\fi
-\section{ The DiLCO Protocol Description}
+\section{\uppercase{Description of the DiLCO protocol}}
\label{sec:The DiLCO Protocol Description}
\noindent In this section, we introduce the DiLCO protocol which is distributed
consumptions into account to evaluate the performance of our protocol.
\fi
-\subsection{ Assumptions and models}
+\subsection{Assumptions and models}
\noindent We consider a sensor network composed of static nodes distributed
independently and uniformly at random. A high density deployment ensures a high
\fi
\subsection{The main idea}
+\label{main_idea}
\noindent We start by applying a divide-and-conquer algorithm to partition the
area of interest into smaller areas called subregions and then our protocol is
Decision) are energy consuming for all the nodes, even nodes that will not be
retained by the leader to keep watch over the corresponding area.
-During the excution of the DiLCO protocol, two kinds of packets will be used:
+During the execution of the DiLCO protocol, two kinds of packets will be used:
%\begin{enumerate}[(a)]
\begin{itemize}
\item INFO packet: sent by each sensor node to all the nodes inside a same
\subsubsection{Information Exchange Phase}
Each sensor node $j$ sends its position, remaining energy $RE_j$, and
-the number of neighbours $NBR_j$ to all wireless sensor nodes in
+the number of neighbors $NBR_j$ to all wireless sensor nodes in
its subregion by using an INFO packet and then listens to the packets
sent from other nodes. After that, each node will have information
about all the sensor nodes in the subregion. In our model, the
select WSNL. The nodes in the same subregion will select the leader
based on the received information from all other nodes in the same
subregion. The selection criteria in order of priority are: larger
-number of neighbours, larger remaining energy, and then in case of
+number of neighbors, larger remaining energy, and then in case of
equality, larger index.
\subsubsection{Decision phase}
\subsubsection{Sensing phase}
-Active sensors in the round will execute their sensing task to
-preserve maximal coverage in the region of interest. We will assume
-that the cost of keeping a node awake (or asleep) for sensing task is
-the same for all wireless sensor nodes in the network. Each sensor
-will receive an Active-Sleep packet from WSNL informing it to stay
-awake or to go to sleep for a time equal to the period of sensing until
-starting a new round. Algorithm 1, which
-will be executed by each node at the beginning of a round, explains how the
-Active-Sleep packet is obtained.
+
+Active sensors in the round will execute their sensing task to preserve maximal
+coverage in the region of interest. We will assume that the cost of keeping a
+node awake (or asleep) for sensing task is the same for all wireless sensor
+nodes in the network. Each sensor will receive an Active-Sleep packet from WSNL
+informing it to stay awake or to go to sleep for a time equal to the period of
+sensing until starting a new round. Algorithm 1, which will be executed by each
+node at the beginning of a round, explains how the Active-Sleep packet is
+obtained.
\fi
\fi
-\section{Coverage problem formulation}
+\section{\uppercase{Coverage problem formulation}}
\label{cp}
\indent Our model is based on the model proposed by \cite{pedraza2006} where the
and based on ~\cite{raghunathan2002energy} with slight modifications. The energy
consumed by the communications is added and the part relative to a variable
sensing range is removed. We also assume that the nodes have the characteristics
-of the Medusa II sensor node platform \cite{raghunathan2002energy}. A sensor
+of the Medusa II sensor node platform \cite{raghunathan2002energy}. A sensor
node typically consists of four units: a MicroController Unit, an Atmels AVR
ATmega103L in case of Medusa II, to perform the computations; a communication
-(adio) unit able to send and receive messages; a sensing unit to collect data; a
-power supply which provides the energy consumed by node. Except the battery, all
-the other unit can be be switched off to save energy according to the node
-status. Table~\ref{table4} summarizes the energy consumed (in milliWatt per
+(radio) unit able to send and receive messages; a sensing unit to collect data;
+a power supply which provides the energy consumed by node. Except the battery,
+all the other unit can be be switched off to save energy according to the node
+status. Table~\ref{table4} summarizes the energy consumed (in milliWatt per
second) by a node for each of its possible status.
\begin{table}[ht]
% is used to refer this table in the text
\end{table}
-% MICHEL - TO BE CONTINUED
-
-For the sake of simplicity we ignore the energy needed to turn on the radio, to
-start up the sensor node, the transition from one status to another, etc.
