\section{\uppercase{Introduction}}
\label{sec:introduction}
\noindent
-Energy efficiency is a crucial issue in wireless sensor networks since sensor
-nodes drain their energy from batteries. In fact, strong constraints on energy
+Energy efficiency is a crucial issue in wireless sensor networks since sensory
consumption, in order to maximize the network lifetime, represent 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
+coverage and connectivity~\cite{conti2014mobile}. Coverage reflects how well a
+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. % TO BE CONTINUED
-Sensor nodes runs on batteries with limited capacities~\cite{Sudip03}
-and it is impossible, difficult or expensive to recharge and/or replace
-batteries in remote, hostile, or unpractical environments. 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 concentrate on the area coverage problem with the objective of
-maximizing the network lifetime by using DiLCO protocol to maintain the coverage
-and to improve the lifetime in WSNs. The area of interest is divided into
-subregions using divide-and-conquer method and an activity scheduling for sensor
-nodes is 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 the subregion, in
-order to choose in a suitable manner a sensor node (the leader) to carry out the
-coverage strategy. Our DiLCO protocol involves solving an integer program,
-which provides the activation of the sensors for the sensing phase of the
-current period.
+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
+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.
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
the DiLCO protocol, followed in Section~\ref{cp} by the coverage model
formulation which is used to schedule the activation of
sensors. Section~\ref{sec:Simulation Results and Analysis} shows the simulation
-results. The paper ends with conclusions and some suggestions for futher work in
-Section~\ref{sec:Conclusion and Future Works}.
+results. The paper ends with conclusions and some suggestions for further work
+in Section~\ref{sec:Conclusion and Future Works}.
\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, ie 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 an interest region 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 has been proposed in literature.
+
+{\it DiLCO protocol works in periods, 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 centralised, 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 neighbours 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 in the literature. Many of the existing algorithms, dealing with the maximisation 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, of the 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 are 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 as 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 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.
+
+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 a Distributed Lifetime Coverage Optimization protocol, which is called DiLCO. It is distributed on each subregion in the area of interest. It is based on two efficient techniques: network leader election and sensor activity scheduling for coverage preservation and energy conservation continuously and efficiently to maximize the lifetime in the network.
-\iffalse The main features of our DiLCO protocol:
-i)It divides the area of interest into subregions by using divide-and-conquer concept, ii)It requires only the information of the nodes within the subregion, iii) it divides the network lifetime into rounds, iv)It based on the autonomous distributed decision by the nodes in the subregion to elect the Leader, v)It apply the activity scheduling based optimization on the subregion, vi) it achieves an energy consumption balancing among the nodes in the subregion by selecting different nodes as a leader during the network lifetime, vii) It uses the optimization to select the best representative set of sensors in the subregion by optimize the coverage and the lifetime over the area of interest, viii)It uses our proposed primary point coverage model, which represent the sensing range of the sensor as a set of points, which are used by the our optimization algorithm, ix) It uses a simple energy model that takes communication, sensing and computation energy consumptions into account to evaluate the performance of our protocol.
+\noindent In this section, we introduce the DiLCO protocol which is distributed
+on each subregion in the area of interest. It is based on two efficient
+techniques: network leader election and sensor activity scheduling for coverage
+preservation and energy conservation, applied periodically to efficiently
+maximize the lifetime in the network.
+\iffalse The main features of our DiLCO protocol: i)It divides the area of
+interest into subregions by using divide-and-conquer concept, ii)It requires
+only the information of the nodes within the subregion, iii) it divides the
+network lifetime into rounds, iv)It based on the autonomous distributed decision
+by the nodes in the subregion to elect the Leader, v)It apply the activity
+scheduling based optimization on the subregion, vi) it achieves an energy
+consumption balancing among the nodes in the subregion by selecting different
+nodes as a leader during the network lifetime, vii) It uses the optimization to
+select the best representative set of sensors in the subregion by optimize the
+coverage and the lifetime over the area of interest, viii)It uses our proposed
+primary point coverage model, which represent the sensing range of the sensor as
+a set of points, which are used by the our optimization algorithm, ix) It uses a
+simple energy model that takes communication, sensing and computation energy
+consumptions into account to evaluate the performance of our protocol.
