\title{{\itshape Perimeter-based Coverage Optimization \\
to Improve Lifetime in Wireless Sensor Networks}}
-\author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$
+\author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$, and Rapha\"el Couturier $^{a}$
$^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, \\
University Bourgogne Franche-Comt\'e, Belfort, France}} \\
$^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}}
lies essentially in the formulation of a new mathematical optimization model
based on the perimeter coverage level to schedule sensors' activities.
Extensive simulation experiments demonstrate that PeCO can offer longer lifetime
-coverage for WSNs in comparison with some other protocols.
+coverage for WSNs compared to other protocols.
\begin{keywords}
Wireless Sensor Networks, Area Coverage, Energy efficiency, Optimization, Scheduling.
\label{sec:introduction}
The continuous progress in Micro Electro-Mechanical Systems (MEMS) and wireless
-communication hardware has given rise to the opportunity to use large networks
+communication hardware has given rise to the opportunity of using large networks
of tiny sensors, called Wireless Sensor Networks
(WSN)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring
tasks. A WSN consists of small low-powered sensors working together by
communicating with one another through multi-hop radio communications. Each node
can send the data it collects in its environment, thanks to its sensor, to the
-user by means of sink nodes. The features of a WSN made it suitable for a wide
-range of application in areas such as business, environment, health, industry,
+user by means of sink nodes. The features of a WSN makes it suitable for a wide
+range of applications in areas such as business, environment, health, industry,
military, and so on~\citep{yick2008wireless}. Typically, a sensor node contains
three main components~\citep{anastasi2009energy}: a sensing unit able to measure
physical, chemical, or biological phenomena observed in the environment; a
processing unit which will process and store the collected measurements; a radio
-communication unit for data transmission and receiving.
+communication unit for data transmission and reception.
The energy needed by an active sensor node to perform sensing, processing, and
-communication is supplied by a power supply which is a battery. This battery has
+communication is provided by a power supply which is a battery. This battery has
a limited energy provision and it may be unsuitable or impossible to replace or
-recharge it in most applications. Therefore it is necessary to deploy WSN with
-high density in order to increase reliability and to exploit node redundancy
-thanks to energy-efficient activity scheduling approaches. Indeed, the overlap
-of sensing areas can be exploited to schedule alternatively some sensors in a
-low power sleep mode and thus save energy. Overall, the main question that must
-be answered is: how to extend the lifetime coverage of a WSN as long as possible
-while ensuring a high level of coverage? These past few years many
+recharge in most applications. Therefore it is necessary to deploy WSN with high
+density in order to increase reliability and to exploit node redundancy thanks
+to energy-efficient activity scheduling approaches. Indeed, the overlap of
+sensing areas can be exploited to schedule alternatively some sensors in a low
+power sleep mode and thus save energy. Overall, the main question that must be
+answered is: how is it possible to extend the lifetime coverage of a WSN as long
+as possible while ensuring a high level of coverage? These past few years many
energy-efficient mechanisms have been suggested to retain energy and extend the
lifetime of the WSNs~\citep{rault2014energy}.
-This paper makes the following contributions.
+This paper makes the following contributions :
\begin{enumerate}
\item A framework is devised to schedule nodes to be activated alternatively
such that the network lifetime is prolonged while ensuring that a certain
architecture.
\item A new mathematical optimization model is proposed. Instead of trying to
cover a set of specified points/targets as in most of the methods proposed in
- the literature, we formulate an integer program based on perimeter coverage of
- each sensor. The model involves integer variables to capture the deviations
- between the actual level of coverage and the required level. Hence, an
- optimal schedule will be obtained by minimizing a weighted sum of these
- deviations.
+ the literature, we formulate a mixed-integer program based on the perimeter
+ coverage of each sensor. The model involves integer variables to capture the
+ deviations between the actual level of coverage and the required level.
+ Hence, an optimal schedule will be obtained by minimizing a weighted sum of
+ these deviations.
