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+\usepackage{xspace}
+\def\bsq#1{%both single quotes
+\lq{#1}\rq}
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\begin{document}
\subsection{ Assumptions and Models}
\noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly distributed in a bounded sensor field is considered. The wireless sensors are deployed in high density to ensure initially a high coverage ratio of the interested area. We assume that all the sensor nodes are homogeneous in terms of communication, sensing, and processing capabilities and heterogeneous in term of energy supply. The location information is available to the sensor node either through hardware such as embedded GPS or through location discovery algorithms. We assume that each sensor node can directly transmit its measurements to a mobile sink node. For example, a sink can be an unmanned aerial vehicle (UAV) is flying regularly over the sensor field to collect measurements from sensor nodes. A mobile sink node collects the measurements and transmits them to the base station. 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 Our protocol is used the perimeter-coverage model which stated in ~\cite{huang2005coverage} as following: The sensor is said to be perimeter covered if all the points on its perimeter are covered by at least one sensor other than itself. According to this model, we named the intersections among the sensor nodes in the sensing field as intersection points. Instead of working with the coverage area, we consider for each sensor a set of intersection points which are determined by using perimeter-coverage model.
+\indent LiCO protocol is used the perimeter-coverage model which stated in ~\cite{huang2005coverage} as following: The sensor is said to be perimeter covered if all the points on its perimeter are covered by at least one sensor other than itself.
+%According to this model, we named the intersections among the sensor nodes in the sensing field as intersection points. Instead of working with the coverage area, we consider for each sensor a set of intersection points which are determined by using perimeter-coverage model.
+Figure~\ref{pcmfig} illuminates the perimeter coverage of the sensor node 0, where L refers to left point of the segment and R refers to right point of the segment.
+
+\begin{figure}[ht!]
+\centering
+\includegraphics[width=75mm]{pcm.pdf}
+\caption{Perimeter coverage of sensor node 0}
+\label{pcmfig}
+\end{figure}
+
+In order to determine the segments of each sensor node, which are perimeter covered by the neighboring sensors, figure~\ref{twosensors} demonstrates the way of locating the left and right points of a segment of the sensor node I covered by a sensor node J. This figure supposed that the neighbor sensor node J is located on the west of a sensor I. It Supposed that the two sensor nodes I and J are located in the positions $(I_x,I_y)$ and $(J_x,J_y)$, respectively. The distance between I and J is computed by $Dist(I,J) = \sqrt{\vert I_x - J_x \vert^2 + \vert I_y - J_y \vert^2}$ . The angle $\alpha = arccos \left(\dfrac{Dist(I,J)}{2R_s} \right) $. So, the $\pi - \alpha$ and the $\pi + \alpha$ of sensor I refers to the left and right points of the segment, which is perimeter covered by sensor node J. If the arch segment of sensor I is located within the angle $[\pi - \alpha,\pi + \alpha]$, this means it is perimeter covered by sensor node J. The left and right points of each segment are put it on the line segment $[0,2\pi]$ and then are sorted in an ascending order so as to determine the level of the perimeter coverage for each left and right point of a segment.
+\begin{figure}[ht!]
+\centering
+\includegraphics[width=75mm]{twosensors.jpg}
+\caption{Locating the segment of I$\rq$s perimeter covered by J.}
+\label{twosensors}
+\end{figure}
+
+\begin{figure}[ht!]
+\centering
+\includegraphics[width=75mm]{expcm.pdf}
+\caption{Perimeter segment coverage levels for sensor node 0.}
+\label{expcm}
+\end{figure}
+
+For example, consider the sensor node 0 in figure~\ref{pcmfig}, which has 9 neighbors. Figure~\ref{expcm} shows the perimeter coverage level for all left and right points of a segments that covered by a neighboring sensor nodes. Based on the figure~\ref{expcm}, the set of sensors for each left and right point of the segments illustrated in figure~\ref{ex2pcm} for the sensor node 0.
+
+\begin{figure}[ht!]
+\centering
+\includegraphics[width=90mm]{ex2pcm.jpg}
+\caption{The set of sensors for each left or right point of segments for sensor node 0.}
+\label{ex2pcm}
+\end{figure}
+
+The optimization algorithm that used by LiCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1.
