X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/LiCO.git/blobdiff_plain/9e60013787affb94c4330a9cc9292a05af573314..6f5a87acc5438d5384b912e12224586f3e757f32:/LiCO_Journal.tex diff --git a/LiCO_Journal.tex b/LiCO_Journal.tex index 8f1949b..7e788d4 100644 --- a/LiCO_Journal.tex +++ b/LiCO_Journal.tex @@ -36,14 +36,16 @@ \DeclareGraphicsRule{.ps}{pdf}{.pdf}{`ps2pdf -dEPSCrop -dNOSAFER #1 \noexpand\OutputFile} \begin{document} -\title{Lifetime Coverage Optimization Protocol \\ - in Wireless Sensor Networks} %LiCO Protocol +%\title{Lifetime Coverage Optimization Protocol \\ +% in Wireless Sensor Networks} +\title{Perimeter-based Coverage Optimization to Improve \\ + Lifetime in Wireless Sensor Networks} \author{Ali Kadhum Idrees,~\IEEEmembership{} Karine Deschinkel,~\IEEEmembership{} Michel Salomon,~\IEEEmembership{} and~Rapha\"el Couturier ~\IEEEmembership{} - \thanks{The authors are with FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comt\'e, + \thanks{The authors are with FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte, Belfort, France. Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}} @@ -53,24 +55,25 @@ \maketitle \begin{abstract} -The most important problem in Wireless Sensor Networks (WSNs) is to optimize the +The most important problem in a Wireless Sensor Network (WSN) is to optimize the use of its limited energy provision, so that it can fulfill its monitoring task as long as possible. Among known available approaches that can be used to improve power management, lifetime coverage optimization provides activity scheduling which ensures sensing coverage while minimizing the energy cost. In -this paper, we propose a such approach called Lifetime Coverage Optimization +this paper, we propose such an approach called Lifetime Coverage Optimization protocol (LiCO). It is a hybrid of centralized and distributed methods: the region of interest is first subdivided into subregions and our protocol is then -distributed among sensor nodes in each subregion. A sensor node which runs LiCO -protocol repeats periodically four stages: information exchange, leader -election, optimization decision, and sensing. More precisely, the scheduling of -nodes' activities (sleep/wake up duty cycles) is achieved in each subregion by a -leader selected after cooperation between nodes within the same subregion. The -novelty of approach lies essentially in the formulation of a new mathematical -optimization model based on perimeter coverage level to schedule sensors' -activities. Extensive simulation experiments have been performed using OMNeT++, -the discrete event simulator, to demonstrate that LiCO is capable to offer -longer lifetime coverage for WSNs in comparison with some other protocols. +distributed among sensor nodes in each subregion. +% A sensor node which runs LiCO protocol repeats periodically four stages: +%information exchange, leader election, optimization decision, and sensing. +%More precisely, the scheduling of nodes' activities (sleep/wake up duty cycles) +%is achieved in each subregion by a leader selected after cooperation between +%nodes within the same subregion. +The novelty of our approach lies essentially in the formulation of a new +mathematical optimization model based on perimeter coverage level to schedule +sensors' activities. Extensive simulation experiments have been performed using +OMNeT++, the discrete event simulator, to demonstrate that LiCO is capable to +offer longer lifetime coverage for WSNs in comparison with some other protocols. \end{abstract} % Note that keywords are not normally used for peerreview papers. @@ -92,7 +95,7 @@ communicating with one another through multi-hop radio communications. Each node can send the data it collects in its environment, thanks to its sensor, to the user by means of sink nodes. The features of a WSN made it suitable for a wide range of application in areas such as business, environment, health, industry, -military, and son~\cite{yick2008wireless}. Typically, a sensor node contains +military, and so on~\cite{yick2008wireless}. Typically, a sensor node contains three main components~\cite{anastasi2009energy}: a sensing unit able to measure physical, chemical, or biological phenomena observed in the environment; a processing unit which will process and store the collected measurements; a radio @@ -119,23 +122,23 @@ lifetime of the WSNs~\cite{rault2014energy}. This paper makes the following contributions. \begin{enumerate} -\item We devise a framework to schedule nodes to be activated alternatively such +\item We have devised a framework to schedule nodes to be activated alternatively such that the network lifetime is prolonged while ensuring that a certain level of - coverage is preserved. A key idea in our framework is to exploit spatial an - temporal subdivision. On the one hand the area of interest if divided into - several smaller subregions and on the other hand the time line is divided into + coverage is preserved. A key idea in our framework is to exploit spatial and + temporal subdivision. On the one hand, the area of interest if divided into + several smaller