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-\begin{document}\r
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-%\jvol{00} \jnum{00} \jyear{2013} \jmonth{April}\r
-\r
-%\articletype{GUIDE}\r
-\r
-\title{{\itshape Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks}}\r
-\r
-\author{Ali Kadhum Idrees$^{a}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$\r
-$^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte,\r
- Belfort, France}};}\r
-\r
-\r
-\maketitle\r
-\r
-\begin{abstract}\r
-The most important problem in a Wireless Sensor Network (WSN) is to optimize the\r
-use of its limited energy provision, so that it can fulfill its monitoring task\r
-as long as possible. Among known available approaches that can be used to\r
-improve power management, lifetime coverage optimization provides activity\r
-scheduling which ensures sensing coverage while minimizing the energy cost. In\r
-this paper, we propose such an approach called Perimeter-based Coverage Optimization\r
-protocol (PeCO). It is a hybrid of centralized and distributed methods: the\r
-region of interest is first subdivided into subregions and our protocol is then\r
-distributed among sensor nodes in each subregion.\r
-The novelty of our approach lies essentially in the formulation of a new\r
-mathematical optimization model based on the perimeter coverage level to schedule\r
-sensors' activities. Extensive simulation experiments have been performed using\r
-OMNeT++, the discrete event simulator, to demonstrate that PeCO can\r
-offer longer lifetime coverage for WSNs in comparison with some other protocols.\r
-\r
-\begin{keywords}Wireless Sensor Networks, Area Coverage, Network Lifetime, Optimization, Scheduling.\r
-\end{keywords}\r
-\r
-\end{abstract}\r
-\r
-\r
-\section{Introduction}\r
-\label{sec:introduction}\r
-\r
-\noindent The continuous progress in Micro Electro-Mechanical Systems (MEMS) and\r
-wireless communication hardware has given rise to the opportunity to use large\r
-networks of tiny sensors, called Wireless Sensor Networks\r
-(WSN)~\cite{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring\r
-tasks. A WSN consists of small low-powered sensors working together by\r
-communicating with one another through multi-hop radio communications. Each node\r
-can send the data it collects in its environment, thanks to its sensor, to the\r
-user by means of sink nodes. The features of a WSN made it suitable for a wide\r
-range of application in areas such as business, environment, health, industry,\r
-military, and so on~\cite{yick2008wireless}. Typically, a sensor node contains\r
-three main components~\cite{anastasi2009energy}: a sensing unit able to measure\r
-physical, chemical, or biological phenomena observed in the environment; a\r
-processing unit which will process and store the collected measurements; a radio\r
-communication unit for data transmission and receiving.\r
-\r
-The energy needed by an active sensor node to perform sensing, processing, and\r
-communication is supplied by a power supply which is a battery. This battery has\r
-a limited energy provision and it may be unsuitable or impossible to replace or\r
-recharge it in most applications. Therefore it is necessary to deploy WSN with\r
-high density in order to increase reliability and to exploit node redundancy\r
-thanks to energy-efficient activity scheduling approaches. Indeed, the overlap\r
-of sensing areas can be exploited to schedule alternatively some sensors in a\r
-low power sleep mode and thus save energy. Overall, the main question that must\r
-be answered is: how to extend the lifetime coverage of a WSN as long as possible\r
-while ensuring a high level of coverage? These past few years many\r
-energy-efficient mechanisms have been suggested to retain energy and extend the\r
-lifetime of the WSNs~\cite{rault2014energy}.\r
-\r
-This paper makes the following contributions.\r
-\begin{enumerate}\r
-\item We have devised a framework to schedule nodes to be activated alternatively such\r
- that the network lifetime is prolonged while ensuring that a certain level of\r
- coverage is preserved. A key idea in our framework is to exploit spatial and\r
- temporal subdivision. On the one hand, the area of interest is divided into\r
- several smaller subregions and, on the other hand, the time line is divided into\r
- periods of equal length. In each subregion the sensor nodes will cooperatively\r
- choose a leader which will schedule nodes' activities, and this grouping of\r
- sensors is similar to typical cluster architecture.\r
-\item We have proposed a new mathematical optimization model. Instead of trying to\r
- cover a set of specified points/targets as in most of the methods proposed in\r
- the literature, we formulate an integer program based on perimeter coverage of\r
- each sensor. The model involves integer variables to capture the deviations\r
- between the actual level of coverage and the required level. Hence, an\r
- optimal scheduling will be obtained by minimizing a weighted sum of these\r
- deviations.\r
-\item We have conducted extensive simulation experiments, using the discrete event\r
- simulator OMNeT++, to demonstrate the efficiency of our protocol. We have compared\r
- our PeCO protocol to two approaches found in the literature:\r
- DESK~\cite{ChinhVu} and GAF~\cite{xu2001geography}, and also to our previous\r
- work published in~\cite{Idrees2} which is based on another optimization model\r
- for sensor scheduling.\r
-\end{enumerate}\r
-\r
-\r
-\r
-\r
-\r
-\r
-The rest of the paper is organized as follows. In the next section we review\r
-some related work in the field. Section~\ref{sec:The PeCO Protocol Description}\r
-is devoted to the PeCO protocol description and Section~\ref{cp} focuses on the\r
-coverage model formulation which is used to schedule the activation of sensor\r
-nodes. Section~\ref{sec:Simulation Results and Analysis} presents simulations\r
-results and discusses the comparison with other approaches. Finally, concluding\r
-remarks are drawn and some suggestions are given for future works in\r
-Section~\ref{sec:Conclusion and Future Works}.\r
-\r
-% that show that our protocol outperforms others protocols.\r
-\section{Related Literature}\r
-\label{sec:Literature Review}\r
-\r
-\noindent In this section, we summarize some related works regarding the\r
-coverage problem and distinguish our PeCO protocol from the works presented in\r
-the literature.\r
-\r
-The most discussed coverage problems in literature can be classified in three\r
-categories~\cite{li2013survey} according to their respective monitoring\r
-objective. Hence, area coverage \cite{Misra} means that every point inside a\r
-fixed area must be monitored, while target coverage~\cite{yang2014novel} refers\r
-to the objective of coverage for a finite number of discrete points called\r
-targets, and barrier coverage~\cite{HeShibo}\cite{kim2013maximum} focuses on\r
-preventing intruders from entering into the region of interest. In\r
-\cite{Deng2012} authors transform the area coverage problem into the target\r
-coverage one taking into account the intersection points among disks of sensors\r
-nodes or between disk of sensor nodes and boundaries. In\r
-\cite{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of\r
-sensors are sufficiently covered it will be the case for the whole area. They\r
-provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of\r
-each sensor, where $d$ denotes the maximum number of sensors that are\r
-neighbors to a sensor and $n$ is the total number of sensors in the\r
-network. {\it In PeCO protocol, instead of determining the level of coverage of\r
- a set of discrete points, our optimization model is based on checking the\r
- perimeter-coverage of each sensor to activate a minimal number of sensors.}\r
-\r
-The major approach to extend network lifetime while preserving coverage is to\r
-divide/organize the sensors into a suitable number of set covers (disjoint or\r
-non-disjoint)\cite{wang2011coverage}, where each set completely covers a region of interest, and to\r
-activate these set covers successively. The network activity can be planned in\r
-advance and scheduled for the entire network lifetime or organized in periods,\r
-and the set of active sensor nodes is decided at the beginning of each period\r
-\cite{ling2009energy}. Active node selection is determined based on the problem\r
-requirements (e.g. area monitoring, connectivity, or power efficiency). For\r
-instance, Jaggi {\em et al.}~\cite{jaggi2006} address the problem of maximizing\r
-the lifetime by dividing sensors into the maximum number of disjoint subsets\r
-such that each subset can ensure both coverage and connectivity. A greedy\r
-algorithm is applied once to solve this problem and the computed sets are\r
-activated in succession to achieve the desired network lifetime. Vu\r
-\cite{chin2007}, \cite{yan2008design}, Padmatvathy {\em et al.}~\cite{pc10}, propose algorithms\r
