\keywords{Wireless Sensor Networks, Area Coverage, Network lifetime,
Optimization, Scheduling.}
-\abstract{One of the fundamental challenges in Wireless Sensor Networks (WSNs) is the
-coverage preservation and the extension of the network lifetime continuously and
-effectively when monitoring a certain area (or region) of interest. In this
-paper, a Distributed Lifetime Coverage Optimization protocol (DiLCO) to maintain
-the coverage and to improve the lifetime in wireless sensor networks is
-proposed. The area of interest is first divided into subregions using a
-divide-and-conquer method and then the DiLCO protocol is distributed on the
-sensor nodes in each subregion. The DiLCO combines two efficient techniques:
-leader election for each subregion, followed by an optimization-based planning
-of activity scheduling decisions for each subregion. The proposed DiLCO works
-into rounds during which a small number of nodes, remaining active for sensing,
-is selected to ensure coverage so as to maximize the lifetime of wireless sensor
-network. Each round consists of four phases: (i)~Information Exchange,
-(ii)~Leader Election, (iii)~Decision, and (iv)~Sensing. The decision process is
-carried out by a leader node, which solves an integer program. Compared with
-some existing protocols, simulation results show that the proposed protocol can
-prolong the network lifetime and improve the coverage performance effectively.}
+\abstract{ One of the main research challenges faced in Wireless Sensor Networks
+ (WSNs) is to preserve continuously and effectively the coverage of an area (or
+ region) of interest to be monitored, while simultaneously preventing as much
+ as possible a network failure due to battery-depleted nodes. In this paper we
+ propose a protocol, called Distributed Lifetime Coverage Optimization protocol
+ (DiLCO), which maintains the coverage and improves the lifetime of a wireless
+ sensor network. As a first step we partition the area of interest into
+ subregions using a classical divide-and-conquer method. Our DiLCO protocol is
+ then distributed on the sensor nodes in each subregion in a second step. To
+ fulfill our objective, the proposed protocol combines two effective
+ techniques: a leader election in each subregion, followed by an
+ optimization-based node activity scheduling performed by each elected leader.
+ This two-step process takes place periodically, in order to choose a small set
+ of nodes remaining active for sensing during a time slot. Each set is built
+ 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
+ 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
+ and provides improved coverage performance. }
\onecolumn \maketitle \normalsize \vfill
\section{\uppercase{Introduction}}
\label{sec:introduction}
\noindent
-Energy efficiency is very important issue in WSNs since sensors are powered by batteries. Therefore, reducing energy consumption and extending network lifetime are the main challenges in the design of WSNs. One of the major 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, is one of the most important performance metrics to measure WSNs. The most discussed coverage problems in literature can be classified
-into three types \cite{li2013survey}: area (blanket) coverage (where every
-point inside an area is to be monitored), target (sweep) coverage (where the main objective is to cover only a finite number of discrete
-points called targets), and barrier coverage (The problem of preventing an intruder from entering a region of interest is referred to as the barrier coverage).
- It is required to monitor the area of interest efficiently~\cite{Nayak04}, but in the same time the power consumption should be minimized. Since sensor nodes have a limited batteries life~\cite{Sudip03} and since it is impossible, difficult or expensive to be recharged and /or replaced after they are deployed 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 by elaborate managing the duty cycle of nodes in WSN.
-
-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 based optimization 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 rounds, where a round starts with a discovery phase to exchange information between sensors of the subregion, in order to choose in a suitable manner a sensor node to carry out a coverage strategy. Our DiLCO protocol involves solving an integer program, which provides the activation of the sensors for the sensing phase of the current round.
-
-The remainder of the paper is organized as follows. The next section reviews the related work in the field. Section~\ref{sec:The DiLCO Protocol Description} is devoted to the DiLCO protocol Description. Section~\ref{cp} gives the coverage model
-formulation which is used to schedule the activation of sensors.
-Section~\ref{sec:Simulation Results and Analysis} shows the simulation results. Finally, we give concluding remarks and some suggestions for
-future works in Section~\ref{sec:Conclusion and Future Works}.
+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
+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
+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 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.
+\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.
