%% %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\chapter{Multiround Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}
+\chapter{Distributed Lifetime Coverage Optimization Protocol}
\label{ch4}
-\section{Summary}
+
+
+\section{Introduction}
\label{ch4:sec:01}
-Coverage and lifetime are two paramount problems in Wireless Sensor Networks (WSNs). In this paper, a method called Multiround Distributed Lifetime Coverage
-Optimization protocol (MuDiLCO) is proposed to maintain the coverage and to improve the lifetime in wireless sensor networks. The area of interest is first
-divided into subregions and then the MuDiLCO protocol is distributed on the sensor nodes in each subregion. The proposed MuDiLCO protocol works in periods
-during which sets of sensor nodes are scheduled to remain active for a number of rounds during the sensing phase, to ensure coverage so as to maximize the
-lifetime of WSN. The decision process is carried out by a leader node, which solves an integer program to produce the best representative sets to be used
-during the rounds of the sensing phase. Compared with some existing protocols, simulation results based on multiple criteria (energy consumption, coverage
-ratio, and so on) show that the proposed protocol can prolong efficiently the network lifetime and improve the coverage performance.
-
-\section{MuDiLCO protocol description}
-\label{ch4:sec:02}
-\noindent In this section, we introduce the MuDiLCO protocol which is distributed on each subregion in the area of interest. It is based on two energy-efficient
-mechanisms: subdividing the area of interest into several subregions (like cluster architecture) using divide and conquer method, where the sensor nodes cooperate within each subregion as independent group in order to achieve a network leader election; and sensor activity scheduling for maintaining the coverage and prolonging the network lifetime, which are applied periodically. MuDiLCO protocol uses the same assumptions and network model that presented in chapter 3, section \ref{ch3:sec:02:01} and it has been used the primary point coverage model which is described in the same chapter, section \ref{ch3:sec:02:02}.
+%Energy efficiency is a crucial issue in wireless sensor networks since the sensory consumption, in order to maximize the network lifetime, represents the major difficulty when designing WSNs. As a consequence, one of the scientific research challenges in WSNs, which has been addressed by a large amount of literature during the last few years, is the design of energy efficient approaches for coverage and connectivity~\cite{ref94}.
+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{ref95}. On the other hand, we want to use as little 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.
-
-\subsection{Background Idea}
-\label{ch4:sec:02:02}
-The area of interest can be divided using the divide-and-conquer strategy into
-smaller areas, called subregions, and then our MuDiLCO protocol will be
-implemented in each subregion in a distributed way.
-
-As can be seen in Figure~\ref{fig2}, our protocol works in periods fashion,
-where each is divided into 4 phases: Information~Exchange, Leader~Election,
-Decision, and Sensing. Each sensing phase may be itself divided into $T$ rounds
-and for each round a set of sensors (a cover set) is responsible for the sensing
-task. In this way a multiround optimization process is performed during each
-period after Information~Exchange and Leader~Election phases, in order to
-produce $T$ cover sets that will take the mission of sensing for $T$ rounds.
-\begin{figure}[ht!]
-\centering \includegraphics[width=160mm]{Figures/ch4/GeneralModel.jpg} % 70mm Modelgeneral.pdf
-\caption{The MuDiLCO protocol scheme executed on each node}
-\label{fig2}
-\end{figure}
+In this chapter, we design a protocol that focuses on the area coverage problem with the objective of maximizing the network lifetime. Our proposition, the Distributed Lifetime Coverage Optimization (DiLCO) protocol, maintains the coverage and improves the lifetime in WSNs. The area of interest is first
+divided into subregions using a divide-and-conquer algorithm and an activity scheduling for sensor nodes is then planned by the elected leader in each subregion. In fact, the nodes in a subregion can be seen as a cluster where each node sends sensing data to the cluster head or the sink node. Furthermore, the activities in a subregion/cluster can continue even if another cluster stops due to too many node failures. Our DiLCO protocol considers periods, where a period starts with a discovery phase to exchange information between sensors of the 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 resulting activation vector is broadcasted by each leader node to every node of its subregion.
+The remainder of this chapter is organized as follows. The next section is devoted to the DiLCO protocol description. Section \ref{ch4:sec:03} gives the primary points based coverage problem formulation which is used to schedule the activation of sensors. Section \ref{ch4:sec:04} shows the simulation results obtained using the discrete event simulator OMNeT++ \cite{ref158}. They fully demonstrate the usefulness of the proposed approach. Finally, we give concluding remarks in section \ref{ch4:sec:05}.
-This protocol minimizes the impact of unexpected node failure (not due to batteries
-running out of energy), 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.
-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 (Information Exchange, Leader Election, and Decision) are energy consuming for some nodes, even when they do not join the network to monitor the area.
+\section{Description of the DiLCO Protocol}
+\label{ch4:sec:02}
+\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 of the network.
-These phases can be described in more details as follow:
-\subsection{Information Exchange Phase}
-\label{ch4:sec:02:02:01}
-The information exchange among the wireless sensor nodes is similar to that one which is described in chapter 3, sections \ref{ch3:sec:02:03:01}.
+\subsection{Assumptions and Network Model}
+\label{ch4:sec:02:01}
+\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 start. 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. Furthermore, we assume that sensor nodes are time synchronized in order to properly coordinate their operations to achieve complex sensing tasks~\cite{ref157}. Two sensor nodes are supposed to be neighbors if the euclidean distance between them is at most equal to 2$R_s$, where $R_s$ is the sensing range.
+
-\subsection{Leader Election phase}
-\label{ch4:sec:02:02:02}
-The leader election in each subregion is similar to that one which is described in chapter 3, sections\ref{ch3:sec:02:03:02}, but the difference in that the elected leader in each subregion is for each period.
+\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 $R_s$, each space point within a disk centered at a sensor with the radius of the sensing range is said to be covered with this sensor. We also assume that the communication range $R_c$ is at least twice the sensing range $R_s$ (i.e., $R_c \geq 2R_s$). In fact, Zhang and Hou~\cite{ref126} 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. we consider multi-hop communication.
+%We assume that each sensor node can directly transmit its measurements toward a mobile sink node.
+%For example, a sink can be an unmanned aerial vehicle (UAV) flying regularly over the sensor field to collect measurements from sensor nodes. The mobile sink node collects the measurements and transmits them to the base station.
-\subsection{Decision phase}
-\label{ch4:sec:02:02:03}
-Each WSNL will solve an integer program to select which cover sets will be
-activated in the following sensing phase to cover the subregion to which it
-belongs. The integer program will produce $T$ cover sets, one for each round.
-The WSNL will send an Active-Sleep packet to each sensor in the subregion based
-on the algorithm's results, indicating if the sensor should be active or not in
-each round of the sensing phase. The integer program is based on the model
-proposed by \cite{ref156} with some modifications, where the objective is
-to find a maximum number of disjoint cover sets. To fulfill 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 variables $X_{t,j}$ to determine the possibility of activating
-sensor $j$ during round $t$ of a given sensing phase. We also consider primary
-points as targets. The set of primary points is denoted by $P$ and the set of
-sensors by $J$. Only sensors able to be alive during at least one round are
-involved in the integer program.
+During the execution of the DiLCO protocol, two kinds of packet will be used:
+\begin{enumerate} [(i)]
+\item \textbf{INFO packet:} sent by each sensor node to all the nodes inside a same subregion for information exchange.
+\item \textbf{ActiveSleep packet:} sent by the leader to all the nodes in its subregion to inform them to stay Active or to go Sleep during the sensing phase.
+\end{enumerate}
-For a primary point $p$, let $\alpha_{j,p}$ denote the indicator function of
-whether the point $p$ is covered, that is:
-\begin{equation}
-\alpha_{j,p} = \left \{
-\begin{array}{l l}
- 1 & \mbox{if the primary point $p$ is covered} \\
- & \mbox{by sensor node $j$}, \\
- 0 & \mbox{otherwise.}\\
-\end{array} \right.
-%\label{eq12}
-\end{equation}
-The number of active sensors that cover the primary point $p$ during
-round $t$ is equal to $\sum_{j \in J} \alpha_{j,p} * X_{t,j}$ where:
-\begin{equation}
-X_{t,j} = \left \{
-\begin{array}{l l}
- 1& \mbox{if sensor $j$ is active during round $t$,} \\
- 0 & \mbox{otherwise.}\\
-\end{array} \right.