\item Extensive simulation experiments are conducted using the discrete event
- simulator OMNeT++, to demonstrate the efficiency of our protocol. We have
+ simulator OMNeT++, to demonstrate the efficiency of our protocol. We have
compared the PeCO protocol to two approaches found in the literature:
DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to our previous
protocol DiLCO published in~\citep{Idrees2}. DiLCO uses the same framework as
targets, and barrier coverage~\citep{HeShibo,kim2013maximum} focuses on
preventing intruders from entering into the region of interest. In
\citep{Deng2012} authors transform the area coverage problem into the target
-coverage one taking into account the intersection points among disks of sensors
-nodes or between disk of sensor nodes and boundaries. In
-\citep{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of
-sensors are sufficiently covered it will be the case for the whole area. They
-provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of
-each sensor. $d$ denotes the maximum number of sensors that are neighbors to a
+coverage one, taking into account the intersection points among disks of sensors
+nodes or between disks of sensor nodes and boundaries. In
+\citep{huang2005coverage} authors prove that if the perimeters of the sensors
+are sufficiently covered it will be the case for the whole area. They provide an
+algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of each
+sensor. $d$ denotes the maximum number of sensors that are neighbors to a
sensor, and $n$ is the total number of sensors in the network. {\it In PeCO
protocol, instead of determining the level of coverage of a set of discrete
points, our optimization model is based on checking the perimeter-coverage of
The major approach to extend network lifetime while preserving coverage is to
divide/organize the sensors into a suitable number of set covers (disjoint or
non-disjoint) \citep{wang2011coverage}, where each set completely covers a
-region of interest, and to activate these set covers successively. The network
+region of interest, and to successively activate these set covers. The network
activity can be planned in advance and scheduled for the entire network lifetime
or organized in periods, and the set of active sensor nodes decided at the
beginning of each period \citep{ling2009energy}. In fact, many authors propose
its own activity scheduling after an information exchange with its neighbors.
The main interest of such an approach is to avoid long range communications and
thus to reduce the energy dedicated to the communications. Unfortunately, since
-each node has only information on its immediate neighbors (usually the one-hop
-ones) it may make a bad decision leading to a global suboptimal solution.
+each node has information on its immediate neighbors only (usually the one-hop
+ones), it may make a bad decision leading to a global suboptimal solution.
Conversely, centralized
algorithms~\citep{cardei2005improving,zorbas2010solving,pujari2011high} always
-provide nearly or close to optimal solution since the algorithm has a global
-view of the whole network. The disadvantage of a centralized method is obviously
-its high cost in communications needed to transmit to a single node, the base
-station which will globally schedule nodes' activities, data from all the other
-sensor nodes in the area. The price in communications can be huge since long
-range communications will be needed. In fact the larger the WSN, the higher the
+provide nearly optimal solutions since the algorithm has a global view of the
+whole network. The disadvantage of a centralized method is obviously its high
+cost in communications needed to transmit to a single node, the base station
+which will globally schedule nodes' activities, data from all the other sensor
+nodes in the area. The price in communications can be huge since long range
+communications will be needed. In fact the larger the WSN, the higher the
communication energy cost. {\it In order to be suitable for large-scale
- networks, in PeCO protocol the area of interest is divided into several
+ networks, in the PeCO protocol the area of interest is divided into several
smaller subregions, and in each one, a node called the leader is in charge of
- selecting the active sensors for the current period. Thus PeCO protocol is
- scalable and a globally distributed method, whereas it is centralized in each
- subregion.}
+ selecting the active sensors for the current period. Thus the PeCO protocol
+ is scalable and a globally distributed method, whereas it is centralized in
+ each subregion.}
Various coverage scheduling algorithms have been developed these past few years.
Many of them, dealing with the maximization of the number of cover sets, are
also been
used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012column}.