-working in a periodic fashion where a cover set is computed at the beginning of\r
-each period. {\it Motivated by these works, PeCO protocol works in periods,\r
- where each period contains a preliminary phase for information exchange and\r
- decisions, followed by a sensing phase where one cover set is in charge of the\r
- sensing task.}\r
-\r
-Various centralized and distributed approaches, or even a mixing of these two\r
-concepts, have been proposed to extend the network lifetime \cite{zhou2009variable}. In distributed algorithms~\cite{Tian02,yangnovel,ChinhVu,qu2013distributed} each sensor decides of its\r
-own activity scheduling after an information exchange with its neighbors. The\r
-main interest of such an approach is to avoid long range communications and thus\r
-to reduce the energy dedicated to the communications. Unfortunately, since each\r
-node has only information on its immediate neighbors (usually the one-hop ones)\r
-it may make a bad decision leading to a global suboptimal solution. Conversely,\r
-centralized\r
-algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high} always\r
-provide nearly or close to optimal solution since the algorithm has a global\r
-view of the whole network. The disadvantage of a centralized method is obviously\r
-its high cost in communications needed to transmit to a single node, the base\r
-station which will globally schedule nodes' activities, data from all the other\r
-sensor nodes in the area. The price in communications can be huge since\r
-long range communications will be needed. In fact the larger the WNS is, the\r
-higher the communication and thus the energy cost are. {\it In order to be\r
- suitable for large-scale networks, in the PeCO protocol, the area of interest\r
- is divided into several smaller subregions, and in each one, a node called the\r
- leader is in charge of selecting the active sensors for the current\r
- period. Thus our protocol is scalable and is a globally distributed method,\r
- whereas it is centralized in each subregion.}\r
-\r
-Various coverage scheduling algorithms have been developed these past few years.\r
-Many of them, dealing with the maximization of the number of cover sets, are\r
-heuristics. These heuristics involve the construction of a cover set by\r
-including in priority the sensor nodes which cover critical targets, that is to\r
-say targets that are covered by the smallest number of sensors\r
-\cite{berman04,zorbas2010solving}. Other approaches are based on mathematical\r
-programming formulations~\cite{cardei2005energy,5714480,pujari2011high,Yang2014}\r
-and dedicated techniques (solving with a branch-and-bound algorithm available in\r
-optimization solver). The problem is formulated as an optimization problem\r
-(maximization of the lifetime or number of cover sets) under target coverage and\r
-energy constraints. Column generation techniques, well-known and widely\r
-practiced techniques for solving linear programs with too many variables, have\r
-also been\r
-used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In the PeCO\r
- protocol, each leader, in charge of a subregion, solves an integer program\r
- which has a twofold objective: minimize the overcoverage and the undercoverage\r
- of the perimeter of each sensor.}\r
-\r
-%\noindent Recently, the coverage problem has been received a high attention, which concentrates on how the physical space could be well monitored after the deployment. Coverage is one of the Quality of Service (QoS) parameters in WSNs, which is highly concerned with power depletion~\cite{zhu2012survey}. Most of the works about the coverage protocols have been suggested in the literature focused on three types of the coverage in WSNs~\cite{mulligan2010coverage}: the first, area coverage means that each point in the area of interest within the sensing range of at least one sensor node; the second, target coverage in which a fixed set of targets need to be monitored; the third, barrier coverage refers to detect the intruders crossing a boundary of WSN. The work in this paper emphasized on the area coverage, so, some area coverage protocols have been reviewed in this section, and the shortcomings of reviewed approaches are being summarized.\r
-\r
-%The problem of k-coverage in WSNs was addressed~\cite{ammari2012centralized}. It mathematically formulated and the spacial sensor density for full k-coverage determined, where the relation between the communication range and the sensing range constructed by this work to retain the k-coverage and connectivity in WSN. After that, a four configuration protocols have proposed for treating the k-coverage in WSNs. \r
-\r
-%In~\cite{rebai2014branch}, the problem of full grid coverage is formulated using two integer linear programming models: the first, a model that takes into account only the overall coverage constraint; the second, both the connectivity and the full grid coverage constraints have taken into consideration. This work did not take into account the energy constraint.\r
-\r
-%Li et al.~\cite{li2011transforming} presented a framework to convert any complete coverage problem to a partial coverage one with any coverage ratio by means of executing a complete coverage algorithm to find a full coverage sets with virtual radii and transforming the coverage sets to a partial coverage sets by adjusting sensing radii. The properties of the original algorithms can be maintained by this framework and the transformation process has a low execution time.\r
-\r
-%The authors in~\cite{liu2014generalized} explained that in some applications of WSNs such as structural health monitoring (SHM) and volcano monitoring, the traditional coverage model which is a geographic area defined for individual sensors is not always valid. For this reason, they define a generalized coverage model, which is not need to have the coverage area of individual nodes, but only based on a function to determine whether a set of\r
-%sensor nodes is capable of satisfy the requested monitoring task for a certain area. They have proposed two approaches to divide the deployed nodes into suitable cover sets, which can be used to prolong the network lifetime. \r
- \r
-%The work in~\cite{wang2010preserving} addressed the target area coverage problem by proposing a geometric-based activity scheduling scheme, named GAS, to fully cover the target area in WSNs. The authors deals with small area (target area coverage), which can be monitored by a single sensor instead of area coverage, which focuses on a large area that should be monitored by many sensors cooperatively. They explained that GAS is capable to monitor the target area by using a few sensors as possible and it can produce as many cover sets as possible.\r
-\r
-%Cho et al.~\cite{cho2007distributed} proposed a distributed node scheduling protocol, which can retain sensing coverage needed by applications\r
-%and increase network lifetime via putting in sleep mode some redundant nodes. In this work, the effective sensing area (ESA) concept of a sensor node is used, which refers to the sensing area that is not overlapping with another sensor's sensing area. A sensor node and by compute it's ESA can be determine whether it will be active or sleep. The suggested work permits to sensor nodes to be in sleep mode opportunistically whilst fulfill the needed sensing coverage.\r
- \r
-%In~\cite{quang2008algorithm}, the authors defined a maximum sensing coverage region problem (MSCR) in WSNs and then proposed an algorithm to solve it. The\r
-%maximum observed area fully covered by a minimum active sensors. In this work, the major property is to getting rid from the redundant sensors in high-density WSNs and putting them in sleep mode, and choosing a smaller number of active sensors so as to be sure that the full area is k-covered, and all events appeared in that area can be precisely and timely detected. This algorithm minimized the total energy consumption and increased the lifetime.\r
-\r
-%A novel method to divide the sensors in the WSN, called node coverage grouping (NCG) suggested~\cite{lin2010partitioning}. The sensors in the connectivity group are within sensing range of each other, and the data collected by them in the same group are supposed to be similar. They are proved that dividing n sensors via NCG into connectivity groups is a NP-hard problem. So, a heuristic algorithm of NCG with time complexity of $O(n^3)$ is proposed.\r
-%For some applications, such as monitoring an ecosystem with extremely diversified environment, It might be premature assumption that sensors near to each other sense similar data.\r
-\r
-%In~\cite{zaidi2009minimum}, the problem of minimum cost coverage in which full coverage is performed by using the minimum number of sensors for an arbitrary geometric shape region is addressed. a geometric solution to the minimum cost coverage problem under a deterministic deployment is proposed. The probabilistic coverage solution which provides a relationship between the probability of coverage and the number of randomly deployed sensors in an arbitrarily-shaped region is suggested. The authors are clarified that with a random deployment about seven times more nodes are required to supply full coverage.\r