subregions and, on the other hand, the time line is divided into periods of equal length. In each subregion the sensor nodes will cooperatively choose a leader which will schedule nodes' activities, and this grouping of sensors is similar to typical cluster architecture. -\item We propose a new mathematical optimization model. Instead of trying to +\item We have proposed a new mathematical optimization model. Instead of trying to cover a set of specified points/targets as in most of the methods proposed in the literature, we formulate an integer program based on perimeter coverage of each sensor. The model involves integer variables to capture the deviations - between the actual level of coverage and the required level. So that an + between the actual level of coverage and the required level. Hence, an optimal scheduling will be obtained by minimizing a weighted sum of these deviations. -\item We conducted extensive simulation experiments, using the discrete event - simulator OMNeT++, to demonstrate the efficiency of our protocol. We compared +\item We have conducted extensive simulation experiments, using the discrete event + simulator OMNeT++, to demonstrate the efficiency of our protocol. We have compared our LiCO protocol to two approaches found in the literature: DESK~\cite{ChinhVu} and GAF~\cite{xu2001geography}, and also to our previous work published in~\cite{Idrees2} which is based on another optimization model @@ -151,7 +154,7 @@ is devoted to the LiCO protocol description and Section~\ref{cp} focuses on the coverage model formulation which is used to schedule the activation of sensor nodes. Section~\ref{sec:Simulation Results and Analysis} presents simulations results and discusses the comparison with other approaches. Finally, concluding -remarks are drawn and some suggestions given for future works in +remarks are drawn and some suggestions are given for future works in Section~\ref{sec:Conclusion and Future Works}. % that show that our protocol outperforms others protocols. @@ -165,7 +168,7 @@ the literature. The most discussed coverage problems in literature can be classified in three categories~\cite{li2013survey} according to their respective monitoring objective. Hence, area coverage \cite{Misra} means that every point inside a -fixed area must be monitored, while target coverage~\cite{yang2014novel} refer +fixed area must be monitored, while target coverage~\cite{yang2014novel} refers to the objective of coverage for a finite number of discrete points called targets, and barrier coverage~\cite{HeShibo}\cite{kim2013maximum} focuses on preventing intruders from entering into the region of interest. In @@ -176,7 +179,7 @@ nodes or between disk of sensor nodes and boundaries. In sensors are sufficiently covered it will be the case for the whole area. They provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of each sensor, where $d$ denotes the maximum number of sensors that are -neighboring to a sensor and $n$ is the total number of sensors in the +neighbors to a sensor and $n$ is the total number of sensors in the network. {\it In LiCO protocol, instead of determining the level of coverage of a set of discrete points, our optimization model is based on checking the perimeter-coverage of each sensor to activate a minimal number of sensors.} @@ -201,28 +204,28 @@ each period. {\it Motivated by these works, LiCO protocol works in periods, decisions, followed by a sensing phase where one cover set is in charge of the sensing task.} -Various centralized and distributed approaches, or even a mixing of these two +Various centralized and distributed approaches, or even a mixing of these two concepts, have been proposed to extend the network lifetime. In distributed -algorithms~\cite{yangnovel,ChinhVu,qu2013distributed} each sensors decides of -its own activity scheduling after an information exchange with its neighbors. -The main interest of a such approach is to avoid long range communications and -thus to reduce the energy dedicated to the communications. Unfortunately, since -each node has only information on its immediate neighbors (usually the one-hop -ones) it may take a bad decision leading to a global suboptimal solution. -Conversely, centralized -algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high} always +algorithms~\cite{yangnovel,ChinhVu,qu2013distributed} each sensor decides of its +own activity scheduling after an information exchange with its neighbors. The +main interest of such an approach is to avoid long range communications and thus +to reduce the energy dedicated to the communications. Unfortunately, since each +node has only information on its immediate neighbors (usually the one-hop ones) +it may take a bad decision leading to a global suboptimal solution. Conversely, +centralized +algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high} always provide nearly or close to optimal solution since the algorithm has a global view of the whole network. The disadvantage of a centralized method is obviously -its high cost in communications needed to transmit to a single node, the base -station which will globally schedule nodes' activities, data from all the other -sensor nodes in the area. The price in communications can be very huge since -long range communications will be needed. In fact the larger the WNS, the higher -the communication and thus energy cost. {\it In order to be suitable for - large-scale networks, in the LiCO protocol the area of interest is divided - into several smaller subregions, and in each one, a node called the leader is - in charge for selecting the active sensors for the current period. Thus our - protocol is scalable and a globally distributed method, whereas it is - centralized in each subregion.