-The work presented in~\cite{luo2014parameterized,tian2014distributed} try 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.
-The work proposed in~\cite{kim2013maximum} considered the barrier-coverage problem in WSNs. The final goal is to maximize the network lifetime such that any penetration of the intruder is detected.
-In \cite{ChinhVu}, the authors are proposed a localized and distributed greedy algorithm named DESK for generating non-disjoint cover sets which provide the k-coverage for the whole network.
-Our Work in~\cite{idrees2014coverage} is proposed a coverage optimization protocol to improve the lifetime in heterogeneous energy wireless sensor networks. In this work, the coverage protocol distributed in each sensor node in the subregion but the optimization take place over the the whole subregion. We are considered only distributing the coverage protocol over two subregions.
-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} considered the coverage problem in WSNs where each sensor has variable sensing radius. The final objective is to maximize the network coverage lifetime in WSNs.
+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.
+
+
+Vu et al.~\cite{ChinhVu} proposed a localized and distributed greedy algorithm named DESK for generating non-disjoint cover sets which provide the k-area coverage for the whole network.
+
+
+Qu et al.~\cite{qu2013distributed} developed a distributed algorithm using adjustable sensing sensors
+for maintaining the full coverage of such sensor networks. The
+algorithm contains two major parts: the first part aims at
+providing $100\%$ coverage and the second part aims at saving
+energy by decreasing the sensing radius.
+
+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.
+
+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.
+
+
+\iffalse
+
+The work in ~\cite{vu2009delaunay} considered the area coverage problem for variable sensing radii in WSNs by improving the energy balancing heuristic proposed in ~\cite{wang2007energy} so that the area of interest can be full covered using Delaunay triangulation structure.
+
+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.
+
+
+In~\cite{xin2009area}, the authors proposed a circle intersection localized coverage algorithm
+to maintain connectivity based on loose connectivity critical condition
+. By using the connected coverage node set, it can maintain network
+connection in the case which loose condition is not meet.
+The authors in ~\cite{vashistha2007energy} addressed the full area coverage problem using information
+coverage. They are proposed a low-complexity heuristic algorithm to obtain full area information covers (FAIC), which they refer to as Grid Based FAIC (GB-FAIC) algorithm. Using these FAICs, they are obtained the optimal schedule for applying the sensing activity of sensor nodes in order to
+achieve increased sensing lifetime of the network.
+
+
+\fi
+
+
+
+In \cite{xu2001geography}, Xu et al. proposed a Geographical Adaptive Fidelity (GAF) algorithm, which uses geographic location information to divide the area of interest into fixed square grids. Within each grid, it keeps only one node staying awake to take the responsibility of sensing and communication.
+
+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,
+(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.
+
+\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 proposed in~\cite{kim2013maximum} considers the barrier-coverage problem in WSNs. The final goal is to maximize the network lifetime such that any penetration of the intruder is detected.
+%inutile de parler de ce papier car il concerne barrier coverage
+In \cite{ChinhVu}, the authors propose a localized and distributed greedy algorithm named DESK for generating non-disjoint cover sets which provide the k-coverage for the whole network.
+Our Work in~\cite{idrees2014coverage} proposes a coverage optimization protocol to improve the lifetime in heterogeneous energy wireless sensor networks. In this work, the coverage protocol distributed in each sensor node in the subregion but the optimization take place over the the whole subregion. We are considered only distributing the coverage protocol over two subregions.
+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.
Yu et al.~\cite{yu2013cwsc} presented a connected k-coverage working sets construction
approach (CWSC) to maintain k-coverage and connectivity. This approach try to select the minimum number of connected sensor nodes that can provide k-coverage ($k \geq 1$).
In~\cite{cheng2014achieving}, the authors are 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.
-\fi
+
In~\cite{yang2013energy}, the authors are investigated full area coverage problem
under the probabilistic sensing model in the sensor networks. %They are designed $\varepsilon-$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.
In \cite{xu2001geography}, Xu et al. proposed a Geographical Adaptive Fidelity (GAF) algorithm, which uses geographic location information to divide the area of interest into fixed square grids. Within each grid, it keeps only one node staying awake to take the responsibility of sensing and communication.