-\r
-%A graph theoretical framework for connectivity-based coverage with configurable coverage granularity was proposed~\cite{dong2012distributed}. A new coverage criterion and scheduling approach is proposed based on cycle partition. This method is capable of build a sparse coverage set in distributed way by means of only connectivity information. This work considers only the communication range of the sensor is smaller two times the sensing range of sensor.\r
-\r
-%Liu et al.~\cite{liu2010energy} formulated maximum disjoint sets problem for retaining coverage and connectivity in WSN. Two algorithms are proposed for solving this problem, heuristic algorithm and network flow algorithm. This work did not take into account the sensor node failure, which is an unpredictable event because the two solutions are full centralized algorithms.\r
-\r
-%The work that presented in~\cite{aslanyan2013optimal} solved the coverage and connectivity problem in sensor networks in\r
-%an integrated way. The network lifetime is divided in a fixed number of rounds. A coverage bitmap of sensors of the domain has been generated in each round and based on this bitmap, it has been decided which sensors\r
-%stay active or turn it to sleep. They checked the connection of the graph via laplacian of adjancy graph of active sensors in each round. the generation of coverage bitmap by using Minkowski technique, the network is able to providing the desired ratio of coverage. They have been defined the connected coverage problem as an optimization problem and a centralized genetic algorithm is used to find the solution.\r
-\r
-%Several algorithms to retain the coverage and maximize the network lifetime were proposed in~\cite{cardei2006energy,wang2011coverage}. \r
-\r
-%\uppercase{\textbf{shortcomings}}. In spite of many energy-efficient protocols for maintaining the coverage and improving the network lifetime in WSNs were proposed, non of them ensure the coverage for the sensing field with optimal minimum number of active sensor nodes, and for a long time as possible. For example, in a full centralized algorithms, an optimal solutions can be given by using optimization approaches, but in the same time, a high energy is consumed for the execution time of the algorithm and the communications among the sensors in the sensing field, so, the full centralized approaches are not good candidate to use it especially in large WSNs. Whilst, a full distributed algorithms can not give optimal solutions because this algorithms use only local information of the neighboring sensors, but in the same time, the energy consumption during the communications and executing the algorithm is highly lower. Whatever the case, this would result in a shorter lifetime coverage in WSNs.\r
-\r
-%\uppercase{\textbf{Our Protocol}}. In this paper, a Lifetime Coverage Optimization Protocol, called (PeCO) in WSNs is suggested. The sensing field is divided into smaller subregions by means of divide-and-conquer method, and a PeCO protocol is distributed in each sensor in the subregion. The network lifetime in each subregion is divided into periods, each period includes 4 stages: Information Exchange, Leader election, decision based activity scheduling optimization, and sensing. The leaders are elected in an independent, asynchronous, and distributed way in all the subregions of the WSN. After that, energy-efficient activity scheduling mechanism based new optimization model is performed by each leader in the subregions. This optimization model is based on the perimeter coverage model in order to producing the optimal cover set of active sensors, which are taken the responsibility of sensing during the current period. PeCO protocol merges between two energy efficient mechanisms, which are used the main advantages of the centralized and distributed approaches and avoids the most of their disadvantages.\r
-\r
-\section{ The P{\scshape e}CO Protocol Description}\r
-\label{sec:The PeCO Protocol Description}\r
-\r
-\noindent In this section, we describe in details our Perimeter-based Coverage\r
-Optimization protocol. First we present the assumptions we made and the models\r
-we considered (in particular the perimeter coverage one), second we describe the\r
-background idea of our protocol, and third we give the outline of the algorithm\r
-executed by each node.\r
-\r
-% It is based on two efficient-energy mechanisms: the first, is partitioning the sensing field into smaller subregions, and one leader is elected for each subregion; the second, a sensor activity scheduling based new optimization model so as to produce the optimal cover set of active sensors for the sensing stage during the period. Obviously, these two mechanisms can be contribute in extend the network lifetime coverage efficiently. \r
-%Before proceeding in the presentation of the main ideas of the protocol, we will briefly describe the perimeter coverage model and give some necessary assumptions and definitions.\r
-\r
-\subsection{Assumptions and Models}\r
-\label{CI}\r
-\r
-\noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly\r
-distributed in a bounded sensor field is considered. The wireless sensors are\r
-deployed in high density to ensure initially a high coverage ratio of the area\r
-of interest. We assume that all the sensor nodes are homogeneous in terms of\r
-communication, sensing, and processing capabilities and heterogeneous from\r
-the energy provision point of view. The location information is available to a\r
-sensor node either through hardware such as embedded GPS or location discovery\r
-algorithms. We assume that each sensor node can directly transmit its\r
-measurements to a mobile sink node. For example, a sink can be an unmanned\r
-aerial vehicle (UAV) flying regularly over the sensor field to collect\r
-measurements from sensor nodes. A mobile sink node collects the measurements and\r
-transmits them to the base station. We consider a Boolean disk coverage model,\r
-which is the most widely used sensor coverage model in the literature, and all\r
-sensor nodes have a constant sensing range $R_s$. Thus, all the space points\r
-within a disk centered at a sensor with a radius equal to the sensing range are\r
-said to be covered by this sensor. We also assume that the communication range\r
-$R_c$ satisfies $R_c \geq 2 \cdot R_s$. In fact, Zhang and Zhou~\cite{Zhang05}\r
-proved that if the transmission range fulfills the previous hypothesis, the\r
-complete coverage of a convex area implies connectivity among active nodes.\r
-\r
-The PeCO protocol uses the same perimeter-coverage model as Huang and\r
-Tseng in~\cite{huang2005coverage}. It can be expressed as follows: a sensor is\r
-said to be perimeter covered if all the points on its perimeter are covered by\r
-at least one sensor other than itself. They proved that a network area is\r
-$k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).\r
-%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. \r
-Figure~\ref{pcm2sensors}(a) shows the coverage of sensor node~$0$. On this\r
-figure, we can see that sensor~$0$ has nine neighbors and we have reported on\r
-its perimeter (the perimeter of the disk covered by the sensor) for each\r
-neighbor the two points resulting from the intersection of the two sensing\r
-areas. These points are denoted for neighbor~$i$ by $iL$ and $iR$, respectively\r
-for left and right from a neighboing point of view. The resulting couples of\r
-intersection points subdivide the perimeter of sensor~$0$ into portions called\r
-arcs.\r
-\r
-\begin{figure}[ht!]\r
- \centering\r
- \begin{tabular}{@{}cr@{}}\r
- \includegraphics[width=75mm]{figure1a.tiff} & \raisebox{3.25cm}{(a)} \\\r
- \includegraphics[width=75mm]{figure1b.tiff} & \raisebox{2.75cm}{(b)}\r
- \end{tabular}\r
- \caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of\r
- $u$'s perimeter covered by $v$.}\r
- \label{pcm2sensors}\r
-\end{figure} \r
-\r
-Figure~\ref{pcm2sensors}(b) describes the geometric information used to find the\r
-locations of the left and right points of an arc on the perimeter of a sensor\r
-node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the\r
-west side of sensor~$u$, with the following respective coordinates in the\r
-sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can\r
-compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert\r
- u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is\r
-obtained through the formula:\r
- \[\r
-\alpha = \arccos \left(\frac{Dist(u,v)}{2R_s}\r
-\right).\r
-\] \r
-The arc on the perimeter of~$u$ defined by the angular interval $[\pi\r
- - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$.\r
-\r
-Every couple of intersection points is placed on the angular interval $[0,2\pi]$\r