{\it In the PeCO protocol, each leader, in charge of a subregion, solves an
- integer program which has a twofold objective: minimize the overcoverage and
+ integer program which has a twofold objective: minimizing the overcoverage and
the undercoverage of the perimeter of each sensor.}
The authors in \citep{Idrees2} propose a Distributed Lifetime Coverage
Optimization (DiLCO) protocol, which maintains the coverage and improves the
lifetime in WSNs. It is an improved version of a research work presented
in~\citep{idrees2014coverage}. First, the area of interest is partitioned into
-subregions using a divide-and-conquer method. DiLCO protocol is then distributed
-on the sensor nodes in each subregion in a second step. Hence this protocol
-combines two techniques: a leader election in each subregion, followed by an
-optimization-based node activity scheduling performed by each elected
+subregions using a divide-and-conquer method. The DiLCO protocol is then
+distributed on the sensor nodes in each subregion in a second step. Hence this
+protocol combines two techniques: a leader election in each subregion, followed
+by an optimization-based node activity scheduling performed by each elected
leader. The proposed DiLCO protocol is a periodic protocol where each period is
decomposed into 4 phases: information exchange, leader election, decision, and
sensing. The simulations show that DiLCO is able to increase the WSN lifetime
and provides improved coverage performance. {\it In the PeCO protocol, a new
mathematical optimization model is proposed. Instead of trying to cover a set
- of specified points/targets as in DiLCO protocol, we formulate an integer
- program based on perimeter coverage of each sensor. The model involves integer
- variables to capture the deviations between the actual level of coverage and
- the required level. The idea is that an optimal scheduling will be obtained by
- minimizing a weighted sum of these deviations.}
+ of specified points/targets as in the DiLCO protocol, we formulate an integer
+ program based on the perimeter coverage of each sensor. The model involves
+ integer variables to capture the deviations between the actual level of
+ coverage and the required level. The idea is that an optimal scheduling will
+ be obtained by minimizing a weighted sum of these deviations.}
\section{ The P{\scshape e}CO Protocol Description}
\label{sec:The PeCO Protocol Description}
sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates the
euclidean distance between nodes~$u$ and $v$ is computed as follows:
$$
- Dist(u,v)=\sqrt{\vert u_x - v_x \vert^2 + \vert u_y-v_y \vert^2},
+ Dist(u,v)=\sqrt{(u_x - v_x)^2 + (u_y-v_y)^2},
$$
while the angle~$\alpha$ is obtained through the formula:
\[
\end{table}
In the PeCO protocol, the scheduling of the sensor nodes' activities is
-formulated with an mixed-integer program based on coverage
+formulated with a mixed-integer program based on coverage
intervals~\citep{doi:10.1155/2010/926075}. The formulation of the coverage
optimization problem is detailed in~Section~\ref{cp}. Note that when a sensor
node has a part of its sensing range outside the WSN sensing field, as in
\label{figure4}
\end{figure}
-We define two types of packets to be used by PeCO protocol:
+We define two types of packets to be used by the PeCO protocol:
\begin{itemize}
\item INFO packet: sent by each sensor node to all the nodes inside a same
subregion for information exchange.
\item ActiveSleep packet: sent by the leader to all the nodes in its subregion
to transmit to them their respective status (stay Active or go Sleep) during
- sensing phase.
+ the sensing phase.
\end{itemize}
Five statuses are possible for a sensor node in the network:
\begin{enumerate}
\item larger number of neighbors;
\item larger remaining energy;
-\item and then in case of equality, larger index.
+\item and then, in case of equality, larger indexes.
\end{enumerate}
Once chosen, the leader collects information to formulate and solve the integer
-program which allows to construct the set of active sensors in the sensing
+program which allows to build the set of active sensors in the sensing
stage.
\section{Perimeter-based Coverage Problem Formulation}
\item $I_j$ designates the set of coverage intervals (CI) obtained for
sensor~$j$.