+
+In the case of sensor node, which has a part of its sensing range outside the the border of the WSN sensing field as in figure~\ref{ex4pcm}, the perimeter coverage level for this segment is set to $\infty$, and the left and right points of the segments will not be taken into account by the optimization algorithm.
+\begin{figure}[ht!]
+\centering
+\includegraphics[width=75mm]{ex4pcm.jpg}
+\caption{Part of sensing range outside the the border of WSN sensing field.}
+\label{ex4pcm}
+\end{figure}
+Figure~\ref{ex5pcm} gives an example to compute the perimeter coverage levels for the left and right points of the segments for a sensor node 0, which has a part of its sensing range exceeding the border of the sensing field of WSN, and it has a six neighbors. In figure~\ref{ex5pcm}, the sensor node 0 has two segments outside the border of the network sensing field, so the left and right points of the two segments called -1L, -1R, -2L, and -2R.
+\begin{figure}[ht!]
+\centering
+\includegraphics[width=75mm]{ex5pcm.jpg}
+\caption{Perimeter coverage levels for sensor node has a part of its sensing range outside the border.}
+\label{ex5pcm}
+\end{figure}
+
\subsection{The Main Idea}
\noindent The area of interest can be divided using the
\If{$ s_k.ID $ is Not previously selected as a Leader }{
\emph{ Execute the perimeter coverage model}\;
- % \emph{ Determine the intersection points using perimeter coverage model}\;
+ % \emph{ Determine the segment points using perimeter coverage model}\;
}
\If{$ (s_k.ID $ is the same Previous Leader) AND (K.CurrentSize = K.PreviousSize)}{
\noindent Algorithm 1 gives a brief description of the protocol applied by each sensor node (denoted by $s_k$ for a sensor node indexed by $k$). In this algorithm, the K.CurrentSize and K.PreviousSize refer to the current size and the previous size of sensor nodes in the subregion respectively.
Initially, the sensor node checks its remaining energy in order to participate in the current period. Each sensor node determines its position and its subregion based Embedded GPS or Location Discovery Algorithm. After that, all the sensors collect position coordinates, remaining energy $RE_k$, sensor node id, and the number of its one-hop live neighbors during the information exchange.
-After the cooperation among the sensor nodes in the same subregion, the leader will be elected in distributed way, where each sensor node and based on it's information decide who is the leader. The selection criteria for the leader in order of priority are: larger number of neighbors, larger remaining energy, and then in case of equality, larger index. Thereafter, if the sensor node is leader, it will execute the perimeter-coverage model for each sensor in the subregion in order to determine the intersection points which would be used in the next stage by the optimization algorithm of the LiCO protocol. Every sensor node is selected as a leader, it is executed the perimeter coverage model only one time during it's life in the network. The leader has the responsibility of applying the integer program algorithm (see section~\ref{cp}), which provides a set of sensors planned to be active in the sensing stage. As leader, it will send an Active-Sleep packet to each sensor in the same subregion to inform it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing stage.
+After the cooperation among the sensor nodes in the same subregion, the leader will be elected in distributed way, where each sensor node and based on it's information decide who is the leader. The selection criteria for the leader in order of priority are: larger number of neighbors, larger remaining energy, and then in case of equality, larger index. Thereafter, if the sensor node is leader, it will execute the perimeter-coverage model for each sensor in the subregion in order to determine the segment points which would be used in the next stage by the optimization algorithm of the LiCO protocol. Every sensor node is selected as a leader, it is executed the perimeter coverage model only one time during it's life in the network. The leader has the responsibility of applying the integer program algorithm (see section~\ref{cp}), which provides a set of sensors planned to be active in the sensing stage. As leader, it will send an Active-Sleep packet to each sensor in the same subregion to inform it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing stage.
\section{Lifetime Coverage problem formulation}
\label{cp}
-In this section, the coverage model are mathematically formulated, where the objective is to find the maximum number of non-disjoint sets of sensor nodes such that each set cover can assure the coverage for the whole region so as to extend the network lifetime in WSN. Our model will use the intersection points which are produced by using the perimeter coverage model~\cite{huang2005coverage} in order to optimize the lifetime coverage in each subregion.