(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,
(5) The improved energy consumption model.
-
+\fi
\section{ The DiLCO Protocol Description}
\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 rounds fashion as shown in figure~\ref{fig2}.
+\subsection{The 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}
-Each round is divided into 4 phases : Information (INFO) Exchange,
-Leader Election, Decision, and Sensing. For each round 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 rounds. 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 round starts, since a new set cover
-will take charge of the sensing task in the next round. 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
-round. 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 excution 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 of it's subregion for information exchange.
-\item ActiveSleep packet: sent by the leader to all the nodes in the same of it's 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 four 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.
-In Algorithm 1, Initially, the sensor node check it's remaining energy in order to participate in the current round. Each sensor node determines it's position and it's subregion based Embedded GPS or Location Discovery Algorithm. 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. The sensor node enter in listening mode waiting to receive ActiveSleep packet from the leader to take the decision. 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}) to optimize the coverage and the lifetime in it's subregion. After the decision, the optimization approach will select the set of sensor nodes to take the mission of coverage during the sensing phase.
-
-
+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}
\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}
\BlankLine
%\emph{Initialize the sensor node and determine it's position and subregion} \;
- \If{ $RE_j \geq E_{R}$ }{
+ \If{ $RE_j \geq E_{th}$ }{
\emph{$s_j.status$ = COMMUNICATION}\;
\emph{Send $INFO()$ packet to other nodes in the subregion}\;
\emph{Wait $INFO()$ packet from other nodes in the subregion}\;
\section{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 phase of the 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.}
Initial Energy & 500-700~joules \\
%\hline
Sensing Period & 60 Minutes \\
-$E_{thr}$ & 36 Joules\\
+$E_{th}$ & 36 Joules\\
$R_s$ & 5~m \\
%\hline
$w_{\Theta}$ & 1 \\
% [1ex] adds vertical space
%\hline
-$w_{U}$ & $|P^2|$
+$w_{U}$ & $|P|^2$
%inserts single line
\end{tabular}
\label{table3}
% is used to refer this table in the text
\end{table}
-25 simulation runs are performed with different network topologies. The results presented hereafter are the average of these 25 runs.
-We performed simulations for five different densities varying from 50 to 250~nodes. Experimental results are obtained from randomly generated networks 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.\\
-
-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}. The energy needed to send or receive a 1-bit is equal to $0.2575 mW$.
+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
+(adio) unit able to send and receive messages; a sensing unit to collect data; a
+power supply which provides the energy consumed by node. Except the battery, all
+the other unit can be be switched off to save energy according to the node
+status. Table~\ref{table4} summarizes the energy consumed (in milliWatt per
+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 (mWs) \\ [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 sake of simplicity we ignore the energy needed to turn on the
-radio, to start up the sensor node, the transition from mode 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 it's 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 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 mWs) 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.\\
+% MICHEL - TO BE CONTINUED
-
-In the simulations, we introduce the following performance metrics to evaluate the efficiency of our approach:
+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:
%\begin{enumerate}[i)]
\begin{itemize}
for calculating the coverage. The coverage ratio can be calculated by:
\begin{equation*}
\scriptsize
-\mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100.
+\mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100.
\end{equation*}
-Where: $n^t$ is the number of covered grid points by the active sensors of all subregions during round $t$ in 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 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.
%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.
\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 rounds. The EC can be computed as follow: \\
+ 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_L} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +
- \sum\limits_{t=1}^{T_L} \left( E^{a}_t+E^{s}_t \right)}{T_L},
+\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*}
%\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 $M_L$ and $T_L$ are respectively the number of periods and rounds during
-$Lifetime_{95}$ or $Lifetime_{50}$. The total energy consumed by the sensors
+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 $m$.
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, $E^a_t$ and $E^s_t$ indicate the energy consummed by the whole
-network in round $t$.
+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,
%\subsection{Performance Analysis for differnet subregions}
\subsection{Performance Analysis}
\label{sub1}
-In this subsection, we are studied the performance of our DiLCO protocol for a 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 did not take the DiLCO-1 protocol in our simulation results because it need high execution time to give the decision leading to consume all it's energy before producing the solution for optimization problem. our DiLCO protocol compared with other two approches. The first approach, called DESK that proposed by ~\cite{ChinhVu}, which 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.