\end{itemize}
-$I_j$ refers to the set of coverage intervals which have been defined according
+$I_j$ refers to the set of coverage intervals which has been defined according
to the method introduced in Subsection~\ref{CI}. For a coverage interval $i$,
let $a^j_{ik}$ denote the indicator function of whether sensor~$k$ is involved
in coverage interval~$i$ of sensor~$j$, that is:
$\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the
relative importance of satisfying the associated level of coverage. For example,
-weights associated with coverage intervals of a specified part of a region may
+weights associated with coverage intervals of the specified part of a region may
be given by a relatively larger magnitude than weights associated with another
region. This kind of mixed-integer program is inspired from the model developed
-for brachytherapy treatment planning for optimizing dose distribution
+for brachytherapy treatment planning to optimize dose distribution
\citep{0031-9155-44-1-012}. The choice of the values for variables $\alpha$ and
$\beta$ should be made according to the needs of the application. $\alpha$
should be large enough to prevent undercoverage and so to reach the highest
obtained by multiplying the energy consumed in the active state (9.72 mW) with
the time in seconds for one period (3600 seconds), and adding the energy for the
pre-sensing phases. According to the interval of initial energy, a sensor may
-be active during at most 20 periods. Information exchange to update the coverage
+be active during at most 20 periods. the information exchange to update the coverage
is executed every hour, but the length of the sensing period could be reduced
-and adapted dynamically. On the one hand a small sensing period would allow to
-be more reliable but would have result in higher communication costs. On the
+and adapted dynamically. On the one hand a small sensing period would allow the network to
+be more reliable but would have resulted in higher communication costs. On the
other hand the choice of a long duration may cause problems in case of nodes
failure during the sensing period.
the other hand, $\beta^j_i$ is assigned to a value which is slightly lower so as
to minimize the number of active sensor nodes which contribute in covering the
interval. Subsection~\ref{sec:Impact} investigates more deeply how the values of
-both parameters affect the performance of PeCO protocol.
+both parameters affect the performance of the PeCO protocol.
The following performance metrics are used to evaluate the efficiency of the
approach.
\subsection{Simulation Results}
In order to assess and analyze the performance of our protocol we have
-implemented PeCO protocol in OMNeT++~\citep{varga} simulator. The simulations
-were run on a DELL laptop with an Intel Core~i3~2370~M (1.8~GHz) processor (2
-cores) whose MIPS (Million Instructions Per Second) rate is equal to 35330. To
-be consistent with the use of a sensor node based on Atmels AVR ATmega103L
-microcontroller (6~MHz) having a MIPS rate equal to 6, the original execution
-time on the laptop is multiplied by 2944.2 $\left(\frac{35330}{2} \times
-\frac{1}{6} \right)$. Energy consumption is calculated according to the power
-consumption values, in milliWatt per second, given in Table~\ref{tab:EC}.
+implemented the PeCO protocol in OMNeT++~\citep{varga} simulator. The
+simulations were run on a DELL laptop with an Intel Core~i3~2370~M (1.8~GHz)
+processor (2 cores) whose MIPS (Million Instructions Per Second) rate is equal
+to 35330. To be consistent with the use of a sensor node based on Atmels AVR
+ATmega103L microcontroller (6~MHz) having a MIPS rate equal to 6, the original
+execution time on the laptop is multiplied by 2944.2 $\left(\frac{35330}{2}
+\times \frac{1}{6} \right)$. Energy consumption is calculated according to the
+power consumption values, in milliWatt per second, given in Table~\ref{tab:EC},
based on the energy model proposed in \citep{ChinhVu}.
\begin{table}[h]
\label{tab:EC}
\begin{tabular}{|l||cccc|}
\hline
- {\bf Sensor status} & MCU & Radio & Sensor & {\it Power (mW)} \\
+ {\bf Sensor status} & MCU & Radio & Sensing & {\it Power (mW)} \\
\hline
LISTENING & On & On & On & 20.05 \\
ACTIVE & On & Off & On & 9.72 \\
for a WSN of 200 sensor nodes, a leader node has to deal with constraints
induced by about 12 sensor nodes. In that case, to solve the optimization
problem a memory consumption of more than 1~MB can be observed with GLPK,
-whereas less than 300~kB would be needed with CPLEX.
+whereas less than 300~KB would be needed with CPLEX.