-We defined some parameters, which are related to our optimization model. In our model, we consider binary variables $X_{k}$, which determine the activation of sensor $k$ in the sensing round. We also consider the intersection points as targets.
-
+In this section, the coverage model is mathematically formulated.
+For convenience, the notations are described first.
+%Then the lifetime problem of sensor network is formulated.
+\noindent $S :$ the set of all sensors in the network.\\
+\noindent $A :$ the set of alive sensors within $S$.\\
+%\noindent $I :$ the set of segment points.\\
+\noindent $I_j :$ the set of coverage intervals (CI) for sensor $j$.\\
-\noindent In this paper, let us define some parameters, which are used in our protocol.
-%the set of intersection points is denoted by $I$, the set of all sensors in the network by $J$, and the set of alive sensors within $J$ by $K$.
+\noindent For a coverage interval $i$, let $a^j_{ik}$ denote the indicator function of whether the sensor $k$ is involved in the coverage interval $i$ of sensor $j$, that is:
-\noindent $J :$ the set of all sensors in the network.\\
-\noindent $K :$ the set of alive sensors within $J$.\\
-%\noindent $I :$ the set of intersection points.\\
-\noindent $I_j :$ the set of intersection points for sensor $j$.\\
-
-\noindent \begin{equation}
-X_{k} = \left \{
-\begin{array}{l l}
- 1& \mbox{if sensor $k$ is active,} \\
- 0 & \mbox{otherwise.}\\
+\begin{equation}
+a^j_{ik} = \left \{
+\begin{array}{lll}
+ 1 & \mbox{if the sensor $k$ is involved in the } \\
+ & \mbox{coverage interval $i$ of sensor $j$}, \\
+ 0 & \mbox{Otherwise.}\\
\end{array} \right.
-%\label{eq11}
+%\label{eq12}
\notag
\end{equation}
+%, where the objective is to find the maximum number of non-disjoint sets of sensor nodes such that each set cover can assure the coverage for the whole region so as to extend the network lifetime in WSN. Our model uses the PCL~\cite{huang2005coverage} in order to optimize the lifetime coverage in each subregion.
+%We defined some parameters, which are related to our optimization model. In our model, we consider binary variables $X_{k}$, which determine the activation of sensor $k$ in the sensing round $k$. .
+We consider binary variables $X_{k}$ ($X_k=1$ if the sensor $k$ is active or 0 otherwise), which determine the activation of sensor $k$ in the sensing phase. We define the integer variable $M^j_i$ which measures the undercoverage for the coverage interval $i$ for sensor $j$. In the same way, we define the integer variable $V^j_i$, which measures the overcoverage for the coverage interval $i$ for sensor $j$. If we decide to sustain a level of coverage equal to $l$ all along the perimeter of the sensor $j$, we have to ensure that at least $l$ sensors involved in each coverage interval $i$ ($i \in I_j$) of sensor $j$ are active. According to the previous notations, the number of active sensors in the coverage interval $i$ of sensor $j$ is given by $\sum_{k \in K} a^j_{ik} X_k$. To extend the network lifetime, the objective is to active a minimal number of sensors in each period to ensure the desired coverage level. As the number of alive sensors decreases, it becomes impossible to satisfy the level of coverage for all covergae intervals. We uses variables $M^j_i$ and $V^j_i$ as a measure of the deviation between the desired number of active sensors in a coverage interval and the effective number of active sensors. And we try to minimize these deviations, first to force the activation of a minimal number of sensors to ensure the desired coverage level, and if the desired level can not be completely satisfied, to reach a coverage level as close as possible that the desired one.
-\noindent $M^j_i (undercoverage): $ integer value $\in \mathbb{N}$ for intersection point $i$ of sensor $j$.
-\noindent $V^j_i (overcoverage): $ integer value $\in \mathbb{N}$ for intersection point $i$ of sensor $j$.
+
+%A system of linear constraints is imposed to attempt to keep the coverage level in each coverage interval to within specified PCL. Since it is physically impossible to satisfy all constraints simultaneously, each constraint uses a variable to either record when the coverage level is achieved, or to record the deviation from the desired coverage level. These additional variables are embedded into an objective function to be minimized.
+
+%\noindent In this paper, let us define some parameters, which are used in our protocol.