} +its high cost in communications needed to transmit to a single node, the base +station which will globally schedule nodes' activities, data from all the other +sensor nodes in the area. The price in communications can be very huge since +long range communications will be needed. In fact the larger the WNS is, the +higher the communication and thus the energy cost are. {\it In order to be + suitable for large-scale networks, in the LiCO protocol, the area of interest + is divided into several smaller subregions, and in each one, a node called the + leader is in charge of selecting the active sensors for the current + period. Thus our protocol is scalable and is a globally distributed method, + whereas it is centralized in each subregion.} Various coverage scheduling algorithms have been developed this last years. Many of them, dealing with the maximization of the number of cover sets, are @@ -237,7 +240,7 @@ optimization solver). The problem is formulated as an optimization problem energy constraints. Column generation techniques, well-known and widely practiced techniques for solving linear programs with too many variables, have also been -used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In LiCO +used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In the LiCO protocol, each leader, in charge of a subregion, solves an integer program which has a twofold objective: minimize the overcoverage and the undercoverage of the perimeter of each sensor.} @@ -315,11 +318,11 @@ $R_c$ satisfies $R_c \geq 2 \cdot R_s$. 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 active nodes. -\indent LiCO protocol uses the same perimeter-coverage model than Huang and +The LiCO protocol uses the same perimeter-coverage model as Huang and Tseng in~\cite{huang2005coverage}. It can be expressed as follows: a sensor is said to be perimeter covered if all the points on its perimeter are covered by at least one sensor other than itself. They proved that a network area is -$k$-covered if and only if each sensor in the network is $k$-perimeter-covered. +$k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors). %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{pcm2sensors}(a) shows the coverage of sensor node~$0$. On this figure, we can see that sensor~$0$ has nine neighbors and we have reported on @@ -333,8 +336,8 @@ arcs. \begin{figure}[ht!] \centering \begin{tabular}{@{}cr@{}} - \includegraphics[width=75mm]{pcm.jpg} & \raisebox{3.25cm}{(a)} - \\ \includegraphics[width=75mm]{twosensors.jpg} & \raisebox{2.75cm}{(b)} + \includegraphics[width=75mm]{pcm.jpg} & \raisebox{3.25cm}{(a)} \\ + \includegraphics[width=75mm]{twosensors.jpg} & \raisebox{2.75cm}{(b)} \end{tabular} \caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of $u$'s perimeter covered by $v$.} @@ -343,29 +346,29 @@ arcs. Figure~\ref{pcm2sensors}(b) describes the geometric information used to find the locations of the left and right points of an arc on the perimeter of a sensor -node~$u$ covered by a sensor node~$v$. Node~$s$ is supposed to be located on the +node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the west side of sensor~$u$, with the following respective coordinates in the sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is -obtained through the formula $\alpha = arccos \left(\dfrac{Dist(u,v)}{2R_s} -\right)$. So, the arc on the perimeter of node~$u$ defined by the angular -interval $[\pi - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor -node $v$. +obtained through the formula: $$\alpha = \arccos \left(\dfrac{Dist(u,v)}{2R_s} +\right).$$ The arc on the perimeter of~$u$ defined by the angular interval $[\pi + - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$. Every couple of intersection points is placed on the angular interval $[0,2\pi]$ in a counterclockwise manner, leading to a partitioning of the interval. Figure~\ref{pcm2sensors}(a) illustrates the arcs for the nine neighbors of -sensor $0$ and figure~\ref{expcm} gives the position of the corresponding arcs +sensor $0$ and Figure~\ref{expcm} gives the position of the corresponding arcs in the interval $[0,2\pi]$. More precisely, we can see that the points are ordered according to the measures of the angles defined by their respective positions. The intersection points are then visited one after another, starting -from first intersection point after point~zero, and the maximum level of +from the first intersection point after point~zero, and the maximum level of coverage is determined