Besides PeCO, three other protocols will be evaluated for comparison
purposes. The first one, called DESK, is a fully distributed coverage algorithm
squares. Then, during the decision phase, in each square, one sensor is chosen
to remain active during the sensing phase. The last one, the DiLCO
protocol~\citep{Idrees2}, is an improved version of a research work we presented
-in~\citep{idrees2014coverage}. Let us notice that PeCO and DiLCO protocols are
-based on the same framework. In particular, the choice for the simulations of a
-partitioning in 16~subregions was made because it corresponds to the
+in~\citep{idrees2014coverage}. Let us notice that the PeCO and DiLCO protocols
+are based on the same framework. In particular, the choice for the simulations
+of a partitioning in 16~subregions was made because it corresponds to the
configuration producing the best results for DiLCO. Of course, this number of
-subregions should be adapted according to the size of the area of interest and
+subregions should be adapted according to the size of the area of interest and
the number of sensors. The protocols are distinguished from one another by the
formulation of the integer program providing the set of sensors which have to be
-activated in each sensing phase. DiLCO protocol tries to satisfy the coverage of
-a set of primary points, whereas PeCO protocol objective is to reach a desired
-level of coverage for each sensor perimeter. In our experimentations, we chose a
-level of coverage equal to one ($l=1$).
+activated in each sensing phase. The DiLCO protocol tries to satisfy the
+coverage of a set of primary points, whereas the objective of the PeCO protocol
+is to reach a desired level of coverage for each sensor perimeter. In our
+experimentations, we chose a level of coverage equal to one ($l=1$).
\subsubsection{Coverage Ratio}
obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better
coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the
98.76\% produced by PeCO for the first periods. This is due to the fact that at
-the beginning DiLCO and PeCO protocols put to sleep status more redundant
-sensors (which slightly decreases the coverage ratio), while the two other
-protocols activate more sensor nodes. Later, when the number of periods is
+the beginning the DiLCO and PeCO protocols put more redundant sensors to sleep
+status (which slightly decreases the coverage ratio), while the two other
+protocols activate more sensor nodes. Later, when the number of periods is
beyond~70, it clearly appears that PeCO provides a better coverage ratio and
keeps a coverage ratio greater than 50\% for longer periods (15 more compared to
DiLCO, 40 more compared to DESK). The energy saved by PeCO in the early periods
\subsubsection{Active Sensors Ratio}
-Having the less active sensor nodes in each period is essential to minimize the
+Minimizing the number of active sensor nodes in each period is essential to minimize the
energy consumption and thus to maximize the network lifetime.
Figure~\ref{figure6} shows the average active nodes ratio for 200 deployed
nodes. We observe that DESK and GAF have 30.36~\% and 34.96~\% active nodes for
-the first fourteen rounds, and DiLCO and PeCO protocols compete perfectly with
+the first fourteen rounds, and the DiLCO and PeCO protocols compete perfectly with
only 17.92~\% and 20.16~\% active nodes during the same time interval. As the
-number of periods increases, PeCO protocol has a lower number of active nodes in
+number of periods increases, the PeCO protocol has a lower number of active nodes in
comparison with the three other approaches and exhibits a slow decrease, while
keeping a greater coverage ratio as shown in Figure \ref{figure5}.
computation, listening, active, and sleep status is studied for different
network densities and the four approaches compared. Figures~\ref{figure7}(a)
and (b) illustrate the energy consumption for different network sizes and for
-$Lifetime95$ and $Lifetime50$. The results show that PeCO protocol is the most
+$Lifetime_{95}$ and $Lifetime_{50}$. The results show that the PeCO protocol is the most
competitive from the energy consumption point of view. As shown by both figures,
PeCO consumes much less energy than the other methods. One might think that the
resolution of the integer program is too costly in energy, but the results show
that it is very beneficial to lose a bit of time in the selection of sensors to
activate. Indeed the optimization program allows to reduce significantly the
-number of active sensors and so the energy consumption while keeping a good
+number of active sensors and also the energy consumption while keeping a good
coverage level. Let us notice that the energy overhead when increasing network
size is the lowest with PeCO.
\subsubsection{Network Lifetime}
-We observe the superiority of both PeCO and DiLCO protocols in comparison with
+We observe the superiority of both the PeCO and DiLCO protocols in comparison with
the two other approaches in prolonging the network lifetime. In
-Figures~\ref{figure8}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for
+Figures~\ref{figure8}(a) and (b), $Lifetime_{95}$ and $Lifetime_{50}$ are shown for
different network sizes. As can be seen in these figures, the lifetime
-increases with the size of the network, and it is clearly largest for DiLCO and
+increases with the size of the network, and it is clearly larger for the DiLCO and
PeCO protocols. For instance, for a network of 300~sensors and coverage ratio
greater than 50\%, we can see on Figure~\ref{figure8}(b) that the lifetime is
-about twice longer with PeCO compared to DESK protocol. The performance
+about twice longer with PeCO compared to the DESK protocol. The performance
difference is more obvious in Figure~\ref{figure8}(b) than in
Figure~\ref{figure8}(a) because the gain induced by our protocols increases with
time, and the lifetime with a coverage over 50\% is far longer than with 95\%.