+%the set of segment points is denoted by $I$, the set of all sensors in the network by $J$, and the set of alive sensors within $J$ by $K$.
+
+
+%\noindent \begin{equation}
+%X_{k} = \left \{
+%\begin{array}{l l}
+ % 1& \mbox{if sensor $k$ is active,} \\
+% 0 & \mbox{otherwise.}\\
+%\end{array} \right.
+%\label{eq11}
+%\notag
+%\end{equation}
+
+%\noindent $M^j_i (undercoverage): $ integer value $\in \mathbb{N}$ for segment point $i$ of sensor $j$.
+
+%\noindent $V^j_i (overcoverage): $ integer value $\in \mathbb{N}$ for segment point $i$ of sensor $j$.
-\noindent For an intersection point $i$, let $a^j_{ik}$ denote the indicator function of whether the sensor $k$ is involved in the intersection point $i$ of sensor $j$, that is:
-\begin{equation}
-a^j_{ik} = \left \{
-\begin{array}{lll}
- 1 & \mbox{If the sensor $k$ is involved in the } \\
- & \mbox{intersection point $i$ of sensor $j$}, \\
- 0 & \mbox{Otherwise.}\\
-\end{array} \right.
-%\label{eq12}
-\notag
-\end{equation}
\noindent Our coverage optimization problem can be mathematically formulated as follows: \\
%Objective:
\begin{equation} \label{eq:ip2r}
\left \{
\begin{array}{ll}
-\min \sum_{j \in J} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
+\min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
\textrm{subject to :}&\\
-\sum_{k \in K} ( a^j_{ik} ~ X_{k}) + M^j_i \geq 1 \\
+\sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in S\\
%\label{c1}
-\sum_{k \in K} ( a^j_{ik} ~ X_{k}) - V^j_i \leq 1 \\
+\sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in S\\
% \label{c2}
% \Theta_{p}\in \mathbb{N}, &\forall p \in P\\
% U_{p} \in \{0,1\}, &\forall p \in P\\
-X_{k} \in \{0,1\}, &\forall k \in K
+X_{k} \in \{0,1\}, \forall k \in A
\end{array}
\right.
\end{equation}
-The first group of constraints indicates that some intersection points $i$
-should be covered by at least one sensor node 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 intersection 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 $\alpha$ and $\beta$ must be properly chosen so as to
-guarantee that the maximum number of intersection points are covered during each round.
+
+\noindent $\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the
+relative importance of satisfying the associated
+level of coverage. For example, weights associated with coverage intervals of a specified part of a region
+may be given a relatively
+larger magnitude than weights associated
+with another region. This kind of integer program is inspired from the model developed for brachytherapy treatment planning for optimizing dose distribution \ref{0031-9155-44-1-012}. The integer program must be solved by the leader in each subregion at the beginning of each sensing phase, whenever the environment has changed (new leader, death of some sensors). Note that the number of constraints in the model is constant (constraints of coverage expressed for all sensors), whereas the number of variables $X_k$ decreases over periods, since we consider only alive sensors (sensors with enough energy to be alive during one sensing phase) in the model.
\section{\uppercase{PERFORMANCE EVALUATION AND ANALYSIS}}
\end{table}
Simulations with five different node densities going from 100 to 250~nodes were
performed considering each time 25~randomly generated networks, to obtain
-experimental results which are relevant.All simulations are repeated 25 times and the results are averaged. 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.
+experimental results which are relevant. All simulations are repeated 25 times and the results are averaged. 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.
Each node has an initial energy level, in Joules, which is randomly drawn in the
interval $[500-700]$. If it's energy provision reaches a value below the
network lifetime. The Active Sensors Ratio is defined as follows:
\begin{equation*}
\scriptsize
-\mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$A_r^p$}}{\mbox{$S$}} \times 100 .
+\mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$A_r$}}{\mbox{$S$}} \times 100 .
\end{equation*}
-Where: $A_r^t$ is the number of active sensors in the subregion $r$ during period $p$ in the current sensing stage, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.
+Where: $A_r^t$ is the number of active sensors in the subregion $r$ in the current sensing stage, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.