-%We also do not consider the need of collecting sensing data. PAS COMPRIS
-Thus, when a sensor becomes active (i.e., it already decides its status), it can
-turn its radio off to save battery. DiLCO protocol uses two types of packets for
-communication. The size of the INFO-Packet and Status-Packet are 112 bits and 24
-bits respectively. The value of energy spent to send a 1-bit-content message is
-obtained by using the equation in ~\cite{raghunathan2002energy} to calculate the
-energy cost for transmitting messages and we propose the same value for
-receiving the packets. The energy needed to send or receive a 1-bit is equal to
-$0.2575 mW$.
-
-The initial energy of each node is randomly set in the interval $[500-700]$.
-Each sensor node will not participate in the next round if its remaining energy
-is less than $E_{th}=36 Joules$, the minimum energy needed for the node to stay
-alive during one round. This value has been computed by multiplying the energy
-consumed in active state (9.72 mW) by the time in second for one round (3600
-seconds). According to the interval of initial energy, a sensor may be alive
-during at most 20 rounds.\\
+Less influent energy consumption sources like when turning on the radio,
+starting the sensor node, changing the status of a node, etc., will be neglected
+for the sake of simplicity. Each node saves energy by switching off its radio
+once it has received its decision status from the corresponding leader (it can
+be itself). As explained previously in subsection~\ref{main_idea}, two kinds of
+packets for communication are considered in our protocol: INFO packet and
+ActiveSleep packet. To compute the energy needed by a node to transmit or
+receive such packets, we use the equation giving the energy spent to send a
+1-bit-content message defined in~\cite{raghunathan2002energy} (we assume
+symmetric communication costs), and we set their respective size to 112 and
+24~bits. The energy required to send or receive a 1-bit is equal to $0.2575 mW$.
+
+Each node has an initial energy level, in Joules, which is randomly drawn in the
+interval $[500-700]$. If it's energy provision reaches a value below
+$E_{th}=36$~Joules, the minimum energy needed for a node to stay active during
+one period, it will no more participate in the coverage task. This value has
+been computed by multiplying the energy consumed in active state (9.72 mW) by
+the time in second for one round (3600 seconds). According to the interval of
+initial energy, a sensor may be active during at most 20 rounds.
In the simulations, we introduce the following performance metrics to evaluate
the efficiency of our approach:
%\begin{enumerate}[i)]
\begin{itemize}
-\item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much the area of a sensor field is covered. In our case, we treated the sensing fields as a grid, and used each grid point as a sample point
-for calculating the coverage. The coverage ratio can be calculated by:
+\item {{\bf Coverage Ratio (CR)}:} it measures how well the WSN is able to
+ observe the area of interest. In our case, we discretized the sensor field
+ as a regular grid, which yields the following equation to compute the
+ coverage ratio:
\begin{equation*}
\scriptsize
\mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100.
\end{equation*}
-where $n$ is the number of covered grid points by the active sensors of all subregions during the current sensing phase and $N$ is total number of grid points in the sensing field of the network. In our simulation $N = 51 \times 26 = 1326$ grid points.
+where $n$ is the number of covered grid points by active sensors of every
+subregions during the current sensing phase and $N$ is total number of grid
+points in the sensing field. In our simulations, we have a layout of $N = 51
+\times 26 = 1326$ grid points.
%The accuracy of this method depends on the distance between grids. In our
%simulations, the sensing field has been divided into 50 by 25 grid points, which means
%there are $51 \times 26~ = ~ 1326$ points in total.