-in a counterclockwise manner, leading to a partitioning of the interval.\r
-Figure~\ref{pcm2sensors}(a) illustrates the arcs for the nine neighbors of\r
-sensor $0$ and Figure~\ref{expcm} gives the position of the corresponding arcs\r
-in the interval $[0,2\pi]$. More precisely, we can see that the points are\r
-ordered according to the measures of the angles defined by their respective\r
-positions. The intersection points are then visited one after another, starting\r
-from the first intersection point after point~zero, and the maximum level of\r
-coverage is determined for each interval defined by two successive points. The\r
-maximum level of coverage is equal to the number of overlapping arcs. For\r
-example, \r
-between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$\r
-(the value is highlighted in yellow at the bottom of Figure~\ref{expcm}), which\r
-means that at most 2~neighbors can cover the perimeter in addition to node $0$. \r
-Table~\ref{my-label} summarizes for each coverage interval the maximum level of\r
-coverage and the sensor nodes covering the perimeter. The example discussed\r
-above is thus given by the sixth line of the table.\r
-\r
-%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). \r
-% to determine the level of the perimeter coverage for each left and right point of a segment.\r
-\r
-\begin{figure*}[t!]\r
-\centering\r
-\includegraphics[width=127.5mm]{figure2.tiff} \r
-\caption{Maximum coverage levels for perimeter of sensor node $0$.}\r
-\label{expcm}\r
-\end{figure*} \r
-\r
-%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 segment 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.\r
-\r
-\r
-\r
- \begin{table}\r
- \tbl{Coverage intervals and contributing sensors for sensor node 0 \label{my-label}}\r
-{\begin{tabular}{|c|c|c|c|c|c|c|c|c|}\r
-\hline\r
-\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\r
-0.0291 & 1L & 2L & 4 & 0 & 1 & 3 & 4 & \\ \hline\r
-0.104 & 2L & 3R & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline\r
-0.3168 & 3R & 4R & 4 & 0 & 1 & 4 & 2 & \\ \hline\r
-0.6752 & 4R & 1R & 3 & 0 & 1 & 2 & & \\ \hline\r
-1.8127 & 1R & 5L & 2 & 0 & 2 & & & \\ \hline\r
-1.9228 & 5L & 6L & 3 & 0 & 2 & 5 & & \\ \hline\r
-2.3959 & 6L & 2R & 4 & 0 & 2 & 5 & 6 & \\ \hline\r
-2.4258 & 2R & 7L & 3 & 0 & 5 & 6 & & \\ \hline\r
-2.7868 & 7L & 8L & 4 & 0 & 5 & 6 & 7 & \\ \hline\r
-2.8358 & 8L & 5R & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline\r
-2.9184 & 5R & 7R & 4 & 0 & 6 & 7 & 8 & \\ \hline\r
-3.3301 & 7R & 9R & 3 & 0 & 6 & 8 & & \\ \hline\r
-3.9464 & 9R & 6R & 4 & 0 & 6 & 8 & 9 & \\ \hline\r
-4.767 & 6R & 3L & 3 & 0 & 8 & 9 & & \\ \hline\r
-4.8425 & 3L & 8R & 4 & 0 & 3 & 8 & 9 & \\ \hline\r
-4.9072 & 8R & 4L & 3 & 0 & 3 & 9 & & \\ \hline\r
-5.3804 & 4L & 9R & 4 & 0 & 3 & 4 & 9 & \\ \hline\r
-5.9157 & 9R & 1L & 3 & 0 & 3 & 4 & & \\ \hline\r
-\end{tabular}}\r
-\r
-\r
-\end{table}\r
-\r
-\r
-%The optimization algorithm that used by PeCO 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.\r
-\r
-In the PeCO protocol, the scheduling of the sensor nodes' activities is formulated with an\r
-integer program based on coverage intervals. The formulation of the coverage\r
-optimization problem is detailed in~section~\ref{cp}. Note that when a sensor\r
-node has a part of its sensing range outside the WSN sensing field, as in\r
-Figure~\ref{ex4pcm}, the maximum coverage level for this arc is set to $\infty$\r
-and the corresponding interval will not be taken into account by the\r
-optimization algorithm.\r
- \r
-\begin{figure}[h!]\r
-\centering\r
-\includegraphics[width=62.5mm]{figure3.tiff} \r
-\caption{Sensing range outside the WSN's area of interest.}\r
-\label{ex4pcm}\r
-\end{figure} \r
-%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 $-2R$.\r
-%\begin{figure}[ht!]\r
-%\centering\r
-%\includegraphics[width=75mm]{ex5pcm.jpg} \r
-%\caption{Coverage intervals and contributing sensors for sensor node 0 having a part of its sensing range outside the border.}\r
-%\label{ex5pcm}\r
-%\end{figure} \r
-\r
-\subsection{The Main Idea}\r
-\r
-\noindent The WSN area of interest is, in a first step, divided into regular\r
-homogeneous subregions using a divide-and-conquer algorithm. In a second step\r
-our protocol will be executed in a distributed way in each subregion\r
-simultaneously to schedule nodes' activities for one sensing period.\r
-\r
-As shown in Figure~\ref{fig2}, node activity scheduling is produced by our\r
-protocol in a periodic manner. Each period is divided into 4 stages: Information\r
-(INFO) Exchange, Leader Election, Decision (the result of an optimization\r
-problem), and Sensing. For each period there is exactly one set cover\r
-responsible for the sensing task. Protocols based on a periodic scheme, like\r
-PeCO, are more robust against an unexpected node failure. On the one hand, if\r
-a node failure is discovered before taking the decision, the corresponding sensor\r
-node will not be considered by the optimization algorithm. On the other\r
-hand, if the sensor failure happens after the decision, the sensing task of the\r
-network will be temporarily affected: only during the period of sensing until a\r
-new period starts, since a new set cover will take charge of the sensing task in\r
-the next period. The energy consumption and some other constraints can easily be\r
-taken into account since the sensors can update and then exchange their\r
-information (including their residual energy) at the beginning of each period.\r
-However, the pre-sensing phases (INFO Exchange, Leader Election, and Decision)\r
-are energy consuming, even for nodes that will not join the set cover to monitor\r
-the area.\r
-\r
-\begin{figure}[t!]\r
-\centering\r
-\includegraphics[width=80mm]{figure4.tiff} \r
-\caption{PeCO protocol.}\r
-\label{fig2}\r
-\end{figure} \r
-\r
-We define two types of packets to be used by PeCO protocol:\r
-%\begin{enumerate}[(a)]\r
-\begin{itemize} \r
-\item INFO packet: sent by each sensor node to all the nodes inside a same\r
- subregion for information exchange.\r
-\item ActiveSleep packet: sent by the leader to all the nodes in its subregion\r
- to transmit to them their respective status (stay Active or go Sleep) during\r
- sensing phase.\r
-\end{itemize}\r
-%\end{enumerate}\r
-\r
-Five status are possible for a sensor node in the network:\r
-%\begin{enumerate}[(a)] \r
-\begin{itemize} \r
-\item LISTENING: waits for a decision (to be active or not);\r
-\item COMPUTATION: executes the optimization algorithm as leader to\r
- determine the activities scheduling;\r
-\item ACTIVE: node is sensing;\r
-\item SLEEP: node is turned off;\r
-\item COMMUNICATION: transmits or receives packets.\r
-\end{itemize}\r
-%\end{enumerate}\r
-%Below, we describe each phase in more details.\r
-\r
-\subsection{PeCO Protocol Algorithm}\r
-\r
-\noindent The pseudocode implementing the protocol on a node is given below.\r
-More precisely, Algorithm~\ref{alg:PeCO} gives a brief description of the\r
-protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.\r
-\r
-\r
-\iffalse\r
-\begin{algorithm} \r
- % \KwIn{all the parameters related to information exchange}\r
-% \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}\r
- \BlankLine\r
- %\emph{Initialize the sensor node and determine it's position and subregion} \; \r
- \r
- \If{ $RE_k \geq E_{th}$ }{\r
- \emph{$s_k.status$ = COMMUNICATION}\;\r
- \emph{Send $INFO()$ packet to other nodes in subregion}\;\r
- \emph{Wait $INFO()$ packet from other nodes in subregion}\; \r
- \emph{Update K.CurrentSize}\;\r
- \emph{LeaderID = Leader election}\;\r
- \If{$ s_k.ID = LeaderID $}{\r
- \emph{$s_k.status$ = COMPUTATION}\;\r
- \r
- \If{$ s_k.ID $ is Not previously selected as a Leader }{\r
- \emph{ Execute the perimeter coverage model}\;\r
- % \emph{ Determine the segment points using perimeter coverage model}\;\r
- }\r
- \r
- \If{$ (s_k.ID $ is the same Previous Leader) And (K.CurrentSize = K.PreviousSize)}{\r
- \r
- \emph{ Use the same previous cover set for current sensing stage}\;\r
- }\r
- \Else{\r
- \emph{Update $a^j_{ik}$; prepare data for IP~Algorithm}\;\r
- \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$)}\;\r
- \emph{K.PreviousSize = K.CurrentSize}\;\r
- }\r
- \r
- \emph{$s_k.status$ = COMMUNICATION}\;\r
- \emph{Send $ActiveSleep()$ to each node $l$ in subregion}\;\r
- \emph{Update $RE_k $}\;\r
- } \r
- \Else{\r
- \emph{$s_k.status$ = LISTENING}\;\r
- \emph{Wait $ActiveSleep()$ packet from the Leader}\;\r
- \emph{Update $RE_k $}\;\r
- } \r
- }\r
- \Else { Exclude $s_k$ from entering in the current sensing stage}\r
- }\r
-%\caption{PeCO($s_k$)}\r
-\label{alg:PeCO}\r
-\end{algorithm}\r
-\fi\r
-\r
-In this algorithm, K.CurrentSize and K.PreviousSize respectively represent the\r
-current number and the previous number of living nodes in the subnetwork of the\r
-subregion. Initially, the sensor node checks its remaining energy $RE_k$, which\r
-must be greater than a threshold $E_{th}$ in order to participate in the current\r