-%\label{eq11}
-\end{equation}
-We define the Overcoverage variable $\Theta_{t,p}$ as:
-\begin{equation}
- \Theta_{t,p} = \left \{
-\begin{array}{l l}
- 0 & \mbox{if the primary point $p$}\\
- & \mbox{is not covered during round $t$,}\\
- \left( \sum_{j \in J} \alpha_{jp} * X_{tj} \right)- 1 & \mbox{otherwise.}\\
-\end{array} \right.
-\label{eq13}
-\end{equation}
-More precisely, $\Theta_{t,p}$ represents the number of active sensor nodes
-minus one that cover the primary point $p$ during round $t$. The
-Undercoverage variable $U_{t,p}$ of the primary point $p$ during round $t$ is
-defined by:
-\begin{equation}
-U_{t,p} = \left \{
-\begin{array}{l l}
- 1 &\mbox{if the primary point $p$ is not covered during round $t$,} \\
- 0 & \mbox{otherwise.}\\
-\end{array} \right.
-\label{eq14}
-\end{equation}
+There are five possible status for each sensor node in the network:
+%and each sensor node will have five possible status in the network:
+\begin{enumerate}[(i)]
+\item \textbf{LISTENING:} sensor is waiting for a decision (to be active or not).
+\item \textbf{COMPUTATION:} sensor applies the optimization process as leader.
+\item \textbf{ACTIVE:} sensor is active.
+\item \textbf{SLEEP:} sensor is turned off.
+\item \textbf{COMMUNICATION:} sensor is transmitting or receiving packet.
+\end{enumerate}
-Our coverage optimization problem can then be formulated as follows:
-\begin{equation}
- \min \sum_{t=1}^{T} \sum_{p=1}^{P} \left(W_{\theta}* \Theta_{t,p} + W_{U} * U_{t,p} \right) \label{eq15}
-\end{equation}
+\subsection{Primary Point Coverage Model}
+\label{ch4:sec:02:02}
+\indent Instead of working with the coverage area, we consider for each sensor a set of points called primary points. We also assume that the sensing disk defined by a sensor is covered if all the primary points of this sensor are covered. By knowing the position (point center: ($p_x,p_y$)) of a wireless sensor node and it's sensing range $R_s$, we calculate the primary points directly based on the proposed model. We use these primary points (that can be increased or decreased if necessary) as references to ensure that the monitored region of interest is covered by the selected set of sensors, instead of using all the points in the area.
+We can calculate the positions of the selected primary
+points in the circle disk of the sensing range of a wireless sensor
+node (see Figure~\ref{fig1}) as follows:\\
+Assuming that the point center of a wireless sensor node is located at $(p_x,p_y)$, we can define up to 25 primary points $X_1$ to $X_{25}$.\\
+%$(p_x,p_y)$ = point center of wireless sensor node\\
+$X_1=(p_x,p_y)$ \\
+$X_2=( p_x + R_s * (1), p_y + R_s * (0) )$\\
+$X_3=( p_x + R_s * (-1), p_y + R_s * (0)) $\\
+$X_4=( p_x + R_s * (0), p_y + R_s * (1) )$\\
+$X_5=( p_x + R_s * (0), p_y + R_s * (-1 )) $\\
+$X_6= ( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (0)) $\\
+$X_7=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (0))$\\
+$X_8=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
+$X_9=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
+$X_{10}=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
+$X_{11}=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
+$X_{12}=( p_x + R_s * (0), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
+$X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
+$X_{14}=( p_x + R_s * (\frac{\sqrt{3}}{2}), p_y + R_s * (\frac{1}{2})) $\\
+$X_{15}=( p_x + R_s * (\frac{-\sqrt{3}}{2}), p_y + R_s * (\frac{1}{2})) $\\
+$X_{16}=( p_x + R_s * (\frac{\sqrt{3}}{2}), p_y + R_s * (\frac{- 1}{2})) $\\
+$X_{17}=( p_x + R_s * (\frac{-\sqrt{3}}{2}), p_y + R_s * (\frac{- 1}{2})) $\\
+$X_{18}=( p_x + R_s * (\frac{\sqrt{3}}{2}), p_y + R_s * (0) $\\
+$X_{19}=( p_x + R_s * (\frac{-\sqrt{3}}{2}), p_y + R_s * (0) $\\
+$X_{20}=( p_x + R_s * (0), p_y + R_s * (\frac{1}{2})) $\\
+$X_{21}=( p_x + R_s * (0), p_y + R_s * (-\frac{1}{2})) $\\
+$X_{22}=( p_x + R_s * (\frac{1}{2}), p_y + R_s * (\frac{\sqrt{3}}{2})) $\\
+$X_{23}=( p_x + R_s * (\frac{- 1}{2}), p_y + R_s * (\frac{\sqrt{3}}{2})) $\\
+$X_{24}=( p_x + R_s * (\frac{- 1}{2}), p_y + R_s * (\frac{-\sqrt{3}}{2})) $\\
+$X_{25}=( p_x + R_s * (\frac{1}{2}), p_y + R_s * (\frac{-\sqrt{3}}{2})) $.
-Subject to
-\begin{equation}
- \sum_{j=1}^{|J|} \alpha_{j,p} * X_{t,j} = \Theta_{t,p} - U_{t,p} + 1 \label{eq16} \hspace{6 mm} \forall p \in P, t = 1,\dots,T
-\end{equation}
-\begin{equation}
- \sum_{t=1}^{T} X_{t,j} \leq \lfloor {RE_{j}/E_{R}} \rfloor \hspace{6 mm} \forall j \in J, t = 1,\dots,T
- \label{eq144}
-\end{equation}
+
+\begin{figure} %[h!]
+\centering
+ \begin{multicols}{2}
+\centering
+\includegraphics[scale=0.33]{Figures/ch4/fig21.pdf}\\~ ~ ~ ~ ~ ~ ~ ~(a)
+\includegraphics[scale=0.33]{Figures/ch4/principles13.pdf}\\~ ~ ~ ~ ~ ~(c)
+\hfill \hfill
+\includegraphics[scale=0.33]{Figures/ch4/fig25.pdf}\\~ ~ ~ ~ ~ ~(e)
+\includegraphics[scale=0.33]{Figures/ch4/fig22.pdf}\\~ ~ ~ ~ ~ ~ ~ ~ ~(b)
+\hfill \hfill
+\includegraphics[scale=0.33]{Figures/ch4/fig24.pdf}\\~ ~ ~ ~ ~ ~ ~(d)
+\includegraphics[scale=0.33]{Figures/ch4/fig26.pdf}\\~ ~ ~ ~ ~ ~ ~(f)
+\end{multicols}
+\caption{Wireless Sensor Node represented by (a) 5, (b) 9, (c) 13, (d) 17, (e) 21 and (f) 25 primary points respectively}
+\label{fig1}
+\end{figure}
+
+
-\begin{equation}
-X_{t,j} \in \lbrace0,1\rbrace, \hspace{10 mm} \forall j \in J, t = 1,\dots,T \label{eq17}
-\end{equation}
-\begin{equation}
-U_{t,p} \in \lbrace0,1\rbrace, \hspace{10 mm}\forall p \in P, t = 1,\dots,T \label{eq18}
-\end{equation}
+\subsection{Main Idea}
+\label{ch4:sec:02:03}
+\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{equation}
- \Theta_{t,p} \geq 0 \hspace{10 mm}\forall p \in P, t = 1,\dots,T \label{eq178}
-\end{equation}
+\begin{figure}[ht!]
+\centering
+\includegraphics[scale=0.90]{Figures/ch4/OneSensingRound.jpg} % 70mm
+\caption{DiLCO protocol}
+\label{FirstModel}
+\end{figure}
+As shown in Figure~\ref{FirstModel}, 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 the coverage until the definition of a new cover set in the next period. Constraints, like 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.
