1. Calculating Probability of Intelligent Vehicles
Collision on Roadway with Markov Model
Mohammad Yahaghifar
Mabna Ertebat Tosan
Email:M.yahaghifar@yahoo.com
Sajjad Yahaghifar
Mabna Ertebat Tosan
Email:yahaghifar@yahoo.com
Abstract—most accidents happen when drivers do not have
enough visibility and well reaction on time during an accident
occurs. Increasing required Time for drivers reaction caused to
decreasing accidents on roadways .intelligent vehicle networks
could bring enough time for reaction by sending alerts and
alternate messages to other vehicles on roadway. Main propose
in this paper is around modulation on Reception interval Safety
message and other effective parameters on vehicles safety at
CCWS applications. Effect of alert and alternate messages will be
examined with Markov chain model.in this paper For verification
simulation result we will used Monte Carlo method and compare
result with each other and calculated probability of collision for
those vehicle which used connected network on roadway.
Index Terms—Markov chain, Monte Carlo, probability of
collision
I. INTRODUCTION
CCWS system start to Assess environmental conditions with
using receipted message from neighborcast [1]. For example
if one vehicle suddenly have an accident ,crashed vehicle
start to alert other drivers with Warning message.calulating
probability of collision is one of most important issue in
intelligent vehicle networks which use CCWS system.in this
network messages should send at unique channel that some
factors such as Interference and attenuation from Congestion
dont have affected on Receive message at destination .so if
messages not received at destination it will had negative effect
on system Operation [2].it is clear that messages dont have
same effect in all conditions.in this paper we model manner
of safety application on connected vehicles. Relative safety
between two vehicles in event of an accident modeled by
Markov chain. Transitions between states will done according
to receive messages and calculate prob
II. MODELING OF SAFETY FOR TWO VEHICLE
Safety Application that uses at vehicles networks send
messages which includes vehicle position and dynamic in-
formation.each Reception message at the Destination with
considering of packets delay, brings Awareness of transmitter
position to the receiver. Relative position, Processed at receiver
and give Appropriate alerts to receiver vehicle in transmission
range. If one or two message lost during 0.1 second it does not
have Impressive Error on calculation. But losing consecutive
messages can be problematic in operation. Getting lost some
specific messages at connected vehicles have unknown proba-
bility distribution [3].in fact, losing each messages absolutely
depends on moment conditions of sending message. Indepen-
dence Messages Provides possibility of modeling with Markov
rules. Predictable and unnecessary state which related to long
distance from accident is not considered. For this purpose we
use Awareness Range concept. Model is not use for vehicle
that stated in safe and unsafe range.
III. MARKOV MODEL
Markov model has two states. First state is completely
safe and end state is completely unsafe.in this partition ve-
hicles couldnt maneuver in close range and each middle
states in chain mention to some lost messages displayed
withsiAccording to Fig.1 Transition Between states accrues
by losing one message. Transition probability between states
calculated by xiaomin[4]. we use his calculation and result in
this paper. As shown in Fig.2 when 4 packet get lost ,second
Fig. 1. Effects of receive and lost messages on awareness.
vehicle goes to dangerous state and for instance if 4 packet lost
during transmission fifth packet received to recivier vehicle
maybe it doesnt have brings enough time for appropriate
reaction [5].so determine number of consecutive lost tolerable
messages (TSML) will be effective at evaluation of vehicles
condition. Determine TSML depends on many parameters
such as velocity, acceleration, distance, interval messages time
and etc.First Step we will calculated the time that vehicle need
to received alert message. crashed Vehicle has vias a velocity
and di as an acceleration so We can find vehicle position by
Eq.(1) that shown as below.
XH(t) =



1
2 di + vi + d breaking
d accident
(1)

2. Trailing vehicle close to accident vehicle with vH velocity
and aH acceleration in Eq. (2) show vehicle position.
Fig. 2. change vehicle states by receiving or not receiving message.
XH(t) =



1
2 aHt2
+ vH − d t ≥ tr + tlatency
1
2 dHt2
+ vtr − dtr t ≤ tr + tlatency
(2)
Value of tlatency is time delivery delay message and tV
is PR time. Velocity and distance of vehicle at breaking time
describe as vtr and dtr .now for calculating number of message
for safety state we need value of tlatency.for reach this purpose
we should solve XH(t) = XL(t) then find tlatency .now can
find TSML value from Eq.(3).
TSML =
tlatency
(1/λ)
(3)
With TSML value we can calculate middle states in
transmission range. More middle states increase safety of
vehicle on roadway. Another parameter use in this paper is
uncertainty which consider pacc variable [6] that is use in
our scenario that will calculated with Markov model .Fig .3
show this scenario. .As it shown in Fig.3 red and yellow
Fig. 3. Effects of receive and lost messages on awareness.
states refers to beginning and end of the CoARB[7]. Our
purpose is around calculate safety of vehicle on roadway so
we need to calculate probability of transition between states.
For reaching this goal we can use Transition matrixas which
shown in below .
TM5,5 =















p 1 − p 0 0 0
1 − p 0 1 − p 0 0
p ∗ (1 − pacc) 0 0 1 − p p ∗ (pacc)
p ∗ (1 − pacc) 0 0 0 p ∗ (pacc)
0 0 0 0 1