-period. Each sensor node determines its position and its subregion using an\r
-embedded GPS or a location discovery algorithm. After that, all the sensors\r
-collect position coordinates, remaining energy, sensor node ID, and the number\r
-of their one-hop live neighbors during the information exchange. The sensors\r
-inside a same region cooperate to elect a leader. The selection criteria for the\r
-leader, in order of priority, are: larger numbers of neighbors, larger remaining\r
-energy, and then in case of equality, larger index. Once chosen, the leader\r
-collects information to formulate and solve the integer program which allows to\r
-construct the set of active sensors in the sensing stage.\r
-\r
-%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 PeCO 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.\r
-\r
-% 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.\r
-\r
-\section{Perimeter-based Coverage Problem Formulation}\r
-\label{cp}\r
-\r
-\noindent In this section, the coverage model is mathematically formulated. We\r
-start with a description of the notations that will be used throughout the\r
-section.\\\r
-First, we have the following sets:\r
-\begin{itemize}\r
-\item $S$ represents the set of WSN sensor nodes;\r
-\item $A \subseteq S $ is the subset of alive sensors;\r
-\item $I_j$ designates the set of coverage intervals (CI) obtained for\r
- sensor~$j$.\r
-\end{itemize}\r
-$I_j$ refers to the set of coverage intervals which have been defined according\r
-to the method introduced in subsection~\ref{CI}. For a coverage interval $i$,\r
-let $a^j_{ik}$ denotes the indicator function of whether sensor~$k$ is involved\r
-in coverage interval~$i$ of sensor~$j$, that is:\r
-\begin{equation}\r
-a^j_{ik} = \left \{ \r
-\begin{array}{lll}\r
- 1 & \mbox{if sensor $k$ is involved in the } \\\r
- & \mbox{coverage interval $i$ of sensor $j$}, \\\r
- 0 & \mbox{otherwise.}\\\r
-\end{array} \right.\r
-%\label{eq12} \r
-%\notag\r
-\end{equation}\r
-Note that $a^k_{ik}=1$ by definition of the interval.\r
-%, 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.\r
-%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 $k$. .\r
-Second, we define several binary and integer variables. Hence, each binary\r
-variable $X_{k}$ determines the activation of sensor $k$ in the sensing phase\r
-($X_k=1$ if the sensor $k$ is active or 0 otherwise). $M^j_i$ is an integer\r
-variable which measures the undercoverage for the coverage interval $i$\r
-corresponding to sensor~$j$. In the same way, the overcoverage for the same\r
-coverage interval is given by the variable $V^j_i$.\r
-\r
-If we decide to sustain a level of coverage equal to $l$ all along the perimeter\r
-of sensor $j$, we have to ensure that at least $l$ sensors involved in each\r
-coverage interval $i \in I_j$ of sensor $j$ are active. According to the\r
-previous notations, the number of active sensors in the coverage interval $i$ of\r
-sensor $j$ is given by $\sum_{k \in A} a^j_{ik} X_k$. To extend the network\r
-lifetime, the objective is to activate a minimal number of sensors in each\r
-period to ensure the desired coverage level. As the number of alive sensors\r
-decreases, it becomes impossible to reach the desired level of coverage for all\r
-coverage intervals. Therefore we use variables $M^j_i$ and $V^j_i$ as a measure\r
-of the deviation between the desired number of active sensors in a coverage\r
-interval and the effective number. And we try to minimize these deviations,\r
-first to force the activation of a minimal number of sensors to ensure the\r
-desired coverage level, and if the desired level cannot be completely satisfied,\r
-to reach a coverage level as close as possible to the desired one.\r
-\r
-%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. \r
-\r
-%\noindent In this paper, let us define some parameters, which are used in our protocol.\r
-%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 $K$.\r
-\r
-\r
-%\noindent \begin{equation}\r
-%X_{k} = \left \{ \r
-%\begin{array}{l l}\r
- % 1& \mbox{if sensor $k$ is active,} \\\r
-% 0 & \mbox{otherwise.}\\\r
-%\end{array} \right.\r
-%\label{eq11} \r
-%\notag\r
-%\end{equation}\r
-\r
-%\noindent $M^j_i (undercoverage): $ integer value $\in \mathbb{N}$ for segment point $i$ of sensor $j$.\r
-\r
-%\noindent $V^j_i (overcoverage): $ integer value $\in \mathbb{N}$ for segment point $i$ of sensor $j$.\r
-\r
-Our coverage optimization problem can then be mathematically expressed as follows: \r
-%Objective:\r
-\begin{equation} %\label{eq:ip2r}\r
-\left \{\r
-\begin{array}{ll}\r
-\min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\\r
-\textrm{subject to :}&\\\r
-\sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in S\\\r
-%\label{c1} \r
-\sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in S\\\r
-% \label{c2}\r
-% \Theta_{p}\in \mathbb{N}, &\forall p \in P\\\r
-% U_{p} \in \{0,1\}, &\forall p \in P\\\r
-X_{k} \in \{0,1\}, \forall k \in A\r
-\end{array}\r
-\right.\r
-%\notag\r
-\end{equation}\r
-$\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the\r
-relative importance of satisfying the associated level of coverage. For example,\r
-weights associated with coverage intervals of a specified part of a region may\r
-be given by a relatively larger magnitude than weights associated with another\r
-region. This kind of integer program is inspired from the model developed for\r
-brachytherapy treatment planning for optimizing dose distribution\r
-\cite{0031-9155-44-1-012}. The integer program must be solved by the leader in\r
-each subregion at the beginning of each sensing phase, whenever the environment\r
-has changed (new leader, death of some sensors). Note that the number of\r
-constraints in the model is constant (constraints of coverage expressed for all\r
-sensors), whereas the number of variables $X_k$ decreases over periods, since we\r
-consider only alive sensors (sensors with enough energy to be alive during one\r
-sensing phase) in the model.\r
-\r
-\section{Performance Evaluation and Analysis} \r
-\label{sec:Simulation Results and Analysis}\r
-%\noindent \subsection{Simulation Framework}\r
-\r
-\subsection{Simulation Settings}\r
-%\label{sub1}\r
-\r
-The WSN area of interest is supposed to be divided into 16~regular subregions\r
-and we use the same energy consumption than in our previous work~\cite{Idrees2}.\r
-Table~\ref{table3} gives the chosen parameters settings.\r
-\r
-\begin{table}[ht]\r
-\tbl{Relevant parameters for network initialization \label{table3}}{\r
-% title of Table\r
-\centering\r
-% used for centering table\r
-\begin{tabular}{c|c}\r
-% centered columns (4 columns)\r
-\hline\r
-Parameter & Value \\ [0.5ex]\r
- \r
-\hline\r
-% inserts single horizontal line\r
-Sensing field & $(50 \times 25)~m^2 $ \\\r
-\r
-WSN size & 100, 150, 200, 250, and 300~nodes \\\r
-%\hline\r
-Initial energy & in range 500-700~Joules \\ \r
-%\hline\r
-Sensing period & duration of 60 minutes \\\r
-$E_{th}$ & 36~Joules\\\r
-$R_s$ & 5~m \\ \r
-%\hline\r
-$\alpha^j_i$ & 0.6 \\\r
-% [1ex] adds vertical space\r
-%\hline\r
-$\beta^j_i$ & 0.4\r
-%inserts single line\r
-\end{tabular}}\r
-\r
-% is used to refer this table in the text\r
-\end{table}\r
-To obtain experimental results which are relevant, simulations with five\r
-different node densities going from 100 to 300~nodes were performed considering\r
-each time 25~randomly generated networks. The nodes are deployed on a field of\r
-interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a\r
-high coverage ratio. Each node has an initial energy level, in Joules, which is\r
-randomly drawn in the interval $[500-700]$. If its energy provision reaches a\r
-value below the threshold $E_{th}=36$~Joules, the minimum energy needed for a\r
-node to stay active during one period, it will no more participate in the\r
-coverage task. This value corresponds to the energy needed by the sensing phase,\r
-obtained by multiplying the energy consumed in active state (9.72 mW) with the\r
-time in seconds for one period (3600 seconds), and adding the energy for the\r
-pre-sensing phases. According to the interval of initial energy, a sensor may\r
-be active during at most 20 periods.\r
-\r
-The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good\r
-network coverage and a longer WSN lifetime. We have given a higher priority to\r
-the undercoverage (by setting the $\alpha^j_i$ with a larger value than\r
-$\beta^j_i$) so as to prevent the non-coverage for the interval~$i$ of the\r
-sensor~$j$. On the other hand, we have assigned to\r
-$\beta^j_i$ a value which is slightly lower so as to minimize the number of active sensor nodes which contribute\r
-in covering the interval.\r
-\r
-We introduce the following performance metrics to evaluate the efficiency of our\r
-approach.\r
-\r
-%\begin{enumerate}[i)]\r
-\begin{itemize}\r
-\item {\bf Network Lifetime}: the lifetime is defined as the time elapsed until\r
- the coverage ratio falls below a fixed threshold. $Lifetime_{95}$ and\r