-\begin{itemize}
-\item $X_{t,j}$: indicates whether or not the sensor $j$ is actively sensing
- during round $t$ (1 if yes and 0 if not);
-\item $\Theta_{t,p}$ - {\it overcoverage}: the number of sensors minus one that
- are covering the primary point $p$ during round $t$;
-\item $U_{t,p}$ - {\it undercoverage}: indicates whether or not the primary
- point $p$ is being covered during round $t$ (1 if not covered and 0 if
- covered).
-\end{itemize}
+Below, we describe each phase in more details.
-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. The constraint given by equation~(\ref{eq144}) guarantees that
-the sensor has enough energy ($RE_j$ corresponds to its remaining energy) to be
-alive during the selected rounds knowing that $E_{R}$ is the amount of energy
-required to be alive during one round.
-
-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.
-%% MS W_theta is smaller than W_u => problem with the following sentence
-In our simulations priority is given to the coverage by choosing $W_{U}$ very
-large compared to $W_{\theta}$.
+\subsubsection{Information Exchange Phase}
+\label{ch4:sec:02:03:01}
+Each sensor node $j$ sends, through multi-hop communication, its position, remaining energy $RE_j$, and the number of neighbors $NBR_j$ to all sensor nodes in its subregion by using an INFO packet (containing information on position coordinates, current remaining energy, sensor node ID, number of its one-hop live neighbors) and then waits for packets sent by other nodes. After that, each node will have information about
+all the sensor nodes in the subregion. In our model, the remaining energy corresponds to the time that a sensor can live in the active mode.
+
+\subsubsection{Leader Election Phase}
+\label{ch4:sec:02:03:02}
+This step includes choosing a wireless sensor node called leader, which will be responsible for executing the coverage algorithm. Each subregion in the area of interest will select its own leader independently for each period. All the sensor nodes cooperate to select the leader. 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 are, in order of importance: larger number of neighbors, larger remaining energy, and then in case of equality, larger ID. Observations on previous simulations suggest using the number of one-hop neighbors as the primary criterion to reduce energy consumption due to the communications.
+
+
+\subsubsection{Decision phase}
+\label{ch4:sec:02:03:03}
+The leader will solve an integer program (see section~\ref{ch4:sec:03}) to select which sensors will be activated in the following sensing phase to cover the subregion. It will send an ActiveSleep packet to each sensor in the subregion based on the algorithm's results.
+
+%($RE_j$) corresponds to its remaining energy) to be alive during the selected periods knowing that $E_{th}$ is the amount of energy required to be alive during one period.
-\subsection{Sensing phase}
-\label{ch4:sec:02:02:04}
-The sensing phase consists of $T$ rounds. Each sensor node in the subregion will
-receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
-sleep for each round of the sensing phase. Algorithm~\ref{alg:MuDiLCO}, which
-will be executed by each node at the beginning of a period, explains how the
-Active-Sleep packet is obtained.
+\subsubsection{Sensing phase}
+\label{ch4:sec:02:03:04}
+Active sensors in the period 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 ActiveSleep packet from the leader informing it to stay awake or to go to sleep for a time equal to the round of sensing until starting a new period.
\begin{algorithm}[h!]
- % \KwIn{all the parameters related to information exchange}
-% \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
+
\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}\;
\emph{LeaderID = Leader election}\;
\If{$ s_j.ID = LeaderID $}{
\emph{$s_j.status$ = COMPUTATION}\;
- \emph{$\left\{\left(X_{1,k},\dots,X_{T,k}\right)\right\}_{k \in J}$ =
- Execute Integer Program Algorithm($T,J$)}\;
+ \emph{$\left\{\left(X_{1},\dots,X_{k},\dots,X_{J}\right)\right\}$ =
+ Execute Integer Program Algorithm($J$)}\;
\emph{$s_j.status$ = COMMUNICATION}\;
- \emph{Send $ActiveSleep()$ to each node $k$ in subregion a packet \\
- with vector of activity scheduling $(X_{1,k},\dots,X_{T,k})$}\;
+ \emph{Send $ActiveSleep()$ to each node $k$ in subregion} \;
\emph{Update $RE_j $}\;
}
\Else{
\emph{$s_j.status$ = LISTENING}\;
\emph{Wait $ActiveSleep()$ packet from the Leader}\;
- % \emph{After receiving Packet, Retrieve the schedule and the $T$ rounds}\;
+
\emph{Update $RE_j $}\;
}
% }
\Else { Exclude $s_j$ from entering in the current sensing phase}
% \emph{return X} \;
-\caption{MuDiLCO($s_j$)}
-\label{alg:MuDiLCO}
+\caption{DiLCO($s_j$)}
+\label{alg:DiLCO}
\end{algorithm}
+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 $j$). In the beginning, a node checks whether it has enough energy to stay active during the next sensing phase (i.e., the remaining energy $RE_j$ $\geq$ $E_{th}$ (the amount of energy required to be alive during one period)). 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 criteria described in section \ref{ch4:sec:02:03:02}.
+%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{ch4:sec:03}) which provides a set of sensors planned to be active in the next sensing phase. As leader, it will send an ActiveSleep 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 ActiveSleep packet to know its state for the coming sensing phase.
+%Primary Points based
+\section{Coverage Problem Formulation}
+\label{ch4:sec:03}
+\indent Our model is based on the model proposed by \cite{ref156} 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 that the binary variable $X_{j}$ determines 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}
+ 1 & \mbox{if the primary point $p$ is covered} \\
+ & \mbox{by sensor node $j$}, \\
+ 0 & \mbox{otherwise.}\\
+\end{array} \right.
+%\label{eq12}
+\end{equation}
+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}
+ 1& \mbox{if sensor $j$ is active,} \\
+ 0 & \mbox{otherwise.}\\
+\end{array} \right.
+%\label{eq11}
+\end{equation}
+We define the Overcoverage variable $\Theta_{p}$ as:
+\begin{equation}
+ \Theta_{p} = \left \{
+\begin{array}{l l}
+ 0 & \mbox{if the primary point}\\
+ & \mbox{$p$ is not covered,}\\
+ \left( \sum_{j \in J} \alpha_{jp} * X_{j} \right)- 1 & \mbox{otherwise.}\\
+\end{array} \right.
+\label{eq13}
+\end{equation}
+\noindent More precisely, $\Theta_{p}$ represents the number of active sensor
+nodes minus one that cover the primary point~$p$. The Undercoverage variable
+$U_{p}$ of the primary point $p$ is defined by:
+\begin{equation}
+U_{p} = \left \{
+\begin{array}{l l}
+ 1 &\mbox{if the primary point $p$ is not covered,} \\
+ 0 & \mbox{otherwise.}\\
+\end{array} \right.
+\label{eq14}
+\end{equation}
+\noindent Our coverage optimization problem can then be formulated as follows:
+\begin{equation} \label{eq:ip2r}
+\left \{
+\begin{array}{ll}
+\min \sum_{p \in P} (w_{\theta} \Theta_{p} + w_{U} U_{p})&\\
+\textrm{subject to :}&\\
+\sum_{j \in J} \alpha_{jp} X_{j} - \Theta_{p}+ U_{p} =1, &\forall p \in P\\
+%\label{c1}
+%\sum_{t \in T} X_{j,t} \leq \frac{RE_j}{e_t} &\forall j \in J \\
+%\label{c2}
+\Theta_{p}\in \mathbb{N}, &\forall p \in P\\
+U_{p} \in \{0,1\}, &\forall p \in P \\
+X_{j} \in \{0,1\}, &\forall j \in J
+\end{array}
+\right.
+\end{equation}
-\section{Experimental Study and Analysis}
-\label{ch4:sec:03}
+\begin{itemize}
+\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}
-\subsection{Simulation Setup}
-\label{ch4:sec:03:01}
-We conducted a series of simulations to evaluate the efficiency and the
-relevance of our approach, using the discrete event simulator OMNeT++
-\cite{ref158}. The simulation parameters are summarized in
-Table~\ref{table3}. Each experiment for a network is run over 25~different
-random topologies and the results presented hereafter are the average of these
-25 runs.
-%Based on the results of our proposed work in~\cite{idrees2014coverage}, we found as the region of interest are divided into larger subregions as the network lifetime increased. In this simulation, the network are divided into 16 subregions.