\fi
-\item {{\bf Network Lifetime}:} we define the network lifetime as the time until the coverage ratio drops below a predefined threshold. We denoted by $Lifetime95$ (respectively $Lifetime50$) as the amount of time during which the network can satisfy an area coverage greater than $95\%$ (repectively $50\%$). We assume that the network
-is alive until all nodes have been drained of their energy or the
-sensor network becomes disconnected . Network connectivity is important because an
-active sensor node without connectivity towards a base station cannot
-transmit information on an event in the area that it monitors.
-
-
-\item {{\bf Energy Consumption}:}
-
- Energy Consumption (EC) can be seen as the total energy consumed by the sensors during the $Lifetime95$ or $Lifetime50$ divided by the number of periods. The EC can be computed as follow: \\
- \begin{equation*}
-\scriptsize
-\mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m + E^{a}+E^{s} \right)}{M_L},
-\end{equation*}
-
-%\begin{equation*}
-%\scriptsize
-%\mbox{EC} = \frac{\mbox{$\sum\limits_{d=1}^D E^c_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D %E^l_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D E^a_d$}}{\mbox{$D$}} + %\frac{\mbox{$\sum\limits_{d=1}^D E^s_d$}}{\mbox{$D$}}.
-%\end{equation*}
-
-where $M$ corresponds to the number of periods. The total energy consumed by the sensors
-(EC) comes through taking into consideration four main energy factors. The first
-one , denoted $E^{\scriptsize \mbox{com}}_m$, represent the energy consumption
-spent by all the nodes for wireless communications during period $m$.
-$E^{\scriptsize \mbox{list}}_m$, the next factor, corresponds to the energy
-consumed by the sensors in LISTENING status before receiving the decision to go
-active or sleep in period $m$. $E^{\scriptsize \mbox{comp}}_m$ refers to the
-energy needed by all the leader nodes to solve the integer program during a
-period. Finally, $E^a_{m}$ and $E^s_{m}$ indicate the energy consumed by the whole network in the sensing round.
+\item {{\bf Energy Consumption}:} energy consumption (EC) can be seen as the
+ total energy consumed by the sensors during $Lifetime_{95}$ or
+ $Lifetime_{50}$, divided by the number of periods. Formally, the computation
+ of EC can be expressed as follows:
+ \begin{equation*}
+ \scriptsize
+ \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m
+ + E^{a}_m+E^{s}_m \right)}{M},
+ \end{equation*}
+
+where $M$ corresponds to the number of periods. The total energy consumed by
+the sensors (EC) comes through taking into consideration four main energy
+factors. The first one , denoted $E^{\scriptsize \mbox{com}}_m$, represent the
+energy consumption spent by all the nodes for wireless communications during
+period $m$. $E^{\scriptsize \mbox{list}}_m$, the next factor, corresponds to
+the energy consumed by the sensors in LISTENING status before receiving the
+decision to go active or sleep in period $m$. $E^{\scriptsize \mbox{comp}}_m$
+refers to the energy needed by all the leader nodes to solve the integer program
+during a period. Finally, $E^a_{m}$ and $E^s_{m}$ indicate the energy consumed
+by the whole network in the sensing phase (active and sleeping nodes).
+
+\item {{\bf Network Lifetime}:} we define the network lifetime as the time until
+ the coverage ratio drops below a predefined threshold. We denote by
+ $Lifetime_{95}$ (respectively $Lifetime_{50}$) the amount of time during which
+ the network can satisfy an area coverage greater than $95\%$ (respectively
+ $50\%$). We assume that the sensor network can fulfill its task until all its
+ nodes have been drained of their energy or it becomes disconnected. Network
+ connectivity is crucial because an active sensor node without connectivity
+ towards a base station cannot transmit any information regarding an observed
+ event in the area that it monitors.