%\end{enumerate}
\subsection{Simulation Results}
-In this section, we present the simulation results of LiCO protocol and the other protocols using a discrete event simulator OMNeT++ \cite{varga} to run different series of simulations. We implemented all protocols precisely 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, the original execution time on the laptop is multiplied by 2944.2 $\left(\frac{35330}{2} \times \frac{1}{6} \right)$ so as to use it by the energy consumption model especially, after the computation and listening.
+In this section, we present the simulation results of LiCO protocol and the other protocols using a discrete event simulator OMNeT++ \cite{varga} to run different series of simulations. We implemented all protocols precisely 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, the original execution time on the laptop is multiplied by 2944.2 $\left(\frac{35330}{2} \times \frac{1}{6} \right)$ so as to use it by the energy consumption model especially, after the computation and listening. Employing the modeling language ????\ref{}, the associated integer program instance is generated 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.
We compared LiCO protocol to three other approaches: the first, called DESK and proposed by ~\cite{ChinhVu} is a fully distributed coverage algorithm; the second, called GAF ~\cite{xu2001geography}, consists in dividing the region
into fixed squares. During the decision phase, in each square, one sensor is
-chosen to remain active during the sensing phase; the third, DiLCO protocol~\cite{Idrees2}, which is improved version on the work in ~\cite{idrees2014coverage}.
+chosen to remain active during the sensing phase; the third, DiLCO protocol~\cite{Idrees2} is an improved version on the work presented in ~\cite{idrees2014coverage}. DNote that the LiCO protocol is based on the same framework as that of DiLCO. For thes two protocols, the division of the region of interest in 16 subregions was chosen since it produces the best results. The difference between the two protocols relies on the use of the integer programming to provide the set of sensors that have to be actived in each sensing phase. Whereas DilCO protocol tries to satisfy the coverage of a set of primary points, LiCO protocol tries to reach a desired level of coverage $l$ for each sensor's perimeter. In the experimentations, we chose a level of coverage equal to 1 ($l=1$).
\subsubsection{\textbf{Coverage Ratio}}
-In this experiment, Figure~\ref{fig333} shows the average coverage ratio for 150 deployed nodes.
-
-\parskip 0pt
-\begin{figure}[h!]
-\centering
- \includegraphics[scale=0.5] {R/CR.pdf}
-\caption{The coverage ratio for 150 deployed nodes}
-\label{fig333}
-\end{figure}
-
-It is shown that DESK, GAF, and LiCO provides a little better coverage ratio with 99.99\%, 99.91\%, and 99.25\% against 99.02\% produced by DiLCO-16 for the lowest number of rounds. This is due to the fact that DiLCO protocol 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, and a little higher in comparison with the optimization algorithm used by LiCO.
-Moreover, when the number of rounds increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO-16 protocol maintains almost a good coverage from the round 31 to the round 50 and it is close to LiCO protocol. This is because it optimizes the coverage and the lifetime in WSN based on the primary points by selecting the best representative sensor nodes for the sensing stage. The coverage ratio of LiCO Protocol seems to be better than other approaches starting from the round 50 because the optimization algorithm used by LiCO has been optimized the lifetime coverage based on the perimeter coverage model, so it provided acceptable coverage for a larger number of periods and prolonging the network lifetime based on the perimeter of the sensor nodes in each subregion of WSN. Although some nodes are dead, sensor activity scheduling based optimization of LiCO selected another nodes to ensure the coverage of the area of interest.
-
-Figure~\ref{figCR200} represents the average coverage ratio provided by
-DiLCO-16, DESK, GAF, and LiCO for 200 deployed nodes while varying the number of periods. The same observation is made as in Figure~\ref{fig333}, i.e. DiLCO-16 showed a good coverage in the beginning then when the number of periods increases, the coverage ratio decreases due to died sensor nodes. Meanwhile, thanks to sensor activity scheduling based new optimization model, which is used by LiCO protocol to ensure a longer lifetime coverage in comparison with other approaches.
+Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes obtained with the four methods.
\parskip 0pt
\begin{figure}[h!]