-We performed simulations for five different densities varying from 50 to
-250~nodes 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 the given sensing
-range.
-
-%%RC these parameters are realistic?
-%% maybe we can increase the field and sensing range. 5mfor Rs it seems very small... what do the other good papers consider ?
+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. In our simulations, priority is given to the coverage by choosing $W_{U}$ very
+large compared to $W_{\theta}$.
+
+\section{Simulation Results and Analysis}
+\label{ch4:sec:04}
+
+\subsection{Simulation Framework}
+\label{ch4:sec:04:01}
+
+To assess the performance of DiLCO protocol, we have used the discrete event simulator OMNeT++ \cite{ref158} to run different series of simulations. Table~\ref{tablech4} gives the chosen parameters setting.
\begin{table}[ht]
\caption{Relevant parameters for network initializing.}
%inserts double horizontal lines
Parameter & Value \\ [0.5ex]
-%Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
-% inserts table
-%heading
+
\hline
% inserts single horizontal line
-Sensing field size & $(50 \times 25)~m^2 $ \\
+Sensing Field & $(50 \times 25)~m^2 $ \\
% inserting body of the table
%\hline
-Network size & 50, 100, 150, 200 and 250~nodes \\
+Nodes Number & 50, 100, 150, 200 and 250~nodes \\
%\hline
-Initial energy & 500-700~joules \\
+Initial Energy & 500-700~joules \\
%\hline
-Sensing time for one round & 60 Minutes \\
-$E_{R}$ & 36 Joules\\
+Sensing Period & 60 Minutes \\
+$E_{th}$ & 36 Joules\\
$R_s$ & 5~m \\
%\hline
-$W_{\Theta}$ & 1 \\
+$R_c$ & 10~m \\
+$w_{\Theta}$ & 1 \\
% [1ex] adds vertical space
%\hline
-$W_{U}$ & $|P|^2$
+$w_{U}$ & $|P|^2$
%inserts single line
\end{tabular}
-\label{table3}
+\label{tablech4}
% is used to refer this table in the text
\end{table}
-
-Our protocol is declined into four versions: MuDiLCO-1, MuDiLCO-3, MuDiLCO-5,
-and MuDiLCO-7, corresponding respectively to $T=1,3,5,7$ ($T$ the number of
-rounds in one sensing period). In the following, we will make comparisons with
-two other methods. The first method, called DESK and proposed by \cite{DESK},
-is a full distributed coverage algorithm. The second method, called
-GAF~\cite{GAF}, consists in dividing the region into fixed squares.
-During the decision phase, in each square, one sensor is then chosen to remain
-active during the sensing phase time.
-
-Some preliminary experiments were performed in chapter 3 to study the choice of the number of
-subregions which subdivides 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 MuDiLCO protocol more robust against random
-network disconnection due to node failures. However, too many subdivisions
-reduce 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, we have set the number of subregions to 16 rather than 32.
-
-We used the modeling language and the optimization solver which are mentioned in chapter 3, section \ref{ch3:sec:04:02}. In addition, we employed an energy consumption model, which is presented in chapter 3, section \ref{ch3:sec:04:03}.
-
-%The initial energy of each node is randomly set in the interval $[500;700]$. A sensor node will not participate in the next round if its remaining energy is less than $E_{R}=36~\mbox{Joules}$, 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.
-
-\subsection{Metrics}
-\label{ch4:sec:03:02}
-To evaluate our approach we consider the following performance metrics:
-
-\begin{enumerate}[i]
-
-\item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much of the area
- of a sensor field is covered. In our case, the sensing field is represented as
- a connected grid of points and we use each grid point as a sample point to
- compute the coverage. The coverage ratio can be calculated by:
+
+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.
+
+
+\subsection{Modeling Language and Optimization Solver}
+\label{ch4:sec:04:02}
+The modeling language for Mathematical Programming (AMPL)~\cite{AMPL} is employed to generate the integer program instance in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method.
+%Obviously, It is infeasible to use GLPK on a real sensor nodes, we use it in the simulation only for simplicity. GLPK is used to compute the optimal schedule.
+
+\subsection{Energy Consumption Model}
+\label{ch4:sec:04:03}
+
+\indent In this dissertation, we used an energy consumption model proposed by~\cite{DESK} and based on \cite{ref112} with slight modifications. The energy consumption for sending/receiving the packets is added, whereas the part related to the dynamic sensing range is removed because we consider a fixed sensing range.
+
+\indent For our energy consumption model, we refer to the sensor node Medusa~II which uses an Atmel's AVR ATmega103L microcontroller~\cite{ref112}. 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, the sensing subsystem that collects data, and the power supply which powers the complete sensor node \cite{ref112}. 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{table1}.
+
+\begin{table}[ht]
+\caption{Energy Consumption Model}
+% title of Table
+\centering
+% used for centering table
+\begin{tabular}{|c|c|c|c|c|}
+% centered columns (4 columns)
+ \hline
+%inserts double horizontal lines
+Sensor status & MCU & Radio & Sensing & Power (mW) \\ [0.5ex]
+\hline
+% inserts single horizontal line
+LISTENING & on & on & on & 20.05 \\
+% inserting body of the table
+\hline
+ACTIVE & on & off & on & 9.72 \\
+\hline
+SLEEP & off & off & off & 0.02 \\
+\hline
+COMPUTATION & on & on & on & 26.83 \\
+%\hline
+%\multicolumn{4}{|c|}{Energy needed to send/receive a 1-bit} & 0.2575\\
+ \hline
+\end{tabular}
+
+\label{table1}
+% is used to refer this table in the text
+\end{table}
+
+\indent For the sake of simplicity we ignore the energy needed to turn on the radio, to start up the sensor node, to move from one status to another, etc. Thus, when a sensor becomes active (i.e., it has already received its status from leader), it can turn its radio off to save battery. DiLCO uses two types of packets
+for communication. The size of the INFO packet and ActiveSleep packet
+are 112 bits and 16 bits respectively. The value of energy spent to send a 1-bit-content message is obtained by using the equation in ~\cite{ref112} 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 packet is equal to $0.2575~mW$.
+
+%We have used an energy consumption model, which is presented in chapter 1, section \ref{ch1:sec9:subsec2}.
+
+The initial energy of each node is randomly set in the interval $[500;700]$. A sensor node will not participate in the next period if its remaining energy is less than $E_{th}=36~\mbox{Joules}$, the minimum energy needed for the node to stay alive during one period. This value has been computed by multiplying the energy consumed in the active state (9.72 mW) by the time in second for one period (3600 seconds), and adding the energy for the pre-sensing phases. According to the interval of initial energy, a sensor may be alive during at most 20 periods.
+
+
+\subsection{Performance Metrics}
+\label{ch4:sec:04:04}
+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)}:} 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{$n^t$}}{\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 the total number
-of grid points in the sensing field of the network. In our simulations $N = 51
+where $n$ is the number of covered grid points by active sensors of every
+subregions during the current sensing phase and $N$ is the total number of grid
+points in the sensing field. In our simulations, we have a layout of $N = 51
\times 26 = 1326$ grid points.
-\item{{\bf Number of Active Sensors Ratio (ASR)}:} it is important to have as
- few active nodes as possible in each round, in order to minimize the
- communication overhead and maximize the network lifetime. The Active Sensors
- Ratio is defined as follows:
+\item {{\bf Energy Consumption}:} energy consumption (EC) can be seen as the
+ total amount of 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 amount of energy consumed by the sensors (EC) comes through taking into consideration four main energy factors. The first one, denoted $E^{\scriptsize \mbox{com}}_m$, represents the energy consumption spent by all the nodes for wireless communications during the 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 the period $m$. $E^{\scriptsize \mbox{comp}}_m$ refers to the energy needed for 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 Number of Active Sensors Ratio (ASR)}:} it is important to have as few active nodes as possible in each period,
+in order to minimize the communication overhead and maximize the
+network lifetime. The Active Sensors Ratio is defined as follows:
\begin{equation*}
-\scriptsize \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R
- \mbox{$A_r^t$}}{\mbox{$|J|$}} \times 100,
+\scriptsize
+\mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$A_r$}}{\mbox{$J$}} \times 100,
\end{equation*}
-where $A_r^t$ is the number of active sensors in the subregion $r$ during round
-$t$ in the current sensing phase, $|J|$ is the total number of sensors in the
-network, and $R$ is the total number of subregions in the network.
