(1 + tanh(C1(S(t)− l)− C2)3
+ λΘ(− ˙S(t)(t)) ˙S(t)(1− tanh(C1(S(t)− l)− C2)3
2.2 Lane changing models
The transfer of a vehicle from one lane to adjacent lane is
defined as lane change. Lane change, as one of the basic
driver behaviors, can never be avoided in the real traffic en-
vironment. Lane changing models are therefore an impor-
tant component in microscopic traffic simulation Modeling
the behavior of a vehicle within its present lane is relatively
straightforward, as the only considerations of any impor-
tance are the speed and location of the preceding vehicle.
Therefore the understanding of lane changing behavior is
important in several application fields such as capacity ana-
lysis and safety studies. These lane changing models are
categorized into four groups:
120 Informatica 42 (2018) 117–125 H. Lazar et al.
– Rule-based models are the most popular ones in mi-
croscopic traffic simulators include those reported in
(22),(23). For this type of models, the subject vehi-
cle’s lane changing reasons is evaluated first. If these
reasons warrant a lane change, a target lane from
the adjacent lane(s) is selected. The gap acceptance
model used to determine whether the available gaps
should be accepted.
– Discrete-choice-based models based on logit or pro-
bit models. The lane changing process is usually mo-
deled as either MLC or DLC. Mandatory lane chan-
ges (MLC) are considered those which occur because
of a blocked lane, traffic regulations or in order to fol-
low one’s route to destination. Discretionary chan-
ges (DLC) are made in order for the subject vehicle to
achieve better lane conditions (24). Discrete-choice-
based lane changing models follow three steps: 1)
checking lane change necessity, 2) choice of target
lane, and 3) gap acceptance.
– Artificial intelligence models are fundamentally dif-
ferent from the rule-based and discrete choice-based
models. A major advantage of them is that they can
better incorporate human experience and reasoning
into the development of lane changing models.
– Incentive-based models have been recently proposed
to modeling lane changing behavior. From their per-
spective, the attractiveness of a lane based on its uti-
lity to the driver, and a safety criterion captures the
risk associated with the lane change (25). A variety
of factors included in these models such as the desire
to follow a route, gain speed, and keep right (26), in
addition to politeness factors that can describe the dif-
ferent driver behaviors (25).
In this paper, we describe briefly one the important
incentive-based lane changes models. We chose MOBIL
(25) as it is the only lane changing model which takes into
account the effect of lane change decisions on the immedi-
ate neighbors. This model based on the simplistic control
rules and it was more appropriate to analyze the affects of
usual lane change behaviors of drivers on the overall traffic
(24). The lane changing algorithm MOBIL (Minimizing
Overall Braking Induced by Lane Changes) is among the
most important components of a microscopic traffic simu-
lator based on a microscopic longitudinal movement mo-
del. A lane change model depends on the two following
vehicles on the present and the target lane, respectively as
shown in Fig. 3. A specific MOBIL lane change based on
the accelerations on the old and the prospective new lanes.
To formulate the lane changing criteria shown in Fig. 3
we use the following notation: the vehicle i refers to the
lane change of the successive vehicles on the target and
present lane referred by n (new one in the target lane) and
o (old follower in the current lane). The tildes ãi, ão and
ãn denotes the new acceleration of vehicle i on the target
lane, the acceleration of the old and new followers after the
Figure 3: Vehicles involved in lane changing process
lane change of vehicle i, respectively. All the accelerati-
ons involved are calculated according to the car-following
model (27). A lane change model based on a safety and
incentive criterion. The safety criterion is satisfied, if the
car-following braking deceleration ãi imposed on the old
vehicle o of the target lane after a possible change does not
exceed a certain limit bsafe this means:
ãi > −bsafe (11)
The second criterion determines the acceleration advan-
tage that would be gained from the event. This criterion
based on the accelerations of the longitudinal model before
and after the lane change and focused on improving the
traffic situation of an individual driver by letting him drive
faster or avoid a slow leader (24). For symmetric overta-
king rules, they neglect differences between the lanes and
propose the following incentive condition for a lane chan-
ging decision of the driver of vehicle i as follows:
︷ ︸︸ ︷
ãi − ai +p(
︷ ︸︸ ︷
ãn − an +
︷ ︸︸ ︷
ão − ao) > 4ath (12)
Equation (11) states that the acceleration advantage to
be gained by the lane change, must be greater than both a
threshold acceleration 4ath used to dampen out changes
with marginal advantage, and a politeness factor p deter-
mines to which degree these vehicles influence the lane-
changing decision. The factor p controls the degree of
cooperation while considering a lane change, from a pu-
rely egoistic behavior (p = 0) to an altruistic one (p ¿ 1)
(25). The politeness factor can be thought of as accounting
for driver aggressiveness. It is this balancing of accelera-
tions that gives rise to the name MOBIL, as Minimizing
Overall Braking Induced by Lane changes (27).