\iffalse
\item {{\bf Execution Time}:} a sensor node has limited energy resources and computing power,
%\end{enumerate}
-%\subsection{Performance Analysis for differnet subregions}
-\subsection{Performance Analysis}
+%\subsection{Performance Analysis for different subregions}
+\subsection{Performance analysis}
\label{sub1}
-We first concentrate on the required number of subregions making effective our
-protocol. Thus our DiLCO protocol is declined into five versions: DiLCO-2,
-DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32, corresponding to $2$, $4$, $8$, $16$
-or $32$ subregions (leaders).
+In this subsection, we first focus on the performance of our DiLCO protocol for
+different numbers of subregions. We consider partitions of the WSN area into
+$2$, $4$, $8$, $16$, and $32$ subregions. Thus the DiLCO protocol is declined in
+five versions: DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32. Simulations
+without partitioning the area of interest, case which corresponds to a
+centralized approach, are not presented because they require high execution
+times to solve the integer program and therefore consume too much energy.
+
+We compare our protocol to two other approaches. The first one, called DESK and
+proposed by ~\cite{ChinhVu} is a fully distributed coverage algorithm. The
+second one, called GAF ~\cite{xu2001geography}, consists in dividing the region
+into fixed squares. During the decision phase, in each square, one sensor is
+chosen to remain active during the sensing phase.
+
+\subsubsection{Coverage ratio}
+
+Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes. It
+can be seen that both DESK and GAF provide a little better coverage ratio
+compared to DiLCO in the first thirty periods. This can be easily explained by
+the number of active nodes: the optimization process of our protocol activates
+less nodes than DESK or GAF, resulting in a slight decrease of the coverage
+ratio. In case of DiLCO-2 (respectively DiLCO-4), the coverage ratio exhibits a
+fast decrease with the number of periods and reaches zero value in period {\bf
+ X} (respectively {\bf Y}), whereas the other versions of DiLCO, DESK, and GAF
+ensure a coverage ratio above 50\% for subsequent periods. We believe that the
+results obtained with these two methods can be explained by a high consumption
+of energy and we will check this assumption in the next subsection.
+
+Concerning DiLCO-8, DiLCO-16, and DiLCO-32, these methods seem to be more
+efficient than DESK and GAF, since they can provide the same level of coverage
+(except in the first periods where DESK and GAF slightly outperform them) for a
+greater number of periods. In fact, when our protocol is applied with a large
+number of subregions (from 8 to 32~regions), it activates a restricted number of
+nodes, and thus allow to extend the network lifetime.
-In this subsection, we study the performance of our DiLCO protocol for different number of subregions (Leaders).
-The DiLCO-1 protocol is a centralized approach on all the area of the interest, while DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 are distributed on two, four, eight, sixteen, and thirty-two subregions respectively. We do not take into account the DiLC0-1 protocol in our simulation results because it requires high execution time to solve the integer program and thus it is too costly in term of energy.
-
-Our method is compared with other two approaches. The first approach, called DESK and proposed by ~\cite{ChinhVu} is a full distributed coverage algorithm. The second approach, called GAF ~\cite{xu2001geography}, consists in dividing the region into fixed squares. During the decision phase, in each square, one sensor is chosen to remain on during the sensing phase time.
-
-
-\subsubsection{Coverage Ratio}
-Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes.
\parskip 0pt
-\begin{figure}[h!]
+\begin{figure}[t!]
\centering
\includegraphics[scale=0.45] {R/CR.pdf}
-\caption{The Coverage Ratio}
+\caption{Coverage ratio}
\label{fig3}
\end{figure}
-Figure~\ref{fig3} shows that DESK and GAF provide a
-a little better coverage ratio compared to DiLCO in the first thirty periods. This is due to the fact that our DiLCO protocol versions put in sleep mode some sensors through optimization process (which slightly decreases the coverage ratio) while there are more active nodes with DESK or GAF. With DiLCO-2 (respectively DiLCO-4), the coverage ratio decreases rapidly to reach zero value in period ... (respectively in period ....) whereas other methods guarantee a coverage ratio greater than $50\%$ after this period. We believe that the results obtained with these two methods can be explained by a high consumption of energy
-and we will check this assumption in the next paragraph. Concerning DiLCO-8, DiLCO-16 and DiLCO-32, these methods seem to be more efficient than DESK and GAF because they can provide the same level of coverage (except in the first periods, slightly lower) for a greater number of periods. Unlike other methods, their strategy enables to activate a restricted number of nodes, and thus extends the lifetime of the network.