for each interval defined by two successive points. The maximum level of coverage is equal to the number of overlapping arcs. For -example, between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$ -(the value is highlighted in yellow at the bottom of figure~\ref{expcm}), which -means that at most 2~neighbors can cover the perimeter in addition to node $0$. +example, +between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$ +(the value is highlighted in yellow at the bottom of Figure~\ref{expcm}), which +means that at most 2~neighbors can cover the perimeter in addition to node $0$. Table~\ref{my-label} summarizes for each coverage interval the maximum level of coverage and the sensor nodes covering the perimeter. The example discussed above is thus given by the sixth line of the table. @@ -373,9 +376,9 @@ above is thus given by the sixth line of the table. %The points reported on the line segment $[0,2\pi]$ separates it in intervals as shown in figure~\ref{expcm}. For example, for each neighboring sensor of sensor 0, place the points $\alpha^ 1_L$, $\alpha^ 1_R$, $\alpha^ 2_L$, $\alpha^ 2_R$, $\alpha^ 3_L$, $\alpha^ 3_R$, $\alpha^ 4_L$, $\alpha^ 4_R$, $\alpha^ 5_L$, $\alpha^ 5_R$, $\alpha^ 6_L$, $\alpha^ 6_R$, $\alpha^ 7_L$, $\alpha^ 7_R$, $\alpha^ 8_L$, $\alpha^ 8_R$, $\alpha^ 9_L$, and $\alpha^ 9_R$; on the line segment $[0,2\pi]$, and then sort all these points in an ascending order into a list. Traverse the line segment $[0,2\pi]$ by visiting each point in the sorted list from left to right and determine the coverage level of each interval of the sensor 0 (see figure \ref{expcm}). For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. Table~\ref{my-label} summarizes the level of coverage for each interval and the sensors involved in for sensor node 0 in figure~\ref{pcm2sensors}(a). % to determine the level of the perimeter coverage for each left and right point of a segment. -\begin{figure*}[ht!] +\begin{figure*}[t!] \centering -\includegraphics[width=137.5mm]{expcm.pdf} +\includegraphics[width=127.5mm]{expcm2.jpg} \caption{Maximum coverage levels for perimeter of sensor node $0$.} \label{expcm} \end{figure*} @@ -393,11 +396,11 @@ above is thus given by the sixth line of the table. \fi - \begin{table}[h] + \begin{table}[h!] \caption{Coverage intervals and contributing sensors for sensor node 0.} \begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline -\begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\ level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in interval coverage\end{tabular}} \\ \hline +\begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\ level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in coverage interval\end{tabular}} \\ \hline 0.0291 & 1L & 2L & 4 & 0 & 1 & 3 & 4 & \\ \hline 0.104 & 2L & 3R & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline 0.3168 & 3R & 4R & 4 & 0 & 1 & 4 & 2 & \\ \hline @@ -424,15 +427,15 @@ above is thus given by the sixth line of the table. %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 LiCO protocol, scheduling of sensor nodes' activities is formulated with an +In the LiCO protocol, scheduling of sensor nodes' activities is formulated with an integer program based on coverage intervals. The formulation of the coverage optimization problem is detailed in~section~\ref{cp}. Note that when a sensor node has a part of its sensing range outside the WSN sensing field, as in -figure~\ref{ex4pcm}, the maximum coverage level for this arc is set to $\infty$ +Figure~\ref{ex4pcm}, the maximum coverage level for this arc is set to $\infty$ and the corresponding interval will not be taken into account by the optimization algorithm. -\begin{figure}[t!] +\begin{figure}[h!] \centering \includegraphics[width=62.5mm]{ex4pcm.jpg} \caption{Sensing range outside the WSN's area of interest.} @@ -453,14 +456,14 @@ homogeneous subregions using a divide-and-conquer algorithm. In a second step our protocol will be executed in a distributed way in each subregion simultaneously to schedule nodes' activities for one sensing period. -As shown in figure~\ref{fig2}, node activity scheduling is produced by our +As shown in Figure~\ref{fig2}, node activity scheduling is produced by our protocol in a periodic manner. Each period is divided into 4 stages: Information (INFO) Exchange, Leader Election, Decision (the result of an optimization problem), and Sensing. For each period there is exactly one set cover responsible for the sensing task. Protocols based on a periodic scheme, like LiCO, are more robust against an unexpected node failure. On the one hand, if -node failure is discovered before taking the decision, the corresponding sensor -node will not be considered by the optimization algorithm, and, on the other +a node failure is discovered before taking the decision, the corresponding sensor +node will not be considered by the optimization algorithm. On the other hand, if the sensor failure happens after the decision, the sensing task of the network will be temporarily affected: only during the period of sensing until a new period starts, since a new set cover will take charge of the sensing task in @@ -474,7 +477,7 @@ the area. \begin{figure}[t!] \centering \includegraphics[width=80mm]{Model.pdf} -\caption{LiCO protocol} +\caption{LiCO protocol.