to ensure coverage at a low energy cost, allowing to optimize the network
lifetime. More precisely, a period consists of four phases: (i)~Information
Exchange, (ii)~Leader Election, (iii)~Decision, and (iv)~Sensing. The
- decision process, which result in an activity scheduling vector, is carried
+ decision process, which results in an activity scheduling vector, is carried
out by a leader node through the solving of an integer program. In comparison
with some other protocols, the simulations done using the discrete event
simulator OMNeT++ show that our approach is able to increase the WSN lifetime
\section{\uppercase{Introduction}}
\label{sec:introduction}
+
\noindent
Energy efficiency is a crucial issue in wireless sensor networks since sensory
-consumption, in order to maximize the network lifetime, represent the major
+consumption, in order to maximize the network lifetime, represents the major
difficulty when designing WSNs. As a consequence, one of the scientific research
challenges in WSNs, which has been addressed by a large amount of literature
during the last few years, is the design of energy efficient approaches for
coverage and connectivity~\cite{conti2014mobile}. Coverage reflects how well a
-sensor field is monitored. The most discussed coverage problems in literature
-can be classified into three types \cite{li2013survey}: area coverage (where
-every point inside an area is to be monitored), target coverage (where the main
-objective is to cover only a finite number of discrete points called targets),
-and barrier coverage (to prevent intruders from entering into the region of
-interest). On the one hand we want to monitor the area of interest in the most
-efficient way~\cite{Nayak04}. On the other hand we want to use as less energy as
-possible. Sensor nodes are battery-powered with no means of recharging or
-replacing, usually due to environmental (hostile or unpractical environments) or
-cost reasons. Therefore, it is desired that the WSNs are deployed with high
-densities so as to exploit the overlapping sensing regions of some sensor nodes
-to save energy by turning off some of them during the sensing phase to prolong
-the network lifetime.
+sensor field is monitored. On the one hand we want to monitor the area of
+interest in the most efficient way~\cite{Nayak04}. On the other hand we want to
+use as less energy as possible. Sensor nodes are battery-powered with no means
+of recharging or replacing, usually due to environmental (hostile or unpractical
+environments) or cost reasons. Therefore, it is desired that the WSNs are
+deployed with high densities so as to exploit the overlapping sensing regions of
+some sensor nodes to save energy by turning off some of them during the sensing
+phase to prolong the network lifetime.
In this paper we design a protocol that focuses on the area coverage problem
with the objective of maximizing the network lifetime. Our proposition, the
-DiLCO protocol, maintains the coverage and improves the lifetime in WSNs. The
-area of interest is first divided into subregions using a divide-and-conquer
-algorithm and an activity scheduling for sensor nodes is then planned by the
-elected leader in each subregion. In fact, the nodes in a subregion can be seen
-as a cluster where each node sends sensing data to the cluster head or the sink
-node. Furthermore, the activities in a subregion/cluster can continue even if
-another cluster stops due to too many node failures. Our Distributed Lifetime
-Coverage Optimization (DILCO) protocol considers periods, where a period starts
-with a discovery phase to exchange information between sensors of a same
+Distributed Lifetime Coverage Optimization (DILCO) protocol, maintains the
+coverage and improves the lifetime in WSNs. The area of interest is first
+divided into subregions using a divide-and-conquer algorithm and an activity
+scheduling for sensor nodes is then planned by the elected leader in each
+subregion. In fact, the nodes in a subregion can be seen as a cluster where each
+node sends sensing data to the cluster head or the sink node. Furthermore, the
+activities in a subregion/cluster can continue even if another cluster stops due
+to too many node failures. Our DiLCO protocol considers periods, where a period
+starts with a discovery phase to exchange information between sensors of a same
subregion, in order to choose in a suitable manner a sensor node (the leader) to
carry out the coverage strategy. In each subregion the activation of the sensors
for the sensing phase of the current period is obtained by solving an integer
-program.
+program. The resulting activation vector is broadcasted by a leader to every
+node of its subregion.
The remainder of the paper continues with Section~\ref{sec:Literature Review}
where a review of some related works is presented. The next section describes
\section{\uppercase{Literature Review}}
\label{sec:Literature Review}
-\noindent In this section, we summarize some related works regarding coverage lifetime maximization and scheduling, and distinguish our DiLCO protocol from the works presented in the literature. Some algorithms have been developed in ~\cite{yang2014energy,ChinhVu,vashistha2007energy,deschinkel2012column,shi2009,qu2013distributed,ling2009energy,xin2009area,cheng2014achieving,ling2009energy} to solve the area coverage problem so as to preserve coverage and prolong the network lifetime.
+
+\noindent In this section, we summarize some related works regarding coverage
+problem and distinguish our DiLCO protocol from the works presented in the
+literature.