+where $A_r$ is the number of active sensors in the subregion $r$ during current period, $J$ is the total number of sensors in the network, and $R$ is the total number of subregions in the network.
-\item {{\bf Network Lifetime}:} is described in chapter 3, section \ref{ch3:sec:04:04}.
+\item {{\bf Execution Time}:} a sensor node has limited energy resources and computing power, therefore it is important that the proposed algorithm has the shortest possible execution time. The energy of a sensor node must be mainly used for the sensing phase, not for the pre-sensing ones. In this dissertation, 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 Atmel's AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6 to run the optimization resolution, this time is multiplied by 2944.2 $\left( \frac{35330}{2} \times \frac{1}{6} \right)$.
+
+\item {{\bf Stopped simulation runs}:} a simulation ends when the sensor network becomes disconnected (some nodes are dead and are not able to send information to the base station). We report the number of simulations that are stopped due to network disconnections and for which period it occurs.% ( in chapter 4, period consists of one round).
-\item {{\bf Energy Consumption (EC)}:} the average energy consumption can be
- seen as the total energy consumed by the sensors during the $Lifetime_{95}$ or
- $Lifetime_{50}$ divided by the number of rounds. EC can be computed as
- follows:
+\end{enumerate}
- % New version with global loops on period
- \begin{equation*}
- \scriptsize
- \mbox{EC} = \frac{\sum\limits_{m=1}^{M_L} \left[ \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T_m} \left( E^{a}_t+E^{s}_t \right) \right]}{\sum\limits_{m=1}^{M_L} T_m},
- \end{equation*}
-where $M_L$ is the number of periods and $T_m$ the number of rounds in a
-period~$m$, both during $Lifetime_{95}$ or $Lifetime_{50}$. The total energy
-consumed by the sensors (EC) comes through taking into consideration four main
-energy factors. The first one , denoted $E^{\scriptsize \mbox{com}}_m$,
-represents 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, $E^a_t$ and $E^s_t$
-indicate the energy consumed by the whole network in round $t$.
+\subsection{Performance Analysis for Different Number of Subregions}
+\label{ch4:sec:04:05}
+
+In this subsection, we study the performance of our DiLCO protocol for different numbers of subregions.
+The DiLCO-1 protocol is a centralized approach for the whole 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 DiLCO-1 protocol in our simulation results because it needs a high execution time to give the decision, leading to consume all its energy before producing the solution for the optimization problem. DiLCO protocol uses 13 primary points.
+\begin{enumerate}[i)]
+\item {{\bf Coverage Ratio}}
+%\subsubsection{Coverage Ratio}
+%\label{ch4:sec:04:02:01}
+
+Figure~\ref{Figures/ch4/R1/CR} shows the average coverage ratio for 150 deployed nodes.
+\parskip 0pt
+\begin{figure}[h!]
+\centering
+ \includegraphics[scale=0.8] {Figures/ch4/R1/CR.pdf}
+\caption{Coverage ratio for 150 deployed nodes}
+\label{Figures/ch4/R1/CR}
+\end{figure}
+It can be seen that DiLCO protocol (with 4, 8, 16 and 32 subregions) gives nearly similar coverage ratios during the first thirty periods.
+DiLCO-2 protocol gives a coverage ratio very close to the other protocols for the first 10 periods, and then the coverage decreases until the death of the network in the period $18^{th}$. In case of only 2 subregions, the energy consumption is high and the network is rapidly disconnected.
+As can be seen in Figure~\ref{Figures/ch4/R1/CR}, as the number of subregions increases, the coverage preservation for the 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 periods. DiLCO-8, DiLCO-16, and DiLCO-32 protocols are slightly more efficient than other protocols, because they subdivide 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.
+
+\item {{\bf Active Sensors Ratio}}
+%\subsubsection{Active Sensors Ratio}
+
+Figure~\ref{Figures/ch4/R1/ASR} shows the average active nodes ratio for 150 deployed nodes.
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R1/ASR.pdf}
+\caption{Active sensors ratio for 150 deployed nodes }
+\label{Figures/ch4/R1/ASR}
+\end{figure}
+
+The results presented in the figure show that increasing the number of subregions lead to the increase of the number of active nodes. The DiLCO-16 and DiLCO-32 protocols have a larger number of active nodes, but they both preserve the coverage for a larger number of periods. The advantage of the DiLCO-16 and DiLCO-32 protocols are that even if a network is disconnected in one subregion, the other ones usually continue the optimization process, and this extends the lifetime of the network.
+
+\item {{\bf Stopped simulation runs}}
+%\subsubsection{The percentage of stopped simulation runs}
+
+Figure~\ref{Figures/ch4/R1/SR} illustrates the percentage of stopped simulation runs per period for 150 deployed nodes. DiLCO-2 is the approach which stops first because it applies the optimization on only two subregions and the high energy consumption accelerate the network disconnection. Thus, as explained previously, in case of DiLCO-16 and DiLCO-32 which have many subregions, the optimization effectively continues as long as a subnetwork in a subregion is still connected. This longer partial coverage optimization participates in extending the network lifetime.
+\begin{figure}[t]
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R1/SR.pdf}
+\caption{Percentage of stopped simulation runs for 150 deployed nodes }
+\label{Figures/ch4/R1/SR}
+\end{figure}
+
+
+
+\item {{\bf Energy Consumption}}
+%\subsubsection{The Energy Consumption}
+
+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 subregions. Figures~\ref{Figures/ch4/R1/EC}(a) and~\ref{Figures/ch4/R1/EC}(b) illustrate the energy consumption for different network sizes for $Lifetime_{95}$ and $Lifetime_{50}$. The results show that DiLCO-16 and DiLCO-32 are the most competitive from the energy consumption point of view. The other approaches have a high energy consumption due to the energy consumed during the different modes of the sensor node.
+
+\begin{figure}[h!]
+\centering
+ %\begin{multicols}{1}
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R1/EC95.pdf}\\~ ~ ~ ~ ~(a) \\
+%\vfill
+\includegraphics[scale=0.8]{Figures/ch4/R1/EC50.pdf}\\~ ~ ~ ~ ~(b)
+
+%\end{multicols}
+\caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
+\label{Figures/ch4/R1/EC}
+\end{figure}
+
+As shown in Figures~\ref{Figures/ch4/R1/EC}(a) and~\ref{Figures/ch4/R1/EC}(b), 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 computation time to solve the optimization problem, as well as the higher energy consumed during the communication. In fact, the distribution of the computation over many subregions greatly reduces the number of communications, the time of listening and computation.
+
+\item {{\bf Execution Time}}
+%\subsubsection{Execution Time}
+
+In this experiment, the execution time of the distributed optimization approach has been studied. Figure~\ref{Figures/ch4/R1/T} gives the average execution times in seconds for the decision phase (solving of the optimization problem) during one period. They are given for the different approaches and various numbers of sensors. The original execution time is computed as described in section \ref{ch4:sec:04:04}. \\ \\ \\ \\
+
+
+
+\begin{figure}[t]
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R1/T.pdf}
+\caption{Execution Time (in seconds)}
+\label{Figures/ch4/R1/T}
+\end{figure}
+
+We can see from Figure~\ref{Figures/ch4/R1/T} that DiLCO-32 has very low execution times in comparison with other DiLCO versions because it is distributed on larger number of small subregions. Conversely, DiLCO-2 requires to solve an optimization problem considering half the nodes in each subregion and thus presents high execution times. Overall, to be able to deal with very large networks, a distributed method is clearly required.
+
+\item {{\bf Network Lifetime}}
+%\subsubsection{The Network Lifetime}
+
+In Figures~\ref{Figures/ch4/R1/LT}(a) and \ref{Figures/ch4/R1/LT}(b), network lifetime, $Lifetime_{95}$ and $Lifetime_{50}$ respectively, are illustrated for different network sizes.
+
+
+\begin{figure}[h!]