- $Lifetime_{50}$ denote, respectively, the amount of time during which is\r
- guaranteed a level of coverage greater than $95\%$ and $50\%$. The WSN can\r
- fulfill the expected monitoring task until all its nodes have depleted their\r
- energy or if the network is no more connected. This last condition is crucial\r
- because without network connectivity a sensor may not be able to send to a\r
- base station an event it has sensed.\r
-\item {\bf Coverage Ratio (CR)} : it measures how well the WSN is able to\r
- observe the area of interest. In our case, we discretized the sensor field as\r
- a regular grid, which yields the following equation:\r
- \r
-%\begin{equation*}\r
-\[\r
- \scriptsize\r
- \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100\r
-\]\r
-% \end{equation*}\r
-\r
- where $n$ is the number of covered grid points by active sensors of every\r
- subregions during the current sensing phase and $N$ is total number of grid\r
- points in the sensing field. In our simulations we have set a layout of\r
- $N~=~51~\times~26~=~1326$~grid points.\r
-\item {\bf Active Sensors Ratio (ASR)}: a major objective of our protocol is to\r
- activate as few nodes as possible, in order to minimize the communication\r
- overhead and maximize the WSN lifetime. The active sensors ratio is defined as\r
- follows:\r
- %\begin{equation*}\r
-\[\r
- \scriptsize\r
- \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|S|$}} \times 100\r
-\]\r
- %\end{equation*}\r
- where $|A_r^p|$ is the number of active sensors in the subregion $r$ in the\r
- current sensing period~$p$, $|S|$ is the number of sensors in the network, and\r
- $R$ is the number of subregions.\r
-\item {\bf Energy Consumption (EC)}: energy consumption can be seen as the total\r
- energy consumed by the sensors during $Lifetime_{95}$ or $Lifetime_{50}$,\r
- divided by the number of periods. The value of EC is computed according to\r
- this formula:\r
- %\begin{equation*}\r
-\[ \r
- \scriptsize\r
- \mbox{EC} = \frac{\sum\limits_{p=1}^{P} \left( E^{\mbox{com}}_p+E^{\mbox{list}}_p+E^{\mbox{comp}}_p \r
- + E^{a}_p+E^{s}_p \right)}{P},\r
-\]\r
- % \end{equation*}\r
- where $P$ corresponds to the number of periods. The total energy consumed by\r
- the sensors comes through taking into consideration four main energy\r
- factors. The first one, denoted $E^{\scriptsize \mbox{com}}_p$, represents the\r
- energy consumption spent by all the nodes for wireless communications during\r
- period $p$. $E^{\scriptsize \mbox{list}}_p$, the next factor, corresponds to\r
- the energy consumed by the sensors in LISTENING status before receiving the\r
- decision to go active or sleep in period $p$. $E^{\scriptsize \mbox{comp}}_p$\r
- refers to the energy needed by all the leader nodes to solve the integer\r
- program during a period. Finally, $E^a_{p}$ and $E^s_{p}$ indicate the energy\r
- consumed by the WSN during the sensing phase (active and sleeping nodes).\r
-\end{itemize}\r
-%\end{enumerate}\r
-\r
-\subsection{Simulation Results}\r
-\r
-In order to assess and analyze the performance of our protocol we have\r
-implemented PeCO protocol in OMNeT++~\cite{varga} simulator. Besides PeCO, two\r
-other protocols, described in the next paragraph, will be evaluated for\r
-comparison purposes. The simulations were run on a DELL laptop with an Intel\r
-Core~i3~2370~M (2.4~GHz) processor (2 cores) whose MIPS (Million Instructions\r
-Per Second) rate is equal to 35330. To be consistent with the use of a sensor\r
-node based on Atmels AVR ATmega103L microcontroller (6~MHz) having a MIPS rate\r
-equal to 6, the original execution time on the laptop is multiplied by 2944.2\r
-$\left(\frac{35330}{2} \times \frac{1}{6} \right)$. The modeling language for\r
-Mathematical Programming (AMPL)~\cite{AMPL} is employed to generate the integer\r
-program instance in a standard format, which is then read and solved by the\r
-optimization solver GLPK (GNU linear Programming Kit available in the public\r
-domain) \cite{glpk} through a Branch-and-Bound method.\r
-\r
-As said previously, the PeCO is compared to three other approaches. The first\r
-one, called DESK, is a fully distributed coverage algorithm proposed by\r
-\cite{ChinhVu}. The second one, called GAF~\cite{xu2001geography}, consists in\r
-dividing the monitoring area into fixed squares. Then, during the decision\r
-phase, in each square, one sensor is chosen to remain active during the sensing\r
-phase. The last one, the DiLCO protocol~\cite{Idrees2}, is an improved version\r
-of a research work we presented in~\cite{idrees2014coverage}. Let us notice that\r
-PeCO and DiLCO protocols are based on the same framework. In particular, the\r
-choice for the simulations of a partitioning in 16~subregions was made because\r
-it corresponds to the configuration producing the best results for DiLCO. The\r
-protocols are distinguished from one another by the formulation of the integer\r
-program providing the set of sensors which have to be activated in each sensing\r
-phase. DiLCO protocol tries to satisfy the coverage of a set of primary points,\r
-whereas the PeCO protocol objective is to reach a desired level of coverage for each\r
-sensor perimeter. In our experimentations, we chose a level of coverage equal to\r
-one ($l=1$).\r
-\r
-\subsubsection{\bf Coverage Ratio}\r
-\r
-Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes\r
-obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better\r
-coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the 98.76\%\r
-produced by PeCO for the first periods. This is due to the fact that at the\r
-beginning the DiLCO protocol puts to sleep status more redundant sensors (which\r
-slightly decreases the coverage ratio), while the three other protocols activate\r
-more sensor nodes. Later, when the number of periods is beyond~70, it clearly\r
-appears that PeCO provides a better coverage ratio and keeps a coverage ratio\r
-greater than 50\% for longer periods (15 more compared to DiLCO, 40 more\r
-compared to DESK). The energy saved by PeCO in the early periods allows later a\r
-substantial increase of the coverage performance.\r
-\r
-\parskip 0pt \r
-\begin{figure}[h!]\r
-\centering\r
- \includegraphics[scale=0.5] {figure5.eps} \r
-\caption{Coverage ratio for 200 deployed nodes.}\r
-\label{fig333}\r
-\end{figure} \r
-\r
-%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 PeCO protocol. The coverage ratio of PeCO protocol is better than other approaches from the period 64.\r
-\r
-%because the optimization algorithm used by PeCO 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 PeCO selected another nodes to ensure the coverage of the area of interest. i.e. DiLCO-16 showed a good coverage in the beginning then PeCO, 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 PeCO protocol to ensure a longer lifetime coverage in comparison with other approaches. \r
-\r
-\r
-\subsubsection{\bf Active Sensors Ratio}\r
-\r
-Having the less active sensor nodes in each period is essential to minimize the\r
-energy consumption and thus to maximize the network lifetime. Figure~\ref{fig444}\r
-shows the average active nodes ratio for 200 deployed nodes. We observe that\r
-DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen\r
-rounds and DiLCO and PeCO protocols compete perfectly with only 17.92~\% and\r
-20.16~\% active nodes during the same time interval. As the number of periods\r
-increases, PeCO protocol has a lower number of active nodes in comparison with\r
-the three other approaches, while keeping a greater coverage ratio as shown in\r
-Figure \ref{fig333}.\r
-\r
-\begin{figure}[h!]\r
-\centering\r
-\includegraphics[scale=0.5]{figure6.eps} \r
-\caption{Active sensors ratio for 200 deployed nodes.}\r
-\label{fig444}\r
-\end{figure} \r
-\r
-\subsubsection{\bf Energy Consumption}\r
-\r
-We studied the effect of the energy consumed by the WSN during the communication,\r
-computation, listening, active, and sleep status for different network densities\r
-and compared it for the four approaches. Figures~\ref{fig3EC}(a) and (b)\r
-illustrate the energy consumption for different network sizes and for\r
-$Lifetime95$ and $Lifetime50$. The results show that our PeCO protocol is the\r
-most competitive from the energy consumption point of view. As shown in both\r
-figures, PeCO consumes much less energy than the three other methods. One might\r
-think that the resolution of the integer program is too costly in energy, but\r
-the results show that it is very beneficial to lose a bit of time in the\r
-selection of sensors to activate. Indeed the optimization program allows to\r
-reduce significantly the number of active sensors and so the energy consumption\r
-while keeping a good coverage level.\r
-\r
-\begin{figure}[h!]\r
- \centering\r
- \begin{tabular}{@{}cr@{}}\r
- \includegraphics[scale=0.475]{figure7a.eps} & \raisebox{2.75cm}{(a)} \\\r
- \includegraphics[scale=0.475]{figure7b.eps} & \raisebox{2.75cm}{(b)}\r
- \end{tabular}\r
