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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 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 segment 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 segment points as targets.
\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 $K$.
+%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 $J :$ 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 $I :$ the set of segment points.\\
+\noindent $I_j :$ the set of segment points for sensor $j$.\\
\noindent \begin{equation}
X_{k} = \left \{
\notag
\end{equation}
-\noindent $M^j_i (undercoverage): $ integer value $\in \mathbb{N}$ for intersection point $i$ of sensor $j$.
+\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 intersection 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:
+\noindent For an segment point $i$, let $a^j_{ik}$ denote the indicator function of whether the sensor $k$ is involved in the segment 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 $j$}, \\
+ & \mbox{segment point $i$ of sensor $j$}, \\
0 & \mbox{Otherwise.}\\
\end{array} \right.
%\label{eq12}
\right.
\end{equation}
-The first group of constraints indicates that some intersection points $i$
+The first group of constraints indicates that some segment 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
+objectives. First, we limit the overcoverage of segment 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.
+guarantee that the maximum number of segment points are covered during each round.
\section{\uppercase{PERFORMANCE EVALUATION AND ANALYSIS}}
chosen to remain active during the sensing phase; the third, DiLCO protocol~\cite{Idrees2}, which is improved version on the work in ~\cite{idrees2014coverage}.
\subsubsection{\textbf{Coverage Ratio}}
-In this experiment, Figure~\ref{fig333} shows the average coverage ratio for 150 deployed nodes.
+In this experiment, Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes.
\parskip 0pt
\begin{figure}[h!]
\centering
- \includegraphics[scale=0.5] {R/CR.pdf}
-\caption{The coverage ratio for 150 deployed nodes}
+ \includegraphics[scale=0.5] {R/CR.eps}
+\caption{The coverage ratio for 200 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.
+It is shown that DESK, GAF, and DiLCO-16 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 rounds. This is due to the fact that DiLCO-16 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.
-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.
-
-\parskip 0pt
-\begin{figure}[h!]
-\centering
- \includegraphics[scale=0.5] {R/CR200.pdf}
-\caption{The coverage ratio for 200 deployed nodes}
-\label{figCR200}
-\end{figure}
+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 63 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. LiCO protocol put in sleep mode a higher number of redundant sensors starting from the round 19 using the new optimization model. The coverage ratio of LiCO Protocol seems to be better than other approaches starting from the round 64 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.
\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.
+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 200 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}
-
-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.
-
-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.
-
-
-\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.
+From figure~~\ref{fig444}, We observed that DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen rounds and DiLCO-16 and LiCO protocols competes perfectly with only 17.92 \% and 20.16 \% active nodes for the first 17 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 $19^{th}$ because it optimizes the lifetime coverage into the subregion based on the perimeter coverage model, which made LiCO improves the coverage ratio and for a longer time in comparison with other approaches.
\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 $Lifetime50$.
\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 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 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.
\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}
\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}}