+
+We first concentrate on the required number of subregions making effective our
+protocol. Thus our DiLCO protocol is declined into five versions: DiLCO-2,
+DiLCO-4, DiLCO-8, DiLCO-16, and DiLCO-32, corresponding to $2$, $4$, $8$, $16$
+or $32$ subregions (leaders).
+
+In this subsection, we study the performance of our DiLCO protocol for different number of subregions (Leaders).
+The DiLCO-1 protocol is a centralized approach on all the area of the interest, while DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 are distributed on two, four, eight, sixteen, and thirty-two subregions respectively. We do not take into account the DiLC0-1 protocol in our simulation results because it requires high execution time to solve the integer program and thus it is too costly in term of energy.
+
+Our method is compared with other two approaches. The first approach, called DESK and proposed by ~\cite{ChinhVu} is a full distributed coverage algorithm. The second approach, called GAF ~\cite{xu2001geography}, consists in dividing the region into fixed squares. During the decision phase, in each square, one sensor is chosen to remain on during the sensing phase time.
\subsubsection{Coverage Ratio}
-In this experiment, Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes.
+Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes.
\parskip 0pt
\begin{figure}[h!]
\centering
\label{fig3}
\end{figure}
-It is shown that DESK and GAF provides a
-a little better coverage ratio with 99.99\% and 99.91\% against 98.9\%, 99.1\%, 99.2\%, 99.1\% and 99.4\% produced by DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 for the lowest number of rounds. This is due to the fact that our DiLCO protocol versions put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more nodes are active in the case of DESK and GAF.
-
-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 rounds. Coverage ratio decreases when the number of rounds 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.
+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{The Energy Consumption}
-Based on the result in figure~\ref{fig3}, we are chose DiLCO-16 and DiLCO-32 protocols to be compared with other approaches. We measure the energy consumed by the sensors during the communication, listening, computation, active, and sleep modes for different network densities and compare it for different approaches. Figure~\ref{fig95} illustrates the energy consumption for different network sizes.
+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 denoted by $DiLCO-16/50$ (respectively $DiLCO-16/95$) as the amount of energy consumed during which the network can satisfy an area coverage greater than $50\%$ (repectively $95\%$) and we refer the same definition for the other approches.
+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}
\label{fig95}
\end{figure}
-The results show that our 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 as well as the energy consumed during the different modes of sensor nodes. 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.
+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.
+
+
+%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}
-In this experiment, we study the the impact of the size of the network on the excution time of the our distributed optimization approach. Figure~\ref{fig8} gives the average execution times in seconds for the decision phase (solving of the optimization problem) during one round. They are given 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 $\left( \frac{35330}{2} \times 6\right)$ and reported on Figure~\ref{fig8} for different network sizes.
+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}.
\begin{figure}[h!]
\centering
\end{figure}
-We can see from figure~\ref{fig8}, that the DiLCO-32 has very low execution times in comparison with other DiLCO versions, because it distributed on larger number of small subregions. Conversely, the DiLCO-2 which requires to solve an optimization problem considering half the nodes in each subregion presents high execution times.
+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.
-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.
+%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{The Network Lifetime}
-In figure~\ref{figLT95}, network lifetime is illustrated for different network sizes. We denoted by $DiLCO-16/50$ (respectively $DiLCO-16/95$) as the amount of time during which the network can satisfy an area coverage greater than $50\%$ ($Lifetime50$)(repectively $95\%$ ($Lifetime95$)) and we refer the same definition for the other approches.
+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 $95\%$ ($Lifetime95$))
\begin{figure}[h!]
\centering
\end{figure}
-As highlighted by figures~\ref{figLT95}, the network lifetime obviously
-increases when the size of the network increases, 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
-suited nodes, for each round, to cover the area of interest and by
-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.
+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.
+
+
+% 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
+% suited nodes, for each round, to cover the area of interest and by
+% 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 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
sensor nodes have limited resources in terms of memory, energy and
which, aggregated together, define a kind of meta-sensing phase.
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.
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\end{document}
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