\centering
- \includegraphics[scale=0.5] {R/CR200.pdf}
+ \includegraphics[scale=0.5] {R/CR.eps}
\caption{The coverage ratio for 200 deployed nodes}
-\label{figCR200}
+\label{fig333}
\end{figure}
+DESK, GAF, and DiLCO provides a little better coverage ratio with 99.99\%, 99.91\%, and 99.02\% against 98.76\% produced by LiCO for the lowest number of periods. This is due to the fact that DiLCO protocol put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more active nodes in the case of others methods. But when the number of periods exceeds 70 periods, it clearly appears that LiCO provides a better coverage ratio and keeps a coverage ratio greater than 50\% for longer periods (15 more compared to DiLCO, 40 more compared to DESK).
-\subsubsection{\textbf{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{fig444} shows the average active nodes ratio for 150 deployed nodes.
-
-\begin{figure}[h!]
-\centering
-\includegraphics[scale=0.5]{R/ASR.pdf}
-\caption{The active sensors ratio for 150 deployed nodes }
-\label{fig444}
-\end{figure}
+%When the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to LiCO protocol. The coverage ratio of LiCO protocol is better than other approaches from the period 64.
-We can observe that DESK and GAF have 37.62 \% and 44.77 \% active nodes for the first fourteen rounds and DiLCO-16 and LiCO protocols competes perfectly with only 24.82 \% and 29.70 \% active nodes for the first 14 rounds. Then as the number of rounds increases our LiCO protocol has a lower number of active nodes in comparison with DiLCO-16, DESK and GAF, especially from the round $15^{th}$ because it optimizes the lifetime coverage into the subregion based on the perimeter coverage model, which made LiCO improves the coverage ratio in comparison with other approaches.
+%because the optimization algorithm used by LiCO has been optimized the lifetime coverage based on the perimeter coverage model, so it provided acceptable coverage for a larger number of periods and prolonging the network lifetime based on the perimeter of the sensor nodes in each subregion of WSN. Although some nodes are dead, sensor activity scheduling based optimization of LiCO selected another nodes to ensure the coverage of the area of interest. i.e. DiLCO-16 showed a good coverage in the beginning then LiCO, when the number of periods increases, the coverage ratio decreases due to died sensor nodes. Meanwhile, thanks to sensor activity scheduling based new optimization model, which is used by LiCO protocol to ensure a longer lifetime coverage in comparison with other approaches.
-The variation of average active sensor nodes
-against the number of periods for 200 deployed sensors is illuminated in figure~\ref{figASR200}. Observe that the number of active nodes, which are provided by DiLCO-16 is lower than the case of LiCO protocol (17.92 of active nodes against 21.8 respectively, for first $17^{th}$ periods). After that, LiCO protocol generates a lower number of active sensors using our optimization algorithm that contributed in extend the lifetime coverage as long as possible.
+\subsubsection{\textbf{Active Sensors Ratio}}
+Having active nodes as few as possible in each period is essential in order to minimize the energy consumption and so maximize the network lifetime. Figure~\ref{fig444} shows the average active nodes ratio for 200 deployed nodes.
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.5]{R/ASR200.pdf}
+\includegraphics[scale=0.5]{R/ASR.eps}
\caption{The active sensors ratio for 200 deployed nodes }
-\label{figASR200}
+\label{fig444}
\end{figure}
-
-%We see that the DESK and GAF have less number of active nodes beginning at the rounds $35^{th}$ and $32^{th}$ because there are many nodes are died due to the high energy consumption by the redundant nodes during the sensing phase.
+We observe that DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen rounds and DiLCO and LiCO protocols compete perfectly with only 17.92 \% and 20.16 \% active nodes during the same time interval. As the number of periods increases, LiCO protocol has a lower number of active nodes in comparison with the three other approaches, while keeping of greater coverage ratio as shown in figure \ref{fig333}.
\subsubsection{\textbf{The Energy Consumption}}
-In this experiment, we study the effect of the energy consumed by the WSN during the communication, computation, listening, active, and sleep modes for different network densities and compare it with other approaches. Figures~\ref{fig3EC95} and ~\ref{fig3EC50} illustrate the energy consumption for different network sizes for $Lifetime95$ and $Lifetime50$.
+We study the effect of the energy consumed by the WSN during the communication, computation, listening, active, and sleep modes for different network densities and compare it for the four approaches. Figures~\ref{fig3EC95} and ~\ref{fig3EC50} illustrate the energy consumption for different network sizes and for $Lifetime95$ and $Lifetime50$.