%As shown in the figure ~\ref{fig3}, as the number of subregions increases, the coverage preservation for area of interest increases for a larger number of periods. Coverage ratio decreases when the number of periods increases due to dead nodes. Although some nodes are dead,
%thanks to DiLCO-8, DiLCO-16 and DiLCO-32 protocols, other nodes are preserved to ensure the coverage. Moreover, when we have a dense sensor network, it leads to maintain the coverage for a larger number of rounds. DiLCO-8, DiLCO-16 and DiLCO-32 protocols are
%slightly more efficient than other protocols, because they subdivides
%the area of interest into 8, 16 and 32~subregions if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.%
+\subsubsection{Energy consumption}
+Based on the results shown in Figure~\ref{fig3}, we focus on the DiLCO-16 and
+DiLCO-32 versions of our protocol, and we compare their energy consumption with
+the DESK and GAF approaches. For each sensor node we measure the energy consumed
+according to its successive status, for different network densities. We denote
+by $\mbox{\it Protocol}/50$ (respectively $\mbox{\it Protocol}/95$) the amount
+of energy consumed while the area coverage is greater than $50\%$ (repectively
+$95\%$), where {\it Protocol} is one of the four protocols we compare.
+Figure~\ref{fig95} presents the energy consumptions observed for network sizes
+going from 50 to 250~nodes. Let us notice that the same network sizes will be
+used for the different performance metrics.
-\subsubsection{The Energy Consumption}
-Based on previous results in figure~\ref{fig3}, we keep DiLCO-16 and DiLCO-32 and we compare their performances in terms of energy consumption with the two other approaches. We measure the energy consumed by the sensors during the communication, listening, computation, active, and sleep modes for different network densities. Figure~\ref{fig95} illustrates the energy consumption for different network sizes.
-% for $Lifetime95$ and $Lifetime50$.
-We denote by $DiLCO-/50$ (respectively $DiLCO-/95$) as the amount of energy consumed during which the network can satisfy an area coverage greater than $50\%$ (repectively $95\%$) and we refer to the same definition for the two other approaches.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.45]{R/EC.pdf}
-\caption{The Energy Consumption}
+\caption{Energy consumption}
\label{fig95}
\end{figure}
-The results show that DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols are the most competitive from the energy consumption point of view. The other approaches have a high energy consumption due to activating a larger number of redundant nodes.
+The results depict the good performance of the different versions of our
+protocol. Indeed, the protocols DiLCO-16/50, DiLCO-32/50, DiLCO-16/95, and
+DiLCO-32/95 consume less energy than their DESK and GAF counterparts for a
+similar level of area coverage. This observation reflects the larger number of
+nodes set active by DESK and GAF.
%In fact, a distributed method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks.
%As shown in Figures~\ref{fig95} and ~\ref{fig50} , DiLCO-2 consumes more energy than the other versions of DiLCO, especially for large sizes of network. This is easy to understand since the bigger the number of sensors involved in the integer program, the larger the time computation to solve the optimization problem as well as the higher energy consumed during the communication.
+\subsubsection{Execution time}
-\subsubsection{Execution Time}
-We observe the impact of the network size and of the number of subregions on the computation time. We report the average execution times in seconds needed to solve the optimization problem for the different approaches and various numbers of sensors.
-The original execution time is computed on a laptop DELL with intel Core i3 2370 M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6 to run the optimization resolution, this time is multiplied by 2944.2 $\left( \frac{35330}{2} \times \frac{1}{6}\right)$ and reported on Figure~\ref{fig8}.
