\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
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}
\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
\fi
-\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.
-
-\item {{\bf Energy Consumption}:} Energy Consumption (EC) can be seen as the
+\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*}
-
-%\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*}
+ \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
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,
therefore it is important that the proposed algorithm has the shortest
%\subsection{Performance Analysis for different subregions}
-\subsection{Performance Analysis}
+\subsection{Performance analysis}
\label{sub1}
In this subsection, we first focus on the performance of our DiLCO protocol for
into fixed squares. During the decision phase, in each square, one sensor is
chosen to remain active during the sensing phase.
-\subsubsection{Coverage Ratio}
+\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
\begin{figure}[t!]
\centering
\includegraphics[scale=0.45] {R/CR.pdf}
-\caption{The Coverage Ratio}
+\caption{Coverage ratio}
\label{fig3}
\end{figure}
%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}
-
-% MICHEL - TO BE CONTINUED
-
-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.
+\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.
+
\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}
-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}.
+\subsubsection{Execution time}
+
+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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