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.5]{R/EC95.pdf}
+\includegraphics[scale=0.5]{R/EC95.eps}
\caption{The Energy Consumption per period with $Lifetime_{95}$}
\label{fig3EC95}
\end{figure}
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.5]{R/EC50.pdf}
+\includegraphics[scale=0.5]{R/EC50.eps}
\caption{The Energy Consumption per period with $Lifetime_{50}$}
\label{fig3EC50}
\end{figure}
-The results show that our LiCO protocol is the most competitive from the energy consumption point of view. As shown in figures Figures~\ref{fig3EC95} and ~\ref{fig3EC50}, LiCO consumes less energy especially when the network size increases because it puts in sleep mode less active sensor number as possible in most periods of the network lifetime. The optimization algorithm, which used by our LiCO protocol, was optimized the lifetime coverage efficiently based on the perimeter coverage model.
+The results show that our LiCO protocol is the most competitive from the energy consumption point of view. As shown in figures~\ref{fig3EC95} and ~\ref{fig3EC50}, LiCO consumes much less energy than the three other methods. One might think that the resolution of the integer program is too costly in energy, but the results show that it is very beneficial to lose a bit of time in the selection of sensors to activate. Indeed this optimization program allows to reduce significantly the number of active sensors and so the energy consumption while keeping a good coverage level.
+%The optimization algorithm, which used by LiCO protocol, was improved the lifetime coverage efficiently based on the perimeter coverage model.
- 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 other approaches have a high energy consumption due to activating a larger number of sensors. 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.
%\subsubsection{Execution Time}
\subsubsection{\textbf{The Network Lifetime}}
-In this experiment, we are observed the superiority of LiCO and DiLCO-16 protocols against other two approaches in prolonging the network lifetime. In figures~\ref{fig3LT95} and \ref{fig3LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes.
+We observe the superiority of LiCO and DiLCO protocols against other two approaches in prolonging the network lifetime. In figures~\ref{fig3LT95} and \ref{fig3LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes.
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.5]{R/LT95.pdf}
+\includegraphics[scale=0.5]{R/LT95.eps}
\caption{The Network Lifetime for $Lifetime_{95}$}
\label{fig3LT95}
\end{figure}
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.5]{R/LT50.pdf}
+\includegraphics[scale=0.5]{R/LT50.eps}
\caption{The Network Lifetime for $Lifetime_{50}$}
\label{fig3LT50}
\end{figure}
-As highlighted by figures~\ref{fig3LT95} and \ref{fig3LT50}, the network lifetime obviously increases when the size of the network increases, with our LiCO and DiLCO-16 protocols that leads to maximize the lifetime of the network compared with other approaches.
+As highlighted by figures~\ref{fig3LT95} and \ref{fig3LT50}, the network lifetime obviously increases when the size of the network increases, and it is clearly larger with DiLCO and LiCO protocols compared with the two other methods. For instance, for a network of 300 sensors, the coverage ratio is greater than 50\% about two times longer with LiCO compared to DESK method.
-By choosing the best suited nodes, for each round, 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 rounds, LiCO protocol efficiently prolonged the network lifetime especially for a coverage ratio greater than $50 \%$, whilst it stayed very near to DiLCO-16 protocol for $95 \%$. Figure~\ref{figLTALL} introduces the comparisons of the lifetime coverage for different coverage ratios between LiCO and DiLCO-16 protocols.
+%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 rounds, LiCO protocol efficiently prolonged the network lifetime especially for a coverage ratio greater than $50 \%$, whilst it stayed very near to DiLCO-16 protocol for $95 \%$.
+Figure~\ref{figLTALL} introduces the comparisons of the lifetime coverage for different coverage ratios for LiCO and DiLCO protocols.
We denote by Protocol/50, Protocol/80, Protocol/85, Protocol/90, and Protocol/95 the amount of time during which the network can satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$ respectively.
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.5]{R/LTALL.pdf}
+\includegraphics[scale=0.5]{R/LTa.eps}
\caption{The Network Lifetime for different coverage ratios}
\label{figLTALL}
\end{figure}
-Comparison shows that our LiCO protocol, which are used distributed optimization over the subregions, is the more relevance one because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. LiCO protocol gave acceptable coverage ratio for a larger number of periods using new optimization algorithm that based on a perimeter coverage model. 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.