3 Proposed approach
In comparison with the existing works above, our propo-
sal in this paper provides a extended car following model
with an interaction of lane change behavior that mainly im-
portant to simulating and to representing the traffic flow in
the real manner. The proposed approach is detailed in the
following section.
Microscopic Evaluation of Extended Car- following Model in. . . Informatica 42 (2018) 117–125 121
3.1 Flowchart of the proposed approach
For an ideal flow of a dynamic traffic simulation study, we
proposed the basic algorithm presented in Fig. 4 which
based on three major steps given as:
– Preparation of the traffic flow simulation: in this step,
we must define the road environment and also we must
specify the initial parameters and variables, including
initialization of position, velocity, and so on.
– Implementation of the model and validation of its dif-
ferent scenarios: in this stage, we adopt our MVSD
model to compute acceleration for each car and then
compute the new speed and position on both lanes for
the next time step. At the same time, we start lane
changes rules, we determine which car change whe-
reto and add these cars to the correct position on the
lane and removed changed cars from their old lane.
– Analysis of results: for the next time step, we update
the network and information state to get a new velo-
city and position state; then we jump to step 2, and we
begin an another cycle.
3.2 Modified velocity separation difference
model
In this paper, we proposed a modified car following model
introducing the lane changing rules just as other studies. In
ref (21), the authors modified an OV model, introducing the
new OV function without using the lane change behavior to
get a model more reactive on braking situation called modi-
fied optimal velocity model (MOVM). The motivation for
our paper comes from the key idea behind the new optimal
velocity function proposed by (21) which we incorporating
this latter on the VSDM model using the lane changing be-
havior. However, the new OV function combined between
the OV function the reference Eq (2) and the weighting fac-
tor Eq (8) that depends on the inverse of time to collision
(TTC). The TTC concept was introduced by the US rese-
archer (28) and it was used in different studies as a time
based surrogate safety measure for evaluating collision risk
(29)(30)(31). In car following situations the TTC indicator
is only defined when the speed of the following vehicle is
higher than the speed of the lead vehicle (31). Rear end
collision risk is defined as the time for the collision of two
vehicles if they continue at their present speed and on the
same lane and at the same speed (see Fig. 5). The time to
collision of a vehicle driver combination n at instant t with
respect to a leading vehiclen1 can be calculated with:
TTC =
S(t)
˙S(t)
;∀ ˙S(t) > 0 (13)
The new optimal velocity function V newopt (S, Ṡ) is ex-
pressed as the combination of the optimal velocity function
proposed by (18) based only on headway stimulus and the
weighting factor established the inverse of time to collision
to make the model more reactive in braking case.
V newopt (S, Ṡ) = Vopt(S) ∗W (S, Ṡ) (14)
Where the weighting factor is :
W (S, Ṡ) = [A(1 + tanhB(
Ṡ
S
+ C)] (15)
The weighting factor must satisfies some proprieties:
– When the relative speed is positive ˙S(t) > 0, the
weighting must maintain the reference OV function
unchanged.
– For negative decreasing relative speed ˙S(t) < 0, it
has to be decreasing and has to go toward zero when
˙S(t)− > infini.