\label{figure8}
\end{figure}
-Figure~\ref{figure9} compares the lifetime coverage of DiLCO and PeCO protocols
+Figure~\ref{figure9} compares the lifetime coverage of the DiLCO and PeCO protocols
for different coverage ratios. We denote by Protocol/50, Protocol/80,
Protocol/85, Protocol/90, and Protocol/95 the amount of time during which the
network can satisfy an area coverage greater than $50\%$, $80\%$, $85\%$,
Table~\ref{my-labelx} shows network lifetime results for different values of
$\alpha$ and $\beta$, and a network size equal to 200 sensor nodes. On the one
-hand, the choice of $\beta \gg \alpha$ prevents the overcoverage, and so limit
-the activation of a large number of sensors, but as $\alpha$ is low, some areas
-may be poorly covered. This explains the results obtained for {\it Lifetime50}
-with $\beta \gg \alpha$: a large number of periods with low coverage ratio. On
-the other hand, when we choose $\alpha \gg \beta$, we favor the coverage even if
-some areas may be overcovered, so high coverage ratio is reached, but a large
-number of sensors are activated to achieve this goal. Therefore network
-lifetime is reduced. The choice $\alpha=0.6$ and $\beta=0.4$ seems to achieve
-the best compromise between lifetime and coverage ratio. That explains why we
-have chosen this setting for the experiments presented in the previous
-subsections.
+hand, the choice of $\beta \gg \alpha$ prevents the overcoverage, and also
+limits the activation of a large number of sensors, but as $\alpha$ is low, some
+areas may be poorly covered. This explains the results obtained for
+$Lifetime_{50}$ with $\beta \gg \alpha$: a large number of periods with low
+coverage ratio. On the other hand, when we choose $\alpha \gg \beta$, we favor
+the coverage even if some areas may be overcovered, so a high coverage ratio is
+reached, but a large number of sensors are activated to achieve this goal.
+Therefore the network lifetime is reduced. The choice $\alpha=0.6$ and
+$\beta=0.4$ seems to achieve the best compromise between lifetime and coverage
+ratio. That explains why we have chosen this setting for the experiments
+presented in the previous subsections.
%As can be seen in Table~\ref{my-labelx}, it is obvious and clear that when $\alpha$ decreased and $\beta$ increased by any step, the network lifetime for $Lifetime_{50}$ increased and the $Lifetime_{95}$ decreased. Therefore, selecting the values of $\alpha$ and $\beta$ depend on the application type used in the sensor nework. In PeCO protocol, $\alpha$ and $\beta$ are chosen based on the largest value of network lifetime for $Lifetime_{95}$.
We plan to extend our framework so that the schedules are planned for multiple
sensing periods. We also want to improve the integer program to take into
account heterogeneous sensors from both energy and node characteristics point of
-views. Finally, it would be interesting to implement PeCO protocol using a
+views. Finally, it would be interesting to implement the PeCO protocol using a
sensor-testbed to evaluate it in real world applications.
-
-\subsection*{Acknowledgements}
+\subsection*{Acknowledgments}
The authors are deeply grateful to the anonymous reviewers for their
constructive advice, which improved the technical quality of the paper. As a
-Ph.D. student, Ali Kadhum IDREES would like to gratefully acknowledge the
+Ph.D. student, Ali Kadhum Idrees would like to gratefully acknowledge the
University of Babylon - Iraq for financial support and Campus France for the
received support. This work is also partially funded by the Labex ACTION program
-(contract ANR-11-LABX-01-01).
-
+(contract ANR-11-LABX-01-01).
+
\bibliographystyle{gENO}
\bibliography{biblio} %articleeo