+\centering
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R1/LT95.pdf}\\~ ~ ~ ~ ~(a) \\
+
+\includegraphics[scale=0.8]{Figures/ch4/R1/LT50.pdf}\\~ ~ ~ ~ ~(b)
+
+\caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
+ \label{Figures/ch4/R1/LT}
+\end{figure}
+
+For DiLCO-2 protocol, execution times quickly become unsuitable for a sensor network, and the energy consumed during the communication, seems to be huge because it is distributed over only two subregions. As highlighted by Figures~\ref{Figures/ch4/R1/LT}(a) and \ref{Figures/ch4/R1/LT}(b), the network lifetime obviously increases when the size of the network increases. The network lifetime also increases with the number of subregions, but only up to a given number. Thus we can see that DiLCO-16 leads to the larger lifetime improvement and not DiLCO-32. In fact, DilCO-32 protocol puts in active mode a larger number of sensor nodes especially near the borders of the subdivisions. It means that distributing the protocol in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is a relevant way to maximize the lifetime of a network.
-\item {{\bf Execution Time}:} is described in chapter 3, section \ref{ch3:sec:04:04}.
-
-\item {{\bf Stopped simulation runs}:} is described in chapter 3, section \ref{ch3:sec:04:04}.
\end{enumerate}
+\subsection{Performance Analysis for Different Number of Primary Points}
+\label{ch4:sec:04:06}
+In this section, we study the performance of DiLCO~16 approach for different numbers of primary points. The objective of this comparison is to select the suitable primary point model to be used by a DiLCO protocol. In this comparison, DiLCO-16 protocol is used with five models, which are called Model-5 (it uses 5 primary points), Model-9, Model-13, Model-17, and Model-21.
-\subsection{Results analysis and Comparison }
-\label{ch4:sec:03:02}
-\subsection{Coverage ratio}
-\label{ch4:sec:03:02:01}
-Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes. We
-can notice that for the first thirty rounds both DESK and GAF provide a coverage
-which is a little bit better than the one of MuDiLCO.
+\begin{enumerate}[i)]
-This is due to the fact that, in comparison with MuDiLCO which uses optimization
-to put in SLEEP status redundant sensors, more sensor nodes remain active with
-DESK and GAF. As a consequence, when the number of rounds increases, a larger
-number of node failures can be observed in DESK and GAF, resulting in a faster
-decrease of the coverage ratio. Furthermore, our protocol allows to maintain a
-coverage ratio greater than 50\% for far more rounds. Overall, the proposed
-sensor activity scheduling based on optimization in MuDiLCO maintains higher
-coverage ratios of the area of interest for a larger number of rounds. It also
-means that MuDiLCO saves more energy, with less dead nodes, at most for several
-rounds, and thus should extend the network lifetime.
+\item {{\bf Coverage Ratio}}
+%\subsubsection{Coverage Ratio}
-\begin{figure}[ht!]
+Figure~\ref{Figures/ch4/R2/CR} shows the average coverage ratio for 150 deployed nodes.
+\parskip 0pt
+\begin{figure}[h!]
\centering
- \includegraphics[scale=0.5] {Figures/ch4/R1/CR.pdf}
-\caption{Average coverage ratio for 150 deployed nodes}
-\label{fig3}
+ \includegraphics[scale=0.8] {Figures/ch4/R2/CR.pdf}
+\caption{Coverage ratio for 150 deployed nodes}
+\label{Figures/ch4/R2/CR}
\end{figure}
+As can be seen in Figure~\ref{Figures/ch4/R2/CR}, at the beginning the models which use a larger number of primary points provide slightly better coverage ratios, but latter they are the worst.
+%Moreover, when the number of periods increases, coverage ratio produced by Model-9, Model-13, Model-17, and Model-21 decreases in comparison with Model-5 due to a larger time computation for the decision process for larger number of primary points.
+Moreover, when the number of periods increases, coverage ratio produced by all models decrease, but Model-5 is the one with the slowest decrease due to a smaller time computation of decision process for a smaller number of primary points.
+As shown in Figure ~\ref{Figures/ch4/R2/CR}, coverage ratio decreases when the number of periods increases due to dead nodes. Model-5 is slightly more efficient than other models, because it offers a good coverage ratio for a larger number of periods in comparison with other models.
-\subsection{Active sensors ratio}
-\label{ch4:sec:03:02:02}
-It is crucial to have as few active nodes as possible in each round, in order to
-minimize the communication overhead and maximize the network
-lifetime. Figure~\ref{fig4} presents the active sensor ratio for 150 deployed
-nodes all along the network lifetime. It appears that up to round thirteen, DESK
-and GAF have respectively 37.6\% and 44.8\% of nodes in ACTIVE status, whereas
-MuDiLCO clearly outperforms them with only 24.8\% of active nodes. After the
-thirty-fifth round, MuDiLCO exhibits larger numbers of active nodes, which agrees
-with the dual observation of higher level of coverage made previously.
-Obviously, in that case DESK and GAF have less active nodes, since they have
-activated many nodes at the beginning. Anyway, MuDiLCO activates the available
-nodes in a more efficient manner.
+\item {{\bf Active Sensors Ratio}}
+%\subsubsection{Active Sensors Ratio}
-\begin{figure}[ht!]
+Figure~\ref{Figures/ch4/R2/ASR} shows the average active nodes ratio for 150 deployed nodes.
+\begin{figure}[h!]
\centering
-\includegraphics[scale=0.5]{Figures/ch4/R1/ASR.pdf}
-\caption{Active sensors ratio for 150 deployed nodes}
-\label{fig4}
+\includegraphics[scale=0.8]{Figures/ch4/R2/ASR.pdf}
+\caption{Active sensors ratio for 150 deployed nodes }
+\label{Figures/ch4/R2/ASR}
\end{figure}
-\subsection{Stopped simulation runs}
-\label{ch4:sec:03:02:03}
-Figure~\ref{fig6} reports the cumulative percentage of stopped simulations runs
-per round for 150 deployed nodes. This figure gives the breakpoint for each method. DESK stops first, after approximately 45~rounds, because it consumes the
-more energy by turning on a large number of redundant nodes during the sensing
-phase. GAF stops secondly for the same reason than DESK. MuDiLCO overcomes
-DESK and GAF because the optimization process distributed on several subregions
-leads to coverage preservation and so extends the network lifetime. Let us
-emphasize that the simulation continues as long as a network in a subregion is
-still connected.
+The results presented in Figure~\ref{Figures/ch4/R2/ASR} show the superiority of the proposed Model-5, in comparison with the other models. The model with fewer number of primary points uses fewer active nodes than the other models.
+According to the results presented in Figure~\ref{Figures/ch4/R2/CR}, we observe that Model-5 continues to a larger number of periods with a better coverage ratio compared with other models. The advantage of Model-5 is to use fewer number of active nodes for each period compared with Model-9, Model-13, Model-17, and Model-21. This led to continuing for a larger number of periods and thus extending the network lifetime.
-\begin{figure}[ht!]
+\item {{\bf Stopped simulation runs}}
+%\subsubsection{The percentage of stopped simulation runs}
+
+Figure~\ref{Figures/ch4/R2/SR} illustrates the percentage of stopped simulation runs per period for 150 deployed nodes.
+
+\begin{figure}[h!]
\centering
-\includegraphics[scale=0.5]{Figures/ch4/R1/SR.pdf}
-\caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes }
-\label{fig6}
+\includegraphics[scale=0.8]{Figures/ch4/R2/SR.pdf}
+\caption{Percentage of stopped simulation runs for 150 deployed nodes }
+\label{Figures/ch4/R2/SR}
\end{figure}
-\subsection{Energy consumption} \label{subsec:EC}
-\label{ch4:sec:03:02:04}
-We measure the energy consumed by the sensors during the communication,
-listening, computation, active, and sleep status for different network densities
-and compare it with the two other methods. Figures~\ref{fig7}(a)
-and~\ref{fig7}(b) illustrate the energy consumption, considering different
-network sizes, for $Lifetime_{95}$ and $Lifetime_{50}$.