There are several functions which behave similarly with
varying only the headway stimulus. Therefore, Here the
new OV function modulates the reactivity of the car follo-
wing model according to the actual headway and relative
speed between the follower and ahead car. In our contribu-
tion, we revised and extended a velocity separation diffe-
rence model by incorporating the new OV function to get a
new model that called a Modified Velocity Separation Dif-
ference (MVSDM). The MVSD model is expressed by the
equation of motion as:
ai(t) = κ(V
new
opt (S(t),
˙S(t))− vi(t)) (16)
+ λH( ˙S(t)) ˙S(t)(1 + tanh(C1(S(t)− l)− C2)3
+ λΘ(− ˙S(t)(t)) ˙S(t)(1− tanh(C1(S(t)− l)− C2)3
To describe real driving behavior on multilane roads,
we need the car following process and the lane changing
process. The lane changing behavior has a significant ef-
fect on traffic flow. Therefore the understanding of lane
changing behavior is important in several application fields
such as capacity analysis and safety studies. We interested,
particularly, the lane changing algorithm MOBIL (Minimi-
zing Overall Braking Induced by Lane Changes) which is
among the most important components of a microscopic
traffic simulator based on a microscopic longitudinal mo-
vement model (25) and is adopted here.
4 Simulation results
In this study, we carry out the simulations to investigate
whether MVSDM can overcome the shortcomings of pre-
vious models and compared MVSDM with MOVM propo-
sed by (21). In this paper, for each model we establish the
122 Informatica 42 (2018) 117–125 H. Lazar et al.
Figure 4: Flowchart of the proposed approach
Figure 5: Time to collision for rear end collision sketch
simulation results for two different scenarios. In the fol-
lowing, we will test the proposed approach (accelerating
and braking behavior) using an open source microscopic
simulator proposed by (4) to validate our approach using
these scenarios. We used two vehicle classes: cars and
trucks. For all simulations, the parameter values used for
optimal velocity function Eq (4) and are adapted from (19)
are V1 = 6.75m/s, V2 = 7.91m/s, C1 = 0.13m−1, and
C2 = 1.57m
−1. The parameter values calibrated for weig-
hting factor (21) are A = 0.5, C = 0.5, and B = 5s.
The sensitivities parameters values are a = 0.6m/s2, and
λ = 0.45m/s2. The parameters values for cars are the
desired velocity V0 = 120km/h, the safe time headway
T = 1.2s, the minimum gap S0 = 2m, and the vehicle
length l = 6m. The parameters values for trucks are the
desired velocity V0 = 80km/h, the safe time headway
T = 1.7s, the minimum gap S0 = 2m, and the vehicle
length l = 10m. The parameters values for lane chan-
ging are the politeness factor p = 0, the changing thres-
hold 4ath = 0.2m/s2, the maximum safe deceleration
bsave = 12m/s
2, and the bias for the slow lane 4abias.
For more information about the simulation results, we built
a video to visualize clearly the validity of our proposed mo-
del MVSDM and the existing model MOVM and VSDM
in the following link https://www.youtube.com/
watch?v=LJ5ddRGVbgA&feature=youtu.be.
When starting the simulation, we extract the necessary
data in excel format in order to represent them in graph
form, and this is done for each car following model and for
each scenario. Figure 6 shows the resulting data (speed,
acceleration, position, type of car, length, etc.)
4.1 Ramp scenario: behavior in stop and go
traffic
Stop and go scenario demonstrates the traffic breakdown
provoking on the main road of the on-ramp. Usually, the
traffic jam occur when the leading car decelerate for cer-
tain reasons. For that, it’s important to study the vehicle
behavior when simulating in such case. Simulation results
depicted in Fig. 7d show that the proposed model avoids
the collision when the leading car decelerate hardly. Howe-
ver, simulating traffic flow with MOV model occurs crashes
between different cars as we can see in Fig. 7b.