} \label{fig2} \end{figure} @@ -497,7 +500,7 @@ Five status are possible for a sensor node in the network: determine the activities scheduling; \item ACTIVE: node is sensing; \item SLEEP: node is turned off; -\item COMMUNICATION: transmits or recevives packets. +\item COMMUNICATION: transmits or receives packets. \end{itemize} %\end{enumerate} %Below, we describe each phase in more details. @@ -539,7 +542,7 @@ protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN. } \emph{$s_k.status$ = COMMUNICATION}\; - \emph{Send $ActiveSleep()$ to each node $l$ in subregion} \; + \emph{Send $ActiveSleep()$ to each node $l$ in subregion}\; \emph{Update $RE_k $}\; } \Else{ @@ -553,20 +556,19 @@ protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN. \label{alg:LiCO} \end{algorithm} -In this algorithm, K.CurrentSize and K.PreviousSize refer to the current size -and the previous size of the subnetwork in the subregion respectively. That -means the number of sensor nodes which are still alive. Initially, the sensor -node checks its remaining energy $RE_k$, which must be greater than a threshold -$E_{th}$ in order to participate in the current period. Each sensor node -determines its position and its subregion using an embedded GPS or a location -discovery algorithm. After that, all the sensors collect position coordinates, -remaining energy, sensor node ID, and the number of its one-hop live neighbors -during the information exchange. The sensors inside a same region cooperate to -elect a 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. Once chosen, the leader collects information to -formulate and solve the integer program which allows to construct the set of -active sensors in the sensing stage. +In this algorithm, K.CurrentSize and K.PreviousSize respectively represent the +current number and the previous number of alive nodes in the subnetwork of the +subregion. Initially, the sensor node checks its remaining energy $RE_k$, which +must be greater than a threshold $E_{th}$ in order to participate in the current +period. Each sensor node determines its position and its subregion using an +embedded GPS or a location discovery algorithm. After that, all the sensors +collect position coordinates, remaining energy, sensor node ID, and the number +of their one-hop live neighbors during the information exchange. The sensors +inside a same region cooperate to elect a 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. Once chosen, the leader +collects information to formulate and solve the integer program which allows to +construct the set of active sensors in 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. @@ -588,7 +590,7 @@ First, we have the following sets: \end{itemize} $I_j$ refers to the set of coverage intervals which have been defined according to the method introduced in subsection~\ref{CI}. For a coverage interval $i$, -let $a^j_{ik}$ denote the indicator function of whether sensor~$k$ is involved +let $a^j_{ik}$ denotes the indicator function of whether sensor~$k$ is involved in coverage interval~$i$ of sensor~$j$, that is: \begin{equation} a^j_{ik} = \left \{ @@ -618,7 +620,7 @@ sensor $j$ is given by $\sum_{k \in A} a^j_{ik} X_k$. To extend the network lifetime, the objective is to activate 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 reach the desired level of coverage for all -coverage intervals. Therefore we uses variables $M^j_i$ and $V^j_i$ as a measure +coverage intervals. Therefore we use 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. And we try to minimize these deviations, first to force the activation of a minimal number of sensors to ensure the @@ -666,7 +668,7 @@ X_{k} \in \{0,1\}, \forall k \in A $\alpha^j_i$ 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 +be given by 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 \cite{0031-9155-44-1-012}. The integer program must be solved by the leader in @@ -736,10 +738,10 @@ be active during at most 20 periods. The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good network coverage and a longer WSN lifetime. We have given a higher priority for the undercoverage (by setting the $\alpha^j_i$ with a larger value than -$\beta^j_i$) so as to prevent the non-coverage for the interval i of the sensor -j. On the other hand, we have given a little bit lower value for $\beta^j_i$ so -as to minimize the number of active sensor nodes which contribute in covering -the interval. +$\beta^j_i$) so as to prevent the non-coverage for the interval~$i$ of the +sensor~$j$. On the other hand, we have given a little bit lower value for +$\beta^j_i$ so as to minimize the number of active sensor nodes which contribute +in covering the interval. We introduce the following performance metrics to evaluate the efficiency of our approach. @@ -751,7 +753,7 @@ approach. $Lifetime_{50}$ denote, respectively, the amount of time during which is guaranteed a level of coverage greater than $95\%$ and $50\%$. The