- \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}\r
- \label{fig3EC}\r
-\end{figure} \r
-\r
-%The optimization algorithm, which used by PeCO protocol, was improved the lifetime coverage efficiently based on the perimeter coverage model.\r
-\r
- %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. \r
-\r
-\r
-%\subsubsection{Execution Time}\r
-\r
-\subsubsection{\bf Network Lifetime}\r
-\r
-We observe the superiority of PeCO and DiLCO protocols in comparison with the\r
-two other approaches in prolonging the network lifetime. In\r
-Figures~\ref{fig3LT}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for\r
-different network sizes. As highlighted by these figures, the lifetime\r
-increases with the size of the network, and it is clearly largest for DiLCO\r
-and PeCO protocols. For instance, for a network of 300~sensors and coverage\r
-ratio greater than 50\%, we can see on Figure~\ref{fig3LT}(b) that the lifetime\r
-is about twice longer with PeCO compared to DESK protocol. The performance\r
-difference is more obvious in Figure~\ref{fig3LT}(b) than in\r
-Figure~\ref{fig3LT}(a) because the gain induced by our protocols increases with\r
- time, and the lifetime with a coverage of 50\% is far longer than with\r
-95\%.\r
-\r
-\begin{figure}[h!]\r
- \centering\r
- \begin{tabular}{@{}cr@{}}\r
- \includegraphics[scale=0.475]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\ \r
- \includegraphics[scale=0.475]{figure8b.eps} & \raisebox{2.75cm}{(b)}\r
- \end{tabular}\r
- \caption{Network Lifetime for (a)~$Lifetime_{95}$ \\\r
- and (b)~$Lifetime_{50}$.}\r
- \label{fig3LT}\r
-\end{figure} \r
-\r
-%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, PeCO protocol efficiently prolonged the network lifetime especially for a coverage ratio greater than $50 \%$, whilst it stayed very near to DiLCO-16 protocol for $95 \%$.\r
-\r
-Figure~\ref{figLTALL} compares the lifetime coverage of our protocols for\r
-different coverage ratios. We denote by Protocol/50, Protocol/80, Protocol/85,\r
-Protocol/90, and Protocol/95 the amount of time during which the network can\r
-satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$\r
-respectively, where the term Protocol refers to DiLCO or PeCO. Indeed there are applications\r
-that do not require a 100\% coverage of the area to be monitored. PeCO might be\r
-an interesting method since it achieves a good balance between a high level\r
-coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three\r
-lower coverage ratios, moreover the improvements grow with the network\r
-size. DiLCO is better for coverage ratios near 100\%, but in that case PeCO is\r
-not ineffective for the smallest network sizes.\r
-\r
-\begin{figure}[h!]\r
-\centering \includegraphics[scale=0.5]{figure9.eps}\r
-\caption{Network lifetime for different coverage ratios.}\r
-\label{figLTALL}\r
-\end{figure} \r
-\r
-%Comparison shows that PeCO 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. PeCO 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.\r
-\r
-\r
-\section{Conclusion and Future Works}\r
-\label{sec:Conclusion and Future Works}\r
-\r
-In this paper we have studied the problem of Perimeter-based Coverage Optimization in\r
-WSNs. We have designed a new protocol, called Perimeter-based Coverage Optimization, which\r
-schedules nodes' activities (wake up and sleep stages) with the objective of\r
-maintaining a good coverage ratio while maximizing the network lifetime. This\r
-protocol is applied in a distributed way in regular subregions obtained after\r
-partitioning the area of interest in a preliminary step. It works in periods and\r
-is based on the resolution of an integer program to select the subset of sensors\r
-operating in active status for each period. Our work is original in so far as it\r
-proposes for the first time an integer program scheduling the activation of\r
-sensors based on their perimeter coverage level, instead of using a set of\r
-targets/points to be covered.\r
-\r
-%To cope with this problem, the area of interest is divided into a smaller subregions using divide-and-conquer method, and then a PeCO protocol for optimizing the lifetime coverage in each subregion. PeCO protocol combines two efficient techniques: network\r
-%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\r
-%in the subregion. \r
-%The network lifetime coverage in each subregion is divided into\r
-%periods, each period consists of four stages: (i) Information Exchange,\r
-%(ii) Leader Election, (iii) a Decision based new optimization model in order to\r
-%select the nodes remaining active for the last stage, and (iv) Sensing.\r
-We have carried out several simulations to evaluate the proposed protocol. The\r
-simulation results show that PeCO is more energy-efficient than other\r
-approaches, with respect to lifetime, coverage ratio, active sensors ratio, and\r
-energy consumption.\r
-%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 have identified different research directions that arise out of the work presented here.\r
-We plan to extend our framework so that the schedules are planned for multiple\r
-sensing periods.\r
-%in order to compute all active sensor schedules in only one step for many periods;\r
-We also want to improve our integer program to take into account heterogeneous\r
-sensors from both energy and node characteristics point of views.\r
-%the third, we are investigating new optimization model based on the sensing range so as to maximize the lifetime coverage in WSN;\r
-Finally, it would be interesting to implement our protocol using a\r
-sensor-testbed to evaluate it in real world applications.\r
-\r
-\bibliographystyle{gENO}\r
-\bibliography{biblio}\r
-\r
-\r
-\end{document}\r
+% gENOguide.tex
+% v4.0 released April 2013
+
+\documentclass{gENO2e}
+%\usepackage[linesnumbered,ruled,vlined,commentsnumbered]{algorithm2e}
+%\renewcommand{\algorithmcfname}{ALGORITHM}
+\usepackage{indentfirst}
+\usepackage{color}
+\usepackage[algo2e,ruled,vlined]{algorithm2e}
+\begin{document}
+
+%\jvol{00} \jnum{00} \jyear{2013} \jmonth{April}
+
+%\articletype{GUIDE}
+
+\title{{\itshape Perimeter-based Coverage Optimization \\
+ to Improve Lifetime in Wireless Sensor Networks}}
+
+\author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$, and Rapha\"el Couturier $^{a}$
+ $^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, \\
+ University Bourgogne Franche-Comt\'e, Belfort, France}} \\
+ $^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}}
+}
+
+\maketitle
+
+\begin{abstract}
+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. We
+propose such an approach called Perimeter-based Coverage Optimization protocol
+(PeCO). It is a hybrid of centralized and distributed methods: the region of
+interest is first subdivided into subregions and the protocol is then
+distributed among sensor nodes in each subregion. The novelty of our approach
+lies essentially in the formulation of a new mathematical optimization model
+based on the perimeter coverage level to schedule sensors' activities.
+Extensive simulation experiments demonstrate that PeCO can offer longer lifetime
+coverage for WSNs compared to other protocols.
+
+\begin{keywords}
+ Wireless Sensor Networks, Area Coverage, Energy efficiency, Optimization, Scheduling.
+\end{keywords}
+
+\end{abstract}
+
+\section{Introduction}
+\label{sec:introduction}
+
+The continuous progress in Micro Electro-Mechanical Systems (MEMS) and wireless
+communication hardware has given rise to the opportunity of using large networks
+of tiny sensors, called Wireless Sensor Networks
+(WSN)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring
+tasks. A WSN consists of small low-powered sensors working together by
+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 makes it suitable for a wide
+range of applications in areas such as business, environment, health, industry,
+military, and so on~\citep{yick2008wireless}. Typically, a sensor node contains
+three main components~\citep{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
+communication unit for data transmission and reception.
+
+The energy needed by an active sensor node to perform sensing, processing, and
+communication is provided by a power supply which is a battery. This battery has
+a limited energy provision and it may be unsuitable or impossible to replace or
+recharge in most applications. Therefore it is necessary to deploy WSN with high
+density in order to increase reliability and to exploit node redundancy thanks
+to energy-efficient activity scheduling approaches. Indeed, the overlap of
+sensing areas can be exploited to schedule alternatively some sensors in a low
+power sleep mode and thus save energy. Overall, the main question that must be
+answered is: how is it possible to extend the lifetime coverage of a WSN as long
+as possible while ensuring a high level of coverage? These past few years many
+energy-efficient mechanisms have been suggested to retain energy and extend the
+lifetime of the WSNs~\citep{rault2014energy}.