At t = 0, all cars start up according to the MOVM,
VSDM, and MVSDM, respectively. From Fig. 8, it can
be seen that the speed maximum of MVSDM is under of
MOVM and VSDM. We can see that MFVDM velocity be-
gins to decrease before MOVM and VSDM velocity rea-
ches its maximum. The simulation results demonstrate that
MOVM and VSDM provokes crashes. In contrast, our pro-
posal MVSDM avoid it and the traffic jams disappear.
To simulate the car motion and to describe the traffic
flow, we examine certain properties of traffic from each car.
Microscopic Evaluation of Extended Car- following Model in. . . Informatica 42 (2018) 117–125 123
Figure 6: Example of resulting data according to MVSDM
Figure 7: Simulation of ramp according to (a) OVM and
(b) MOVM(c) VSDM and (d) MVSDM
Figure 8: Time evolution of velocity variation according to
MOVM, VSDM, and MVSDM
Figure 9: Position variation according to MOVM, VSDM,
and MVSDM
Figure 9 gives the position evolution of four simulated cars,
it’s seen that the previous models provokes the collision. In
contrast, our proposed approach avoids it.
4.2 Traffic lights scenario: behavior at
stopping and approaching traffic signal
The traffic lights scenario describes the driving behavior of
the vehicle when approaching a traffic signal. First a traf-
fic signal is red and a queue of vehicles is waiting which
the optimal velocity is 0. When the signal turn to green,
at t = 0, vehicles start. For that, the traffic lights signal is
represented by virtual obstacles in each lane which is re-
moved when the light turns to green. Figure 10 represents
the velocity variation of two vehicles using the MVSDM
in the case of several changes. At the beginning, vehicle
1 follows vehicle 2 in the same lane 0, after a few mo-
ments vehicle 1 change the lane 0 towards the lane 1 that is
why two vehicles show themselves in parallel when appro-
aching traffic lights at t = 57. In approaching phase, and at
t = 72 vehicles should decelerate smoothly which clearly
shown that the vehicles stopped completely at a red light,
and their velocity goes to 0. When the signal changes to
green, vehicles begin to accelerate.
Figure 11 shows the behavior of vehicle according
MOVM, MVSDM, and VSDM. Through these results, we
deducted that the velocity of vehicle applying MOVM
doesn’t go to 0 that means all vehicles don’t stop at a red
light. However, when we simulate applying VSDM and
MVSDM, all vehicles behave correctly by stopping at a
124 Informatica 42 (2018) 117–125 H. Lazar et al.
Figure 10: Driving behavior of two vehicles according
MVSDM in each lane
Figure 11: Simulation results according to MOVM, VSDM
and MVSDM when approaching traffic lights signal
red light and moves when its turn to green. It’s show cle-
arly that the MVSD model react the realistic manner than
MOVM and VSDM in braking case.
Figure 12 represents the snapshot of vehicle motion and
their behavior according to MVSD, VSD, OV, and MOV
models. Through these results, and when approaching traf-
fic lights, it can be observed that the vehicles collide in the
previous models. However, the problems of collision in
emergency case were solved. Furthermore, the simulation
results show that our proposed approach can exactly des-
cribe the driver’s behavior when approaching traffic signal,
where no crash occurs.
Figure 12: Simulation at traffic signal results according to
OVM, MOVM, VSDM and MVSDM when approaching
and stopping traffic lights signal
5 Conclusion
Through introducing the new optimal velocity function
which takes into account not only the headway, but also
the relative speed parameter into the VSDM, the modified
velocity-separation difference model (MVSDM) is presen-
ted considering the driving behavior of the vehicle in bra-
king case. In addition, to simulate in a realistic manner, we
proposed to combine the proposed model with lane change
model. The MVSDM can exactly describe the driver beha-
vior under two proposed scenarios: when approaching traf-
fic signal and an on ramp road, where no collision occurs.
We can see that MVSDM is much close to the reality. Ho-
wever, the collision and crashes occur in the previous mo-
dels. We proposed as a future work, to validate the model
in bidirectional road scenario with multilane.
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