\fi
-\subsection{ Assumptions and Models}
-\noindent We consider a randomly and uniformly deployed network consisting of
-static wireless sensors. The wireless sensors are deployed in high
-density to ensure initially a high coverage ratio of the interested area. We
-assume that all nodes are homogeneous in terms of communication and
-processing capabilities and heterogeneous in term of energy provision.
-The location information is available to the sensor node either
-through hardware such as embedded GPS or through location discovery
-algorithms. We consider a boolean disk coverage model which is the most
-widely used sensor coverage model in the literature. Each sensor has a
-constant sensing range $R_s$. All space points within a disk centered
-at the sensor with the radius of the sensing range is said to be
-covered by this sensor. We also assume that the communication range $R_c \geq 2R_s$.
-In fact, Zhang and Zhou~\cite{Zhang05} proved that if the transmission range fulfills the
-previous hypothesis, a complete coverage of a convex area implies
-connectivity among the working nodes in the active mode.
-
-\indent Instead of working with the coverage area, we consider for each
-sensor a set of points called primary points~\cite{idrees2014coverage}. We also assume that the
-sensing disk defined by a sensor is covered if all the primary points of
-this sensor are covered.
+
+\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
+coverage ratio of the interested area at the starting. The nodes are supposed to
+have homogeneous characteristics from a communication and a processing point of
+view, whereas they have heterogeneous energy provisions. Each node has access
+to its location thanks, either to a hardware component (like a GPS unit), or a
+location discovery algorithm.
+
+\indent We consider a boolean disk coverage model which is the most widely used
+sensor coverage model in the literature. Thus, since a sensor has a constant
+sensing range $R_s$, every space points within a disk centered at a sensor with
+the radius of the sensing range is said to be covered by this sensor. We also
+assume that the communication range $R_c \geq 2R_s$. In fact, Zhang and
+Zhou~\cite{Zhang05} proved that if the transmission range fulfills the previous
+hypothesis, a complete coverage of a convex area implies connectivity among the
+working nodes in the active mode.
+
+\indent For each sensor we also define a set of points called primary
+points~\cite{idrees2014coverage} to approximate the area coverage it provides,
+rather than working with a continuous coverage. Thus, a sensing disk
+corresponding to a sensor node is covered by its neighboring nodes if all its
+primary points are covered. Obviously, the approximation of coverage is more or
+less accurate according to the number of primary points.
\iffalse
By knowing the position (point center: ($p_x,p_y$)) of a wireless
\fi
-\subsection{The Main Idea}
-\noindent The area of interest can be divided using the
-divide-and-conquer strategy into smaller areas called subregions and
-then our coverage protocol will be implemented in each subregion
-simultaneously. Our DiLCO protocol works in periods fashion as shown in figure~\ref{fig2}.
+\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
+executed simultaneously in each subregion.
+
\begin{figure}[ht!]
\centering
\includegraphics[width=75mm]{FirstModel.pdf} % 70mm
\label{fig2}
\end{figure}
-%Modifier la figure pour faire apparaitre des periodes et dans le schema en bleu, indiquer sensing round au lieu de sensing tout seul.
-
-Each period is divided into 4 phases : Information (INFO) Exchange,
-Leader Election, Decision, and Sensing. For each period there is
-exactly one set cover responsible for the sensing task. This protocol is
-more reliable against an unexpected node failure because it works
-in periods. On the one hand, if a node failure is detected before
-making the decision, the node will not participate to this phase, and,
-on the other hand, if the node failure occurs after the decision, the
-sensing task of the network will be temporarily affected: only during
-the period of sensing until a new period starts, since a new set cover
-will take charge of the sensing task in the next period. The energy
-consumption and some other constraints can easily be taken into
-account since the sensors can update and then exchange their
-information (including their residual energy) at the beginning of each
-period. However, the pre-sensing phases (INFO Exchange, Leader
-Election, Decision) are energy consuming for some nodes, even when
-they do not join the network to monitor the area.