+When the number of primary points is increased, the percentage of the stopped simulation runs per period is increased. The reason behind the increase is the increasing number of dead sensors when the primary points increase. Model-5 is better than other models because it conserves more energy by turning on less sensors during the sensing phase and in the same time it preserves a good coverage for a larger number of periods in comparison with other models. Model~5 seems to be more suitable to be used in wireless sensor networks. \\
+
+
+\item {{\bf Energy Consumption}}
+%\subsubsection{The Energy Consumption}
+
+In this experiment, we study the effect of increasing the primary points to represent the area of the sensor on the energy consumed by the wireless sensor network for different network densities. Figures~\ref{Figures/ch4/R2/EC}(a) and~\ref{Figures/ch4/R2/EC}(b) illustrate the energy consumption for different network sizes for $Lifetime_{95}$ and $Lifetime_{50}$.
\begin{figure}[h!]
- \centering
- \begin{tabular}{cl}
- \parbox{9.5cm}{\includegraphics[scale=0.5]{Figures/ch4/R1/EC95.pdf}} & (a) \\
- \verb+ + \\
- \parbox{9.5cm}{\includegraphics[scale=0.5]{Figures/ch4/R1/EC50.pdf}} & (b)
- \end{tabular}
- \caption{Energy consumption for (a) $Lifetime_{95}$ and
- (b) $Lifetime_{50}$}
- \label{fig7}
-\end{figure}
+\centering
+ %\begin{multicols}{1}
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R2/EC95.pdf}\\~ ~ ~ ~ ~(a) \\
+%\vfill
+\includegraphics[scale=0.8]{Figures/ch4/R2/EC50.pdf}\\~ ~ ~ ~ ~(b)
-The results show that MuDiLCO is 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 status of the sensor node. Among the different
-versions of our protocol, the MuDiLCO-7 one consumes more energy than the other
-versions. This is easy to understand since the bigger the number of rounds and
-the number of sensors involved in the integer program are, the larger the time
-computation to solve the optimization problem is. To improve the performances of
-MuDiLCO-7, we should increase the number of subregions in order to have less
-sensors to consider in the integer program.
+%\end{multicols}
+\caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
+\label{Figures/ch4/R2/EC}
+\end{figure}
+We see from the results presented in both figures that the energy consumed by the network for each period increases when the number of primary points increases. Indeed, the decision for the optimization process requires more time, which leads to consuming more energy during the listening mode. The results show that Model-5 is the most competitive from the energy consumption point of view and the coverage ratio point of view. The other models have a high energy consumption due to the increase in the primary points. In fact, Model-5 is a good candidate to be used by wireless sensor network because it preserves a good coverage ratio with a suitable energy consumption in comparison with other models.
-\subsection{Execution time}
-\label{ch4:sec:03:02:05}
-We observe the impact of the network size and of the number of rounds on the
-computation time. Figure~\ref{fig77} gives the average execution times in
-seconds (needed to solve optimization problem) for different values of $T$. The original execution time is computed as described in chapter 3, section \ref{ch3:sec:04:02}.
+\item {{\bf Execution Time}}
+%\subsubsection{Execution Time}
-%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{fig77} for different network sizes.
+In this experiment, we study the impact of the increase in primary points on the execution time of DiLCO protocol. Figure~\ref{Figures/ch4/R2/T} gives the average execution times in seconds for the decision phase (solving of the optimization problem) during one period. The original execution time is computed as described in section \ref{ch4:sec:04:04}.
-\begin{figure}[ht!]
+\begin{figure}[h!]
\centering
-\includegraphics[scale=0.5]{Figures/ch4/R1/T.pdf}
+\includegraphics[scale=0.8]{Figures/ch4/R2/T.pdf}
\caption{Execution Time (in seconds)}
-\label{fig77}
+\label{Figures/ch4/R2/T}
\end{figure}
-As expected, the execution time increases with the number of rounds $T$ taken
-into account to schedule the sensing phase. The times obtained for $T=1,3$
-or $5$ seem bearable, but for $T=7$ they become quickly unsuitable for a sensor
-node, especially when the sensor network size increases. Again, we can notice
-that if we want to schedule the nodes activities for a large number of rounds,
-we need to choose a relevant number of subregions in order to avoid a complicated
-and cumbersome optimization. On the one hand, a large value for $T$ permits to
-reduce the energy-overhead due to the three pre-sensing phases, on the other
-hand a leader node may waste a considerable amount of energy to solve the
-optimization problem.
-
-\subsection{Network lifetime}
-\label{ch4:sec:03:02:06}
-The next two figures, Figures~\ref{fig8}(a) and \ref{fig8}(b), illustrate the
-network lifetime for different network sizes, respectively for $Lifetime_{95}$
-and $Lifetime_{50}$. Both figures show that the network lifetime increases
-together with the number of sensor nodes, whatever the protocol, thanks to the
-node density which results in more and more redundant nodes that can be
-deactivated and thus save energy. Compared to the other approaches, our MuDiLCO
-protocol maximizes the lifetime of the network. In particular the gain in
-lifetime for a coverage over 95\% is greater than 38\% when switching from GAF
-to MuDiLCO-3. The slight decrease that can be observed for MuDiLCO-7 in case
-of $Lifetime_{95}$ with large wireless sensor networks results from the
-difficulty of the optimization problem to be solved by the integer program.
-This point was already noticed in subsection \ref{subsec:EC} devoted to the
-energy consumption, since network lifetime and energy consumption are directly
-linked.
-
-\begin{figure}[t!]
- \centering
- \begin{tabular}{cl}
- \parbox{9.5cm}{\includegraphics[scale=0.5]{Figures/ch4/R1/LT95.pdf}} & (a) \\
- \verb+ + \\
- \parbox{9.5cm}{\includegraphics[scale=0.5]{Figures/ch4/R1/LT50.pdf}} & (b)
- \end{tabular}
- \caption{Network lifetime for (a) $Lifetime_{95}$ and
- (b) $Lifetime_{50}$}
- \label{fig8}
+They are given for the different primary point models and various numbers of sensors. We can see from Figure~\ref{Figures/ch4/R2/T}, that Model-5 has lower execution time in comparison with other models because it used the smaller number of primary points to represent the area of the sensor. Conversely, the other primary point models have presented higher execution times.
+Moreover, Model-5 has more suitable execution times and coverage ratio that lead to continue for a larger number of period extending the network lifetime. We think that a good primary point model is one that balances between the coverage ratio and the number of periods during the lifetime of the network.
+
+\item {{\bf Network Lifetime}}
+%\subsubsection{The Network Lifetime}
+
+Finally, we study the effect of increasing the primary points on the lifetime of the network.
+%In Figure~\ref{Figures/ch4/R2/LT95} and in Figure~\ref{Figures/ch4/R2/LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes.
+As highlighted by Figures~\ref{Figures/ch4/R2/LT}(a) and \ref{Figures/ch4/R2/LT}(b), the network lifetime obviously increases when the size of the network increases, with Model-5 that leads to the larger lifetime improvement. \\ \\
+
+Comparison shows that Model-5, which uses less number of primary points, is the best one because it is less energy consuming during the network lifetime. It is also the better one from the point of view of coverage ratio. Our proposed Model-5 efficiently prolongs the network lifetime with a good coverage ratio in comparison with other models. Therefore, we have chosen Model-5 for all the experiments presented thereafter.
+
+
+\begin{figure}[h!]
+\centering
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R2/LT95.pdf}\\~ ~ ~ ~ ~(a) \\
+
+\includegraphics[scale=0.8]{Figures/ch4/R2/LT50.pdf}\\~ ~ ~ ~ ~(b)
+
+\caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
+ \label{Figures/ch4/R2/LT}
+\end{figure}
+
+\end{enumerate}
+
+\subsection{Performance Comparison with other Approaches}
+\label{ch4:sec:04:07}
+
+Based on the results, conducted in the previous subsections, \ref{ch4:sec:04:02} and \ref{ch4:sec:04:03}, DiLCO-16 and DiLCO-32 protocols, both with Model-5, seem to be the best candidates to be compared with other approaches. The first approach is called DESK~\cite{DESK}, which is a fully distributed coverage algorithm. The second approach called GAF~\cite{GAF}, 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 time. \\ \\
+
+\begin{enumerate}[i)]
+\item {{\bf Coverage Ratio}}
+%\subsubsection{Coverage Ratio}
+
+The average coverage ratio for 150 deployed nodes is demonstrated in Figure~\ref{Figures/ch4/R3/CR}.