+
+The most discussed coverage problems in literature
+can be classified into three types \cite{li2013survey}: area coverage (where
+every point inside an area is to be monitored), target coverage (where the main
+objective is to cover only a finite number of discrete points called targets),
+and barrier coverage (to prevent intruders from entering into the region of
+interest).
+{\it In DiLCO protocol, the area coverage, i.e. the coverage of every point in
+ the sensing region, is transformed to the coverage of a fraction of points
+ called primary points. }
+
+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) where each set completely covers a region of interest and to
+activate these set covers successively. 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 is decided at the beginning of each period.
+Active node selection is determined based on the problem requirements (e.g. area
+monitoring, connectivity, power efficiency). Different methods have been
+proposed in literature.
+{\it DiLCO protocol works in periods, where each period contains a preliminary
+ phase for information exchange and decisions, followed by a sensing phase
+ where one cover set is in charge of the sensing task.}
+
+Various approaches, including centralized, distributed, and localized
+algorithms, have been proposed to extend the network lifetime.
+%For instance, in order to hide the occurrence of faults, or the sudden unavailability of
+%sensor nodes, some distributed algorithms have been developed in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02}.
+In distributed algorithms~\cite{yangnovel,ChinhVu,qu2013distributed},
+information is disseminated throughout the network and sensors decide
+cooperatively by communicating with their neighbors which of them will remain in
+sleep mode for a certain period of time. The centralized
+algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high} always
+provide nearly or close to optimal solution since the algorithm has global view
+of the whole network, but such a method has the disadvantage of requiring high
+communication costs, since the node (located at the base station) making the
+decision needs information from all the sensor nodes in the area.
+
+A large variety of coverage scheduling algorithms have been proposed. Many of
+the existing algorithms, dealing with the maximization of the number of cover
+sets, are heuristics. These heuristics involve the construction of a cover set
+by including in priority the sensor nodes which cover critical targets, that is
+to say targets that are covered by the smallest number of sensors. Other
+approaches are based on mathematical programming formulations and dedicated
+techniques (solving with a branch-and-bound algorithms available in optimization
+solver). The problem is formulated as an optimization problem (maximization of
+the lifetime or number of cover sets) under target coverage and energy
+constraints. Column generation techniques, well-known and widely practiced
+techniques for solving linear programs with too many variables, have been also
+used~\cite{castano2013column,rossi2012exact,deschinkel2012column}.
+
+Diongue and Thiare~\cite{diongue2013alarm} proposed an energy aware sleep
+scheduling algorithm for lifetime maximization in wireless sensor networks
+(ALARM). The proposed approach permits to schedule redundant nodes according to
+the weibull distribution. This work did not analyze the ALARM scheme under the
+coverage problem.
+
+Shi et al.~\cite{shi2009} modeled the Area Coverage Problem (ACP), which will be
+changed into a set coverage problem. By using this model, they proposed an
+Energy-Efficient central-Scheduling greedy algorithm, which can reduces energy
+consumption and increases network lifetime, by selecting a appropriate subset of
+sensor nodes to support the networks periodically.
+
+In ~\cite{chenait2013distributed}, the authors presented a coverage-guaranteed
+distributed sleep/wake scheduling scheme so ass to prolong network lifetime
+while guaranteeing network coverage. This scheme mitigates scheduling process to
+be more stable by avoiding useless transitions between states without affecting
+the coverage level required by the application.
+
+The work in~\cite{cheng2014achieving} presented a unified sensing architecture
+for duty cycled sensor networks, called uSense, which comprises three ideas:
+Asymmetric Architecture, Generic Switching and Global Scheduling. The objective
+is to provide a flexible and efficient coverage in sensor networks.
+
+In~\cite{ling2009energy}, the lifetime of a sensor node is divided into
+epochs. At each epoch, the base station deduces the current sensing coverage
+requirement from application or user request. It then applies the heuristic
+algorithm in order to produce the set of active nodes which take the mission of
+sensing during the current epoch. After that, the produced schedule is sent to
+the sensor nodes in the network.
+
+{\it In DiLCO protocol, the area coverage is divided into several smaller
+ subregions, and in each of which, a node called the leader is on charge for
+ selecting the active sensors for the current period.}
+
+Yang et al.~\cite{yang2014energy} investigated full area coverage problem under
+the probabilistic sensing model in the sensor networks. They have studied the
+relationship between the coverage of two adjacent points mathematically and then
+convert the problem of full area coverage into point coverage problem. They
+proposed $\varepsilon$-full area coverage optimization (FCO) algorithm to select
+a subset of sensors to provide probabilistic area coverage dynamically so as to
+extend the network lifetime.
+
+The work proposed by \cite{qu2013distributed} considers the coverage problem in
+WSNs where each sensor has variable sensing radius. The final objective is to
+maximize the network coverage lifetime in WSNs.