+Another interesting point to investigate is the evolution of the execution time
+with the size of the WSN and the number of subregions. Therefore, we report for
+every version of our protocol the average execution times in seconds needed to
+solve the optimization problem for different WSN sizes. The execution times are
+obtained on a laptop DELL which has an Intel Core~i3~2370~M~(2.4~GHz) dual core
+processor and a MIPS rating equal to 35330. The corresponding execution times on
+a MEDUSA II sensor node are then extrapolated according to the MIPS rate of the
+Atmels AVR ATmega103L microcontroller (6~MHz), which is equal to 6, by
+multiplying the laptop times by $\left(\frac{35330}{2} \times
+\frac{1}{6}\right)$. The expected times on a sensor node are reported on
+Figure~\ref{fig8}.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.45]{R/T.pdf}
-\caption{Execution Time (in seconds)}
+\caption{Execution time in seconds}
\label{fig8}
\end{figure}
-
-Figure~\ref{fig8} shows that DiLCO-32 has very low execution times in comparison with other DiLCO versions, because the activity scheduling is tackled by a larger number of leaders and each leader solves an integer problem with a limited number of variables and constraints. Conversely, DiLCO-2 requires to solve an optimization problem with half of the network nodes and thus presents a high execution time. Nevertheless if we refer to figure~\ref{fig3}, we observe that DiLCO-32 is slightly less efficient than DilCO-16 to maintain as long as possible high coverage. Excessive subdivision of the area of interest prevents to ensure good coverage especially on the borders of the subregions.
+Figure~\ref{fig8} shows that DiLCO-32 has very low execution times in comparison
+with other DiLCO versions, because the activity scheduling is tackled by a
+larger number of leaders and each leader solves an integer problem with a
+limited number of variables and constraints. Conversely, DiLCO-2 requires to
+solve an optimization problem with half of the network nodes and thus presents a
+high execution time. Nevertheless if we refer to Figure~\ref{fig3}, we observe
+that DiLCO-32 is slightly less efficient than DilCO-16 to maintain as long as
+possible high coverage. In fact excessive subdivision of the area of interest
+prevents to ensure good coverage especially on the borders of the
+subregions. Thus, the optimal number of subregions can be seen as a trade-off
+between execution time and coverage performance.
%The DiLCO-32 has more suitable times in the same time it turn on redundent nodes more. We think that in distributed fashion the solving of the optimization problem in a subregion can be tackled by sensor nodes. Overall, to be able to deal with very large networks, a distributed method is clearly required.
+\subsubsection{Network lifetime}
-\subsubsection{The Network Lifetime}
-In figure~\ref{figLT95}, network lifetime is illustrated for different network sizes. The term $/50$ (respectively $/95$) next to the name of the method refers to the amount of time during which the network can satisfy an area coverage greater than $50\%$ ($Lifetime50$)(repectively $95\%$ ($Lifetime95$))
+In the next figure, the network lifetime is illustrated. Obviously, the lifetime
+increases with the network size, whatever the considered protocol, since the
+correlated node density also increases. A high network density means a high
+node redundancy which allows to turn-off many nodes and thus to prolong the
+network lifetime.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.45]{R/LT.pdf}
-\caption{The Network Lifetime}
+\caption{Network lifetime}
\label{figLT95}
\end{figure}
-
-As highlighted by figure~\ref{figLT95}, the network lifetime obviously
-increases when the size of the network increases. For the same level of coverage, DiLCO outperforms DESK and GAF for the lifetime of the network. If we focus on level of coverage greater than $95\%$, The subdivision in $16$ subregions seems to be the most appropriate.
-
+As highlighted by Figure~\ref{figLT95}, when the coverage level is relaxed
+($50\%$) the network lifetime also improves. This observation reflects the fact
+that the higher the coverage performance, the more nodes must be active to
+ensure the wider monitoring. For a same level of coverage, DiLCO outperforms
+DESK and GAF for the lifetime of the network. More specifically, if we focus on
+the larger level of coverage ($95\%$) in case of our protocol, the subdivision
+in $16$~subregions seems to be the most appropriate.