-We define two types of packets to be used by our DiLCO protocol.
+As shown in Figure~\ref{fig2}, the proposed DiLCO protocol is a periodic
+protocol where each period is decomposed into 4~phases: Information Exchange,
+Leader Election , Decision, and Sensing. For each period there will be exactly
+one cover set in charge of the sensing task. A periodic scheduling is
+interesting because it enhances the robustness of the network against node
+failures. First, a node that has not enough energy to complete a period, or
+which fails before the decision is taken, will be excluded from the scheduling
+process. Second, if a node fails later, whereas it was supposed to sense the
+region of interest, it will only affect the quality of coverage until the
+definition of a new cover set in the next period. Constraints, like the energy
+consumption, can be easily taken into consideration since the sensors can update
+and exchange their information during the first phase. Let us notice that the
+phases before the sensing one (Information Exchange, Leader Election, and
+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 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 subregion for information exchange.
-\item ActiveSleep packet: sent by the leader to all the nodes in its subregion to inform them to be Active or Sleep during the sensing phase.
+\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 inform them to be stay Active or to go Sleep during the sensing phase.
\end{itemize}
%\end{enumerate}
-
-There are five status for each sensor node in the network :
+and each sensor node will have five possible status in the network:
%\begin{enumerate}[(a)]
\begin{itemize}
-\item LISTENING: Sensor is waiting for a decision (to be active or not)
-\item COMPUTATION: Sensor applies the optimization process as leader
-\item ACTIVE: Sensor is active
-\item SLEEP: Sensor is turned off
-\item COMMUNICATION: Sensor is transmitting or receiving packet
+\item LISTENING: sensor is waiting for a decision (to be active or not);
+\item COMPUTATION: sensor applies the optimization process as leader;
+\item ACTIVE: sensor is active;
+\item SLEEP: sensor is turned off;
+\item COMMUNICATION: sensor is transmitting or receiving packet.
\end{itemize}
%\end{enumerate}
-%Below, we describe each phase in more details.
-Algorithm 1 gives a brief description of the protocol applied by each sensor node (denoted by $s_j$ for a sensor node indexed by $j$).
-Initially, the sensor node checks its remaining energy in order to participate in the current period. After that, all the sensors collect position coordinates, remaining energy $RE_j$, sensor node id, and the number of its one-hop live neighbors during the information exchange.
-Then all the sensor nodes in the same subregion will select the leader based on the received informations. The selection criteria for the leader in order of priority are: larger number of neighbours, larger remaining energy, and then in case of equality, larger index. After that, if the sensor node is leader, it will execute the integer program algorithm (see section~\ref{cp}) which provides a set of sensors planned to be active in the sensing round. As leader, it will send an Active-Sleep packet to each sensor in the same subregion to indicate it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing round.
-
+An outline of the protocol implementation is given by Algorithm~\ref{alg:DiLCO}
+which describes the execution of a period by a node (denoted by $s_j$ for a
+sensor node indexed by $j$). At the beginning a node checks whether it has
+enough energy to stay active during the next sensing phase. If yes, it exchanges
+information with all the other nodes belonging to the same subregion: it
+collects from each node its position coordinates, remaining energy ($RE_j$), ID,
+and the number of one-hop neighbors still alive. Once the first phase is
+completed, the nodes of a subregion choose a leader to take the decision based
+on the following criteria with decreasing importance: larger number of
+neighbors, larger remaining energy, and then in case of equality, larger index.
+After that, if the sensor node is leader, it will execute the integer program
+algorithm (see Section~\ref{cp}) which provides a set of sensors planned to be
+active in the next sensing phase. As leader, it will send an Active-Sleep packet
+to each sensor in the same subregion to indicate it if it has to be active or
+not. Alternately, if the sensor is not the leader, it will wait for the
+Active-Sleep packet to know its state for the coming sensing phase.
\iffalse
\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
\iffalse
\subsection{DiLCO protocol Algorithm}
-we first show the pseudo-code of DiLCO protocol, which is executed by each sensor in the subregion and then describe it in more detail.