WSN can fulfill the expected monitoring task until all its nodes have depleted their - energy or if the network is not more connected. This last condition is crucial + energy or if the network is no more connected. This last condition is crucial because without network connectivity a sensor may not be able to send to a base station an event it has sensed. \item {\bf Coverage Ratio (CR)} : it measures how well the WSN is able to @@ -771,7 +773,7 @@ approach. follows: \begin{equation*} \scriptsize - \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r|$}}{\mbox{$|S|$}} \times 100 + \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|S|$}} \times 100 \end{equation*} where $|A_r^p|$ is the number of active sensors in the subregion $r$ in the current sensing period~$p$, $|S|$ is the number of sensors in the network, and @@ -827,7 +829,7 @@ it corresponds to the configuration producing the better results for DiLCO. The protocols are distinguished from one another by the formulation of the integer program providing the set of sensors which have to be activated in each sensing phase. DiLCO protocol tries to satisfy the coverage of a set of primary points, -whereas LICO protocol objectif is to reach a desired level of coverage for each +whereas LiCO protocol objective is to reach a desired level of coverage for each sensor perimeter. In our experimentations, we chose a level of coverage equal to one ($l=1$). @@ -868,7 +870,7 @@ 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 a greater coverage ratio as shown in -figure \ref{fig333}. +Figure \ref{fig333}. \begin{figure}[h!] \centering @@ -881,7 +883,7 @@ figure \ref{fig333}. We study the effect of the energy consumed by the WSN during the communication, computation, listening, active, and sleep status for different network densities -and compare it for the fours approaches. Figures~\ref{fig3EC}(a) and (b) +and compare it for the four approaches. Figures~\ref{fig3EC}(a) and (b) illustrate the energy consumption for different network sizes and for $Lifetime95$ and $Lifetime50$. The results show that our LiCO protocol is the most competitive from the energy consumption point of view. As shown in both @@ -912,16 +914,17 @@ while keeping a good coverage level. \subsubsection{\bf Network Lifetime} We observe the superiority of LiCO and DiLCO protocols in comparison against the -two other approaches in prolonging the network WSN. In figures~\ref{fig3LT}(a) -and (b), $Lifetime95$ and $Lifetime50$ are shown for different network sizes. -As highlighted by these figures, the lifetime increases with the size of the -network, and it is clearly the larger for DiLCO and LiCO protocols. For -instance, for a network of 300 sensors and coverage ratio greater than 50\%, we -can see on figure~\ref{fig3LT}(b) that the lifetime is about two times longer -with LiCO compared to DESK protocol. The performance difference is more obvious -in figure~\ref{fig3LT}(b) than in figure~\ref{fig3LT}(a) because the gain -induced by our protocols increases with the time, and the lifetime with a -coverage of 50\% is far more longer than with 95\%. +two other approaches in prolonging the network lifetime. In +Figures~\ref{fig3LT}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for +different network sizes. As highlighted by these figures, the lifetime +increases with the size of the network, and it is clearly the larger for DiLCO +and LiCO protocols. For instance, for a network of 300~sensors and coverage +ratio greater than 50\%, we can see on Figure~\ref{fig3LT}(b) that the lifetime +is about two times longer with LiCO compared to DESK protocol. The performance +difference is more obvious in Figure~\ref{fig3LT}(b) than in +Figure~\ref{fig3LT}(a) because the gain induced by our protocols increases with +the time, and the lifetime with a coverage of 50\% is far more longer than with +95\%. \begin{figure}[h!] \centering @@ -945,8 +948,8 @@ that do not require a 100\% coverage of the area to be monitored. LiCO might be an interesting method since it achieves a good balance between a high level coverage ratio and network lifetime. LiCO always outperforms DiLCO for the three lower coverage ratios, moreover the improvements grow with the network -size. DiLCO is better for coverage ratios near 100\%, but LiCO is not so bad for -the smallest network sizes. +size. DiLCO is better for coverage ratios near 100\%, but in that case LiCO is +not so bad for the smallest network sizes. \begin{figure}[h!] \centering \includegraphics[scale=0.5]{R/LTa.eps} @@ -962,7 +965,7 @@ the smallest network sizes. In this paper we have studied the problem of lifetime coverage optimization in WSNs. We designed a new protocol, called Lifetime Coverage Optimization, which -schedules node' activities (wake up and sleep stages) with the objective of +schedules nodes' activities (wake up and sleep stages) with the objective of maintaining a good coverage ratio while maximizing the network lifetime. This protocol is applied in a distributed way in regular subregions obtained after partitioning the area of interest in a preliminary step. It works in periods and