+%Comparison shows that LiCO protocol, which are used distributed optimization over the subregions, is the more relevance one for most coverage ratios and WSN sizes because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. LiCO protocol gave acceptable coverage ratio for a larger number of periods using new optimization algorithm that based on a perimeter coverage model. 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.
\section{\uppercase{Conclusion and Future Works}}
\label{sec:Conclusion and Future Works}
-In this paper, we have studied the problem of lifetime coverage optimization in
-WSNs. To cope with this problem, the area of interest is divided into a smaller subregions using divide-and-conquer method, and then a LiCO protocol for optimizing the lifetime coverage in each subregion. LiCO protocol combines two efficient techniques: the first, network
-leader election, which executes the perimeter coverage model (only one time), the optimization algorithm, and sending the schedule produced by the optimization algorithm to other nodes in the subregion ; the second, sensor activity scheduling based optimization in which a new lifetime coverage optimization model is proposed. The main challenges include how to select the most efficient leader in each subregion and the best schedule of sensor nodes that will optimize the network lifetime coverage
-in the subregion. The network lifetime coverage in each subregion is divided into
-periods, each period consists of four stages: (i) Information Exchange,
-(ii) Leader Election, (iii) a Decision based new optimization model in order to
-select the nodes remaining active for the last stage, and (iv) Sensing.
-The simulation results show that LiCO is is more energy-efficient than other approaches, with respect to lifetime, coverage ratio, active sensors ratio, and energy consumption. Indeed, when dealing with large and dense WSNs, a distributed optimization approach on the subregions of WSN like the one we are proposed 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.
-
-Our future work is four-fold: the first, we plan to extend a lifetime coverage optimization problem in order to computes all active sensor schedules in only one step for many periods;
+In this paper we have studied the problem of lifetime coverage optimization in
+WSNs. We designed a protocol LiCO that schedules node activities (wakeup and sleep) with the objective of maintaining a good coverage ratio while maximizing the network lifetime. This protocol is applied on each subregion of the area of interest. It works in periods and is based on the resolution of an integer program to select the subset of sensors operating in active mode for each period. Our work is original in so far as it proposes for the first time an integer program scheduling the activation of sensors based on their perimeter coverage level instead of using a set of targets/points to be covered.
+
+ We carried out severals simulations to evaluate the proposed protocol.
+
+
+%To cope with this problem, the area of interest is divided into a smaller subregions using divide-and-conquer method, and then a LiCO protocol for optimizing the lifetime coverage in each subregion. LiCO protocol combines two efficient techniques: network
+%leader election, which executes the perimeter coverage model (only one time), the optimization algorithm, and sending the schedule produced by the optimization algorithm to other nodes in the subregion ; the second, sensor activity scheduling based optimization in which a new lifetime coverage optimization model is proposed. The main challenges include how to select the most efficient leader in each subregion and the best schedule of sensor nodes that will optimize the network lifetime coverage
+%in the subregion.
+%The network lifetime coverage in each subregion is divided into
+%periods, each period consists of four stages: (i) Information Exchange,
+%(ii) Leader Election, (iii) a Decision based new optimization model in order to
+%select the nodes remaining active for the last stage, and (iv) Sensing.
+The simulation results show that LiCO is is more energy-efficient than other approaches, with respect to lifetime, coverage ratio, active sensors ratio, and energy consumption.
+%Indeed, when dealing with large and dense WSNs, a distributed optimization approach on the subregions of WSN like the one we are proposed 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.
+
+We plan to extend a lifetime coverage optimization problem in order to computes all active sensor schedules in only one step for many periods;
the second, we focus on extend our protocol and optimization algorithm to take into account the heterogeneous sensors, which do not have the same energy, processing, sensing and communication capabilities;
-the third, we are investigating new optimization model based on the sensing range so as to maximize the lifetime coverage in WSN;
+%the third, we are investigating new optimization model based on the sensing range so as to maximize the lifetime coverage in WSN;
Finally, our final goal is to implement our protocol using a sensor-testbed to evaluate their performance in real world applications.
\section*{\uppercase{Acknowledgements}}