-\fi
+we first show the pseudo-code of DiLCO protocol, which is executed by each
+sensor in the subregion and then describe it in more detail. \fi
\begin{algorithm}[h!]
% \KwIn{all the parameters related to information exchange}
\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 objective is to find a maximum number of
-disjoint cover sets. To accomplish this goal, authors proposed an
-integer program, which forces undercoverage and overcoverage of targets
-to become minimal at the same time. They use binary variables
-$x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our
-model, we consider binary variables $X_{j}$, which determine the
-activation of sensor $j$ in the sensing round. We also
-consider primary points as targets. The set of primary points is
-denoted by $P$ and the set of sensors by $J$.
-
-\noindent For a primary point $p$, let $\alpha_{jp}$ denote the
-indicator function of whether the point $p$ is covered, that is:
+\indent Our model is based on the model proposed by \cite{pedraza2006} where the
+objective is to find a maximum number of disjoint cover sets. To accomplish
+this goal, the authors proposed an integer program which forces undercoverage
+and overcoverage of targets to become minimal at the same time. They use binary
+variables $x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our
+model, we consider binary variable $X_{j}$ which determine the activation of
+sensor $j$ in the sensing phase. We also consider primary points as targets.
+The set of primary points is denoted by $P$ and the set of sensors by $J$.
+
+\noindent Let $\alpha_{jp}$ denote the indicator function of whether the primary
+point $p$ is covered, that is:
\begin{equation}
\alpha_{jp} = \left \{
\begin{array}{l l}
\end{array} \right.
%\label{eq12}
\end{equation}
-The number of active sensors that cover the primary point $p$ is equal
-to $\sum_{j \in J} \alpha_{jp} * X_{j}$ where:
+The number of active sensors that cover the primary point $p$ can then be
+computed by $\sum_{j \in J} \alpha_{jp} * X_{j}$ where:
\begin{equation}
X_{j} = \left \{
\begin{array}{l l}
\label{eq14}
\end{equation}
-\noindent Our coverage optimization problem can then be formulated as follows
+\noindent Our coverage optimization problem can then be formulated as follows:
\begin{equation} \label{eq:ip2r}
\left \{
\begin{array}{ll}
\right.
\end{equation}
-
-
\begin{itemize}
-\item $X_{j}$ : indicates whether or not the sensor $j$ is actively
- sensing in the round (1 if yes and 0 if not);
-\item $\Theta_{p}$ : {\it overcoverage}, the number of sensors minus
- one that are covering the primary point $p$;
-\item $U_{p}$ : {\it undercoverage}, indicates whether or not the primary point
+\item $X_{j}$ : indicates whether or not the sensor $j$ is actively sensing (1
+ if yes and 0 if not);
+\item $\Theta_{p}$ : {\it overcoverage}, the number of sensors minus one that
+ are covering the primary point $p$;
+\item $U_{p}$ : {\it undercoverage}, indicates whether or not the primary point
$p$ is being covered (1 if not covered and 0 if covered).
\end{itemize}
-The first group of constraints indicates that some primary point $p$
-should be covered by at least one sensor and, if it is not always the
-case, overcoverage and undercoverage variables help balancing the
-restriction equations by taking positive values. There are two main
-objectives. First, we limit the overcoverage of primary points in order to
-activate a minimum number of sensors. Second we prevent the absence of monitoring on
- some parts of the subregion by minimizing the undercoverage. The
-weights $w_\theta$ and $w_U$ must be properly chosen so as to
-guarantee that the maximum number of points are covered during each
-round.
-
-
-
-
-\section{\uppercase{Simulation Results and Analysis}}
+The first group of constraints indicates that some primary point $p$ should be
+covered by at least one sensor and, if it is not always the case, overcoverage
+and undercoverage variables help balancing the restriction equations by taking
+positive values. Two objectives can be noticed in our model. First, we limit the
+overcoverage of primary points to activate as few sensors as possible. Second,
+to avoid a lack of area monitoring in a subregion we minimize the
+undercoverage. Both weights $w_\theta$ and $w_U$ must be carefully chosen in
+order to guarantee that the maximum number of points are covered during each
+period.