For the general cases the transition matrix is produced by
Eq.(4).
TMk,k =



p
1 − p i = j + 1, j = k, j = k − 1
p ∗ (pacc) R ≤ i, j < Rcvs
p ∗ (1 − pacc) Rcv ≤ i < Rcvs, j = k
p ∗ (pacc) + 1 − p i = k − 1, j = k
1 i = j, i = k
(4)
Rv andRca and Rcab mention to required package for passing
each awareness board [8].probability of each state is equal
pk = (1 − p)k
probability of sate in safe and unsafe state
calculate by equation (5) and(6)
psafe =
(
m
i=1)
1 − p
p +
p(1 − pacc)(
n
i=m+1)p
1 − p
(5)
punsafe = pn(p(pacc) + 1 − p) + p(p(pacc) + 1 − p)
+p(pacc)(
n
i=m+1
pi)
(6)
n is TSML value and m consider for needed message for
passing CoARB range.
IV. SIMULATION PARAMETERS
Simulation parameters includes two parts.one of them is
network Specifications ,another is Moving Vehicle Specifica-
tions.Network Specifications consider constant at MAC layer
shown in Table 1. Moving Vehicle Specifications are included
PR time, velocity, acceleration and vehicle distance ,all of
these variable will token completely random samples that is
shown in table 2. For Measure accuracy of different models
we consider 10000 repetition between two vehicle and 1000
repetition in vehicles chain.
TABLE I
PARAMETERS FOR NERTWORK SPECIFICATION
Parameter Value
Channel data rate 6 Mbit/s
DIFS for 802.11a 64µs
transmitter domain 500 m
packet size of sending message 200 byte
Header MAC layer 192+271 bit
Contention Window 15

3. TABLE II
PARAMETERS FOR VEHICLE MOVING SPECIFICATION
Parameter Value
Velocity Uniform distribution( 20-33 )
acceleration Uniform distribution (2 )
PR time Uniform distribution (0.3-0.7)
Distance between vehicle Exponential distribution
with average( 50-100)
V. MEASUREMENT ACCURACY MODEL WITH
SIMULATION
A. effet of distance
Markov Model and Monte Carlo result will be calculated
and then will checked manner of them in simulation. First sim-
ulation is about effect of distance on probability of collision.
Near distance is an important parameter in most accident.as
shown in fig.4 increasing distance has an increasing effect on
TSML parameter. This means number of middle states will
increased too and can proof it from equation (3). Also as
shown in fig.4 Markov Model and Monte Carlo has almost
same manner in simulation of distance effect on probability
of collision.
Fig. 4. effect of distance on probability of collision
B. effect of packet interval
Packet interval is one of Adjustable parameter on connected
network. This variable effected on Congestion and probability
of reception. [4,8,9] more previous research [10] recommend
matching data rate for solving collision avoidance.as shown
in Fig.5 decreasing data rate and increasing packet interval
probability of collision Will increased. According to simu-
lations Pattern in this paper we try to calculate probability
of collision with Markov model for those vehicles which use
DSRC network for connecting with together and proof our
model with Monte Carlo method .as shown in simulation both
results have same manner so this show Markov modulation is
useful model for simulate probability of collision in connected
wireless network. For future work, vehicles could simulate in
two way-roads at high velocity and crowded roadway .And
also add vehicles communication protocol in simulation such
as RNP[1] .and add fuzzy logic for better performance.they
both have same manner that it can proof our recommended
model accuracy.
Fig. 5. effecet of packet interval on probability of collision
C. Effect of velocity
Velocity has undeniable effect on accident. most damage-
able accident happens at high velocity .we simulate velocity
of vehicles at range 15-33 (m/s).as shown in fig.6 increasing
velocity cause increase probability of accident and two simula-
tion has same manner.Avaerge distance in this scenario is 100
meter and interval time between sequence message transitions
consider 0.1 second.
Fig. 6. effect of velocity on probability of collision .velocity is between 15-33
(m/s)

4. D. effect of PRR
Reliability in connected networks is necessary at safety
application.in fact operation of awareness layer in CCWS
depends on communication operator layer. Increasing PR time
will caused decreasing transfer probability of states with
factor 1-p [4].as shown in Fig.7 increase PR time decrease
probability of collision.
Fig. 7. effect of PRR on probability of collision
E. effect of uncertainty
In this paper uncertainty means to Lack of driver’s reliability
from any accident that happen included and add as pacc[11] to
model. For instance if vehicle fall in situation that cannot know
what happen in road driver Cant have Successful reaction
in time. But if vehicle has additional time and distance for
reaction, uncertainty will not ha affectted on result.in fact
predicted probability of collision with considering pacc has an
error. Because pacc depends on several variables and we do
not have enough information about pacc .anyway this variable
effects results comes in Fig.8.
F. effect of conneted vehicle on accidents chains
In this part we consider 10 vehicles with different message
generation rate for our simulation. Average distance between
vehicles are 70 meter.as shown in Fig.9 increasing interval
messages generation rate could cause increasing average prob-
ability of collision in vehicles chain too. Vehicles demonstrate
with V1 to V10.vehicles that located at end of chain have less
effect and be safer from collision. And also vehicles located
at first of chain have more effect from collision that can see
as follows.
VI. CONCLUSION
in this paper we try to calculate probability of collision with
Markov model for those vehicles which use DSRC network
for connecting with together and proof our model with Monte
Fig. 8. effect of PRR on probability of collision
Fig. 9. effect of message generation on average probability of collision at 10
vehicles chain.
Carlo method .as shown in simulation both results have same
manner so this show Markov modulation is useful model
for simulate probability of collision in connected wireless
network. For future work, vehicles could simulate in two way-
roads at high velocity and crowded range.And also add vehicle
communication protocol in simulation such as RNP[1] and etc
.and also add fuzzy logic for better performance.
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