+\parskip 0pt
+\begin{figure}[h!]
+\centering
+ \includegraphics[scale=0.8] {Figures/ch4/R3/CR.eps}
+\caption{Coverage ratio for 150 deployed nodes}
+\label{Figures/ch4/R3/CR}
\end{figure}
+DESK and GAF provide a little better coverage ratio with 99.99\% and 99.91\% against 98.4\% and 98.9\% produced by DiLCO-16 and DiLCO-32 for the lowest number of periods. \\ \\ \\
+
+This is due to the fact that DiLCO protocol versions put in sleep mode redundant sensors thanks to the optimization (which lightly decreases the coverage ratio), while there are more active nodes in the case of DESK and GAF.
+
+Moreover, when the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases.
+%This is due to dead nodes. However, DiLCO-16 protocol and DiLCO-32 protocol maintain almost a good coverage.
+GAF exhibits in particular a fast decrease. Our protocols also provide decreasing coverage ratio, but far more better than those of DESK and GAF. DiLCO-16 and DiLCO-32 clearly outperform DESK and GAF for number of periods between 32 and 103.
+This is because they optimize the coverage and the lifetime in wireless sensor network by selecting the best representative sensor nodes to take the responsibility of coverage during the sensing phase.
+%, and this will lead to continuing for a larger number of periods and prolonging the network lifetime. Furthermore, although some nodes are dead, sensor activity scheduling of our protocol chooses other nodes to ensure the coverage of the area of interest.
+\item {{\bf Active Sensors Ratio}}
+%\subsubsection{Active Sensors Ratio}
+
+It is important to have as few active nodes as possible in each period, in order to minimize the energy consumption and maximize the network lifetime. Figure~\ref{Figures/ch4/R3/ASR} shows the average active nodes ratio for 150 deployed nodes.
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R3/ASR.eps}
+\caption{Active sensors ratio for 150 deployed nodes }
+\label{Figures/ch4/R3/ASR}
+\end{figure}
+
+The results presented in Figure~\ref{Figures/ch4/R3/ASR} show the superiority of the proposed DiLCO-16 protocol and DiLCO-32 protocol, in comparison with the other approaches. DESK and GAF have, respectively, 37.5 \% and 44.5 \% active nodes, whereas DiLCO-16 and DiLCO-32 protocols compete perfectly with only 23.7 \% and 25.8 \% active nodes for the first 14 periods. Then as the number of periods increases DiLCO-16 and DiLCO-32 protocols have larger number of active nodes in comparison with DESK and GAF, especially from period $35^{th}$ because they give a better coverage ratio than other approaches. We see that DESK and GAF have less number of active nodes beginning at the periods $35^{th}$ and $32^{th}$ because there are many dead nodes due to the high energy consumption by the redundant nodes during the previous sensing phases. \\
+
+
+\item {{\bf Stopped simulation runs}}
+%\subsubsection{The percentage of stopped simulation runs}
+%The results presented in this experiment, are to show the comparison of DiLCO-16 protocol and DiLCO-32 protocol with other two approaches from the point of view of stopped simulation runs per period.
+
+Figure~\ref{Figures/ch4/R3/SR} illustrates the percentage of stopped simulation runs per period for 150 deployed nodes.
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R3/SR.eps}
+\caption{Percentage of stopped simulation runs for 150 deployed nodes }
+\label{Figures/ch4/R3/SR}
+\end{figure}
+On the one hand, DESK is the approach which stops first because it consumes more energy for communication as well as it turns on a large number of redundant nodes during the sensing phase. On the other hand, DiLCO-16 protocol and DiLCO-32 protocol have less stopped simulation runs in comparison with DESK and GAF because they distribute the optimization on several subregions.
+% in order to optimize the coverage and the lifetime of the network by activating a less number of nodes during the sensing phase leading to extending the network lifetime and coverage preservation. The optimization effectively continues as long as a network in a subregion is still connected.
+
+
+\item {{\bf Energy Consumption}}
+%\subsubsection{The Energy Consumption}
+%In this experiment, we have studied the effect of the energy consumed by the wireless sensor network during the communication, computation, listening, active, and sleep modes for different network densities and compare it with other approaches.
+
+Figures~\ref{Figures/ch4/R3/EC}(a) and~\ref{Figures/ch4/R3/EC}(b) illustrate the energy consumption for different network sizes for $Lifetime_{95}$ and $Lifetime_{50}$.
+
+\begin{figure}[h!]
+\centering
+ %\begin{multicols}{1}
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R3/EC95.eps}\\~ ~ ~ ~ ~(a) \\
+%\vfill
+\includegraphics[scale=0.8]{Figures/ch4/R3/EC50.eps}\\~ ~ ~ ~ ~(b)
+
+%\end{multicols}
+\caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
+\label{Figures/ch4/R3/EC}
+\end{figure}
+
+
+DiLCO-16 protocol and DiLCO-32 protocol 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, the distribution of computation over the subregions greatly reduces the number of communications and the time of listening, thanks to the partitioning of the initial network into several independent subnetworks.
+
+
+\item {{\bf Network Lifetime}}
+%\subsubsection{The Network Lifetime}
+%In this experiment, we have observed the superiority of DiLCO-16 protocol and DiLCO-32 protocol against other two approaches in prolonging the network lifetime.
+
+%In figures~\ref{Figures/ch4/R3/LT95} and \ref{Figures/ch4/R3/LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes.
+
+\begin{figure}[h!]
+\centering
+% \begin{multicols}{0}
+\centering
+\includegraphics[scale=0.8]{Figures/ch4/R3/LT95.eps}\\~ ~ ~ ~ ~(a) \\
+%\hfill
+\includegraphics[scale=0.8]{Figures/ch4/R3/LT50.eps}\\~ ~ ~ ~ ~(b)
+
+%\end{multicols}
+\caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
+ \label{Figures/ch4/R3/LT}
+\end{figure}
+
+As highlighted by Figures~\ref{Figures/ch4/R3/LT}(a) and \ref{Figures/ch4/R3/LT}(b), the network lifetime obviously increases when the size of the network increases, with DiLCO-16 protocol and DiLCO-32 protocol which lead to maximize the lifetime of the network compared with other approaches.
+By choosing the best suited nodes, for each period, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next periods, DiLCO-16 protocol and DiLCO-32 protocol efficiently prolong the network lifetime.
+Comparison shows that DiLCO-16 protocol and DiLCO-32 protocol, which use distributed optimization over the subregions, are the best ones because they are robust to network disconnection during the network lifetime as well as they consume less energy in comparison with other approaches.
+%It also means that distributing the algorithm 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.
+
+
+\end{enumerate}
\section{Conclusion}
-\label{ch4:sec:04}
+\label{ch4:sec:05}
+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 longer 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 chapter 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 in electing 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 studied 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 improves the lifetime. The more subregions there are, the more robust the network is 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.
+
-We have addressed the problem of the coverage and of 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 we propose a protocol which
-optimizes coverage and lifetime performances in each subregion. Our protocol,
-called MuDiLCO (Multiround Distributed Lifetime Coverage Optimization) combines
-two efficient techniques: network leader election and sensor activity
-scheduling.
-
-The activity scheduling in each subregion works in periods, where each period
-consists of four phases: (i) Information Exchange, (ii) Leader Election, (iii)
-Decision Phase to plan the activity of the sensors over $T$ rounds, (iv) Sensing
-Phase itself divided into T rounds.
-
-Simulations results show the relevance of the proposed protocol in terms of
-lifetime, coverage ratio, active sensors ratio, energy consumption, execution
-time. Indeed, when dealing with large wireless sensor networks, a distributed
-approach, like the one we propose, allows to reduce the difficulty of a single
-global optimization problem by partitioning it in many smaller problems, one per
-subregion, that can be solved more easily. Nevertheless, results also show that
-it is not possible to plan the activity of sensors over too many rounds, because
-the resulting optimization problem leads to too high resolution times and thus to
-an excessive energy consumption.