% with our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols
% that leads to the larger lifetime improvement in comparison with other approaches. By choosing the best
% letting the other ones sleep in order to be used later in next rounds. Comparison shows that our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols, which are used distributed optimization over the subregions, are the best one because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. It also means that distributing the protocol in each node and subdividing the sensing field into many subregions, which are managed
% independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
+\section{\uppercase{Conclusion and future work}}
+\label{sec:Conclusion and Future Works}
+
+A crucial problem in WSN is to schedule the sensing activities of the different
+nodes in order to ensure both coverage of the area of interest and longest
+network lifetime. The inherent limitations of sensor nodes, in energy provision,
+communication and computing capacities, require protocols that optimize the use
+of the available resources to fulfill the sensing task. To address this
+problem, this paper proposes a two-step approach. Firstly, the field of sensing
+is divided into smaller subregions using the concept of divide-and-conquer
+method. Secondly, a distributed protocol called Distributed Lifetime Coverage
+Optimization is applied in each subregion to optimize the coverage and lifetime
+performances. In a subregion, our protocol consists to elect a leader node
+which will then perform a sensor activity scheduling. The challenges include how
+to select the most efficient leader in each subregion and the best
+representative set of active nodes to ensure a high level of coverage. To assess
+the performance of our approach, we compared it with two other approaches using
+many performance metrics like coverage ratio or network lifetime. We have also
+study the impact of the number of subregions chosen to subdivide the area of
+interest, considering different network sizes. The experiments show that
+increasing the number of subregions allows to improves the lifetime. The more
+there are subregions, the more the network is robust against random
+disconnection resulting from dead nodes. However, for a given sensing field and
+network size there is an optimal number of subregions. Therefore, in case of
+our simulation context a subdivision in $16$~subregions seems to be the most
+relevant. The optimal number of subregions will be investigated in the future.
-
-
-\section{\uppercase{Conclusion and Future Works}}
-\label{sec:Conclusion and Future Works}
-In this paper, we have addressed the problem of the coverage and the lifetime
-optimization in wireless sensor networks. This is a key issue as
-sensor nodes have limited resources in terms of memory, energy and
-computational power. To cope with this problem, the field of sensing
-is divided into smaller subregions using the concept of divide-and-conquer method, and then a DiLCO protocol for optimizing the coverage and lifetime performances in each subregion.
-The proposed protocol combines two efficient techniques: network
-leader election and sensor activity scheduling, where the challenges
-include how to select the most efficient leader in each subregion and
-the best representative set of active nodes to ensure a high level of coverage.
-We have compared this method with two other approaches using many metrics as coverage ratio, execution time, lifetime.
-Some experiments have been performed to study the choice of the number of
-subregions which subdivide the sensing field, considering different network
-sizes. They show that as the number of subregions increases, so does the network
-lifetime. Moreover, it makes the DiLCO protocol more robust against random
-network disconnection due to node failures. However, too much subdivisions
-reduces the advantage of the optimization. In fact, there is a balance between
-the benefit from the optimization and the execution time needed to solve
-it. Therefore, the subdivision in $16$ subregions seems to be the most appropriate.
\iffalse
\noindent In this paper, we have addressed the problem of the coverage and the lifetime
optimization in wireless sensor networks. This is a key issue as
The computation of all cover sets in one time is far more
difficult, but will reduce the communication overhead. \fi
\fi
-\section*{\uppercase{Acknowledgements}}
-\noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully acknowledge the University of Babylon - IRAQ for the financial support and Campus France for the received support.
-
-
+\section*{\uppercase{Acknowledgements}}
+\noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully
+acknowledge the University of Babylon - IRAQ for the financial support and
+Campus France for the received support.
%\vfill
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\bibliography{Example}}
-
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