+
+{\it In DiLCO protocol, each leader, in each subregion, solves an integer
+ program with a double objective consisting in minimizing the overcoverage and
+ limiting the undercoverage. This program is inspired from the work of
+ \cite{pedraza2006} where the objective is to maximize the number of cover
+ sets.}
+
+\iffalse
+
+Some algorithms have been developed in ~\cite{yang2014energy,ChinhVu,vashistha2007energy,deschinkel2012column,shi2009,qu2013distributed,ling2009energy,xin2009area,cheng2014achieving,ling2009energy} to solve the area coverage problem so as to preserve coverage and prolong the network lifetime.
Yang et al.~\cite{yang2014energy} investigated full area coverage problem
a sensor node is divided into epochs. At each epoch, the
base station deduces the current sensing coverage requirement
from application or user request. It then applies the heuristic algorithm in order to produce the set of active nodes which take the mission of sensing during the current epoch. After that, the produced schedule is sent to the sensor nodes in the network.
-
+\fi
\iffalse
achieve increased sensing lifetime of the network.
-\fi
+
The main contributions of our DiLCO Protocol can be summarized as follows:
(1) The distributed optimization over the subregions in the area of interest,
-(2) The distributed dynamic leader election at each round by each sensor node in the subregion,
+(2) The distributed dynamic leader election at each period by each sensor node in the subregion,
(3) The primary point coverage model to represent each sensor node in the network,
(4) The activity scheduling based optimization on the subregion, which are based on the primary point coverage model to activate as less number as possible of sensor nodes to take the mission of the coverage in each subregion, and (5) The improved energy consumption model.
-
+\fi
\iffalse
The work presented in~\cite{luo2014parameterized,tian2014distributed} tries to solve the target coverage problem so as to extend the network lifetime since it is easy to verify the coverage status of discreet target.
%Je ne comprends pas la phrase ci-dessus
The work presented in ~\cite{Zhang} focuses on a distributed clustering method, which aims to extend the network lifetime, while the coverage is ensured.
The work proposed by \cite{qu2013distributed} considers the coverage problem in WSNs where each sensor has variable sensing radius. The final objective is to maximize the network coverage lifetime in WSNs.
-\fi
-\iffalse
+
+
Casta{\~n}o et al.~\cite{castano2013column} proposed a multilevel approach based on column generation (CG) to extend the network lifetime with connectivity and coverage constraints. They are included two heuristic methods within the CG framework so as to accelerate the solution process.
In \cite{diongue2013alarm}, diongue is proposed an energy Aware sLeep scheduling AlgoRithm for lifetime maximization in WSNs (ALARM) algorithm for coverage lifetime maximization in wireless sensor networks. ALARM is sensor node scheduling approach for lifetime maximization in WSNs in which it schedule redundant nodes according to the weibull distribution taking into consideration frequent nodes failure.
Yu et al.~\cite{yu2013cwsc} presented a connected k-coverage working sets construction
\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
\end{array} \right.
\label{eq13}
\end{equation}
-\noindent More precisely, $\Theta_{p}$ represents the number of active
-sensor nodes minus one that cover the primary point $p$.\\
-The Undercoverage variable $U_{p}$ of the primary point $p$ is defined
-by:
+\noindent More precisely, $\Theta_{p}$ represents the number of active sensor
+nodes minus one that cover the primary point~$p$. The Undercoverage variable
+$U_{p}$ of the primary point $p$ is defined by:
\begin{equation}
U_{p} = \left \{
\begin{array}{l l}
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 $0.2575 mW$.
+24~bits. The energy required to send or receive a 1-bit-content message is thus
+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
+interval $[500-700]$. If it's energy provision reaches a value below the
+threshold $E_{th}=36$~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 corresponds to the energy needed by the sensing phase, obtained by
+multiplying the energy consumed in active state (9.72 mW) by 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 rounds.
+
+In the simulations, we introduce the follow80ing performance metrics to evaluate
the efficiency of our approach:
%\begin{enumerate}[i)]
\begin{itemize}
+\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 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
\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).
+
\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
-possible execution time. The energy of a sensor node must be mainly
-used for the sensing phase, not for the pre-sensing ones.
+\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 possible execution time. The energy of a sensor node must be mainly
+ used for the sensing phase, not for the pre-sensing ones.
-\item {{\bf Stopped simulation runs}:} A simulation
-ends when the sensor network becomes
-disconnected (some nodes are dead and are not able to send information to the base station). We report the number of simulations that are stopped due to network disconnections and for which round it occurs.
+\item {{\bf Stopped simulation runs}:} A simulation ends when the sensor network
+ becomes disconnected (some nodes are dead and are not able to send information
+ to the base station). We report the number of simulations that are stopped due
+ to network disconnections and for which round it occurs.
\fi
%\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
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.
+fast decrease with the number of periods and reaches zero value in period~18
+(respectively 46), 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
\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.
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