+
+\section{\uppercase{Protocol evaluation}}
\label{sec:Simulation Results and Analysis}
-\noindent \subsection{Simulation Framework}
-In this subsection, we conducted a series of simulations to evaluate the
-efficiency and the relevance of our DiLCO protocol, using the discrete event
-simulator OMNeT++ \cite{varga}. The simulation parameters are summarized in
-Table~\ref{table3}.
+\noindent \subsection{Simulation framework}
+
+To assess the performance of our DiLCO protocol, we have used the discrete
+event simulator OMNeT++ \cite{varga} to run different series of simulations.
+Table~\ref{table3} gives the chosen parameters setting.
\begin{table}[ht]
\caption{Relevant parameters for network initializing.}
% is used to refer this table in the text
\end{table}
-We performed simulations for five different densities varying from 50 to 250~nodes. Experimental results are the average obtained from 25 randomly generated networks (25 for each network density) in which nodes are deployed over a $(50 \times 25)~m^2 $ sensing field. More precisely, the deployment is controlled at a coarse scale in order to ensure that the deployed nodes can cover the sensing field with a high coverage ratio.\\
-
-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).
-
-We use an energy consumption model proposed by~\cite{ChinhVu} and based on ~\cite{raghunathan2002energy} with slight modifications.
-The energy consumption for sending/receiving the packets is added whereas the part related to the sensing range is removed because we consider a fixed sensing range.
-% We are took into account the energy consumption needed for the high computation during executing the algorithm on the sensor node.
-%The new energy consumption model will take into account the energy consumption for communication (packet transmission/reception), the radio of the sensor node, data sensing, computational energy of Micro-Controller Unit (MCU) and high computation energy of MCU.
-%revoir la phrase
-
-For our energy consumption model, we refer to the sensor node Medusa II which uses Atmels AVR ATmega103L microcontroller~\cite{raghunathan2002energy}. The typical architecture of a sensor is composed of four subsystems : the MCU subsystem which is capable of computation, communication subsystem (radio) which is responsible for
-transmitting/receiving messages, sensing subsystem that collects data, and the power supply which powers the complete sensor node ~\cite{raghunathan2002energy}. Each of the first three subsystems can be turned on or off depending on the current status of the sensor. Energy consumption (expressed in milliWatt per second) for the different status of the sensor is summarized in Table~\ref{table4}.
+Simulations with five different node densities going from 50 to 250~nodes were
+performed considering each time 25~randomly generated networks, to obtain
+experimental results which are relevant. The nodes are deployed on a field of
+interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
+high coverage ratio.
+
+We chose as energy consumption model the one proposed proposed by~\cite{ChinhVu}
+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
+node typically consists of four units: a MicroController Unit, an Atmels AVR
+ATmega103L in case of Medusa II, to perform the computations; a communication
+(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]
-\caption{The Energy Consumption Model}
+\caption{Energy consumption model}
% title of Table
\centering
% used for centering table
+{\scriptsize
\begin{tabular}{|c|c|c|c|c|}
% centered columns (4 columns)
\hline
%inserts double horizontal lines
-Sensor mode & MCU & Radio & Sensing & Power (mW) \\ [0.5ex]
+Sensor status & MCU & Radio & Sensing & Power (mW) \\ [0.5ex]
\hline
% inserts single horizontal line
Listening & ON & ON & ON & 20.05 \\
%\multicolumn{4}{|c|}{Energy needed to send/receive a 1-bit} & 0.2575\\
\hline
\end{tabular}
+}
\label{table4}
% is used to refer this table in the text
\end{table}
-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.\\
-
-
-In the simulations, we introduce the following performance metrics to evaluate the efficiency of our approach:
+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 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)}:} 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 $Lifetime_{95}$ 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 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.
\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}
-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.
+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
+ 18} (respectively {\bf 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
+(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.
-\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.
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