+
+This paper makes the following contributions :
+\begin{enumerate}
+\item A framework is devised 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 the proposed framework is to
+ exploit spatial and temporal subdivision. On the one hand, the area of
+ interest is 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 A new mathematical optimization model is proposed. Instead of trying to
+ cover a set of specified points/targets as in most of the methods proposed in
+ the literature, we formulate a mixed-integer program based on the perimeter
+ coverage of each sensor. The model involves integer variables to capture the
+ deviations between the actual level of coverage and the required level.
+ Hence, an optimal schedule will be obtained by minimizing a weighted sum of
+ these deviations.
+\item Extensive simulation experiments are conducted using the discrete event
+ simulator OMNeT++, to demonstrate the efficiency of our protocol. We have
+ compared the PeCO protocol to two approaches found in the literature:
+ DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to our previous
+ protocol DiLCO published in~\citep{Idrees2}. DiLCO uses the same framework as
+ PeCO but is based on another optimization model for sensor scheduling.
+\end{enumerate}
+
+The rest of the paper is organized as follows. In the next section some related
+work in the field is reviewed. Section~\ref{sec:The PeCO Protocol Description}
+is devoted to the PeCO 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 are given for future works in
+Section~\ref{sec:Conclusion and Future Works}.
+
+\section{Related Literature}
+\label{sec:Literature Review}
+
+This section summarizes some related works regarding the coverage problem and
+presents specific aspects of the PeCO protocol common with other literature
+works.
+
+The most discussed coverage problems in literature can be classified in three
+categories~\citep{li2013survey} according to their respective monitoring
+objective. Hence, area coverage \citep{Misra} means that every point inside a
+fixed area must be monitored, while target coverage~\citep{yang2014novel} refers
+to the objective of coverage for a finite number of discrete points called
+targets, and barrier coverage~\citep{HeShibo,kim2013maximum} focuses on
+preventing intruders from entering into the region of interest. In
+\citep{Deng2012} authors transform the area coverage problem into the target
+coverage one, taking into account the intersection points among disks of sensors
+nodes or between disks of sensor nodes and boundaries. In
+\citep{huang2005coverage} authors prove that if the perimeters of the 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. $d$ denotes the maximum number of sensors that are neighbors to a
+sensor, and $n$ is the total number of sensors in the network. {\it In PeCO
+ 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.}
+
+The major approach to extend network lifetime while preserving coverage is to
+divide/organize the sensors into a suitable number of set covers (disjoint or
+non-disjoint) \citep{wang2011coverage}, where each set completely covers a
+region of interest, and to successively activate these set covers. The network
+activity can be planned in advance and scheduled for the entire network lifetime
+or organized in periods, and the set of active sensor nodes decided at the
+beginning of each period \citep{ling2009energy}. In fact, many authors propose
+algorithms working in such a periodic fashion
+\citep{chin2007,yan2008design,pc10}. Active node selection is determined based
+on the problem requirements (e.g. area monitoring, connectivity, or power
+efficiency). For instance, \citet{jaggi2006} address the problem of maximizing
+the lifetime by dividing sensors into the maximum number of disjoint subsets
+such that each subset can ensure both coverage and connectivity. A greedy
+algorithm is applied once to solve this problem and the computed sets are
+activated in succession to achieve the desired network lifetime. {\it Motivated
+ by these works, PeCO protocol works in periods, where each period contains a
+ preliminary phase for information exchange and 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
+concepts, have been proposed to extend the network lifetime
+\citep{zhou2009variable}. In distributed
+algorithms~\citep{ChinhVu,qu2013distributed,yangnovel} 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 information on its immediate neighbors only (usually the one-hop
+ones), it may make a bad decision leading to a global suboptimal solution.
+Conversely, centralized
+algorithms~\citep{cardei2005improving,zorbas2010solving,pujari2011high} always
+provide nearly optimal solutions 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 huge since long range
+communications will be needed. In fact the larger the WSN, the higher the
+communication energy cost. {\it In order to be suitable for large-scale
+ networks, in the PeCO 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 the PeCO protocol
+ is scalable and a globally distributed method, whereas it is centralized in
+ each subregion.}
+
+Various coverage scheduling algorithms have been developed these past few years.
+Many of them, dealing with the maximization of the number of cover sets, are
+heuristics. These heuristics involve the construction of a cover set by
+including in priority the sensor nodes which cover critical targets, that is to
+say targets that are covered by the smallest number of sensors
+\citep{berman04,zorbas2010solving}. Other approaches are based on mathematical
+programming
+formulations~\citep{cardei2005energy,5714480,pujari2011high,Yang2014} and
+dedicated techniques (solving with a branch-and-bound algorithm available in
+optimization solver). The problem is formulated as an optimization problem
+(maximization of the lifetime or number of cover sets) under target coverage and
+energy constraints. Column generation techniques, well-known and widely
+practiced techniques for solving linear programs with too many variables, have
+also been
+used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012column}.
+{\it In the PeCO protocol, each leader, in charge of a subregion, solves an
+ integer program which has a twofold objective: minimizing the overcoverage and
+ the undercoverage of the perimeter of each sensor.}
+
+The authors in \citep{Idrees2} propose a Distributed Lifetime Coverage
+Optimization (DiLCO) protocol, which maintains the coverage and improves the
+lifetime in WSNs. It is an improved version of a research work presented
+in~\citep{idrees2014coverage}. First, the area of interest is partitioned into
+subregions using a divide-and-conquer method. The DiLCO protocol is then
+distributed on the sensor nodes in each subregion in a second step. Hence this
+protocol combines two techniques: a leader election in each subregion, followed
+by an optimization-based node activity scheduling performed by each elected
+leader. The proposed DiLCO protocol is a periodic protocol where each period is
+decomposed into 4 phases: information exchange, leader election, decision, and
+sensing. The simulations show that DiLCO is able to increase the WSN lifetime
+and provides improved coverage performance. {\it In the PeCO protocol, a new
+ mathematical optimization model is proposed. Instead of trying to cover a set
+ of specified points/targets as in the DiLCO protocol, we formulate an integer
+ program based on the perimeter coverage of each sensor. The model involves
+ integer variables to capture the deviations between the actual level of
+ coverage and the required level. The idea is that an optimal scheduling will
+ be obtained by minimizing a weighted sum of these deviations.}
+
+\section{ The P{\scshape e}CO Protocol Description}
+\label{sec:The PeCO Protocol Description}
+
+%In this section, the Perimeter-based Coverage
+%Optimization protocol is decribed in details. First we present the assumptions we made and the models
+%we considered (in particular the perimeter coverage one), second we describe the
+%background idea of our protocol, and third we give the outline of the algorithm
+%executed by each node.
+
+
+\subsection{Assumptions and Models}
+\label{CI}
+
+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 area
+of interest. All the sensor nodes are supposed to be homogeneous in terms of
+communication, sensing, and processing capabilities and heterogeneous from the
+energy provision point of view. The location information is available to a
+sensor node either through hardware such as embedded GPS or location discovery
+algorithms. A Boolean disk coverage model, which is the most widely used sensor
+coverage model in the literature, is considered and all sensor nodes have a
+constant sensing range $R_s$. Thus, all the space points within a disk centered
+at a sensor with a radius equal to the sensing range are said to be covered by
+this sensor. We also assume that the communication range $R_c$ satisfies $R_c
+\geq 2 \cdot R_s$. In fact, \citet{Zhang05} proved that if the transmission
+range fulfills the previous hypothesis, the complete coverage of a convex area
+implies connectivity among active nodes.
+
+The PeCO protocol uses the same perimeter-coverage model as
+\citet{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. Authors \citet{huang2005coverage} proved that a
+network area is $k$-covered (every point in the area is covered by at least
+$k$~sensors) if and only if each sensor in the network is $k$-perimeter-covered
+(perimeter covered by at least $k$ sensors).
+
+Figure~\ref{figure1}(a) shows the coverage of sensor node~$0$. On this figure,
+sensor~$0$ has nine neighbors and we have reported on its perimeter (the
+perimeter of the disk covered by the sensor) for each neighbor the two points
+resulting from the intersection of the two sensing areas. These points are
+denoted for neighbor~$i$ by $iL$ and $iR$, respectively for left and right from
+a neighboring point of view. The resulting couples of intersection points
+subdivide the perimeter of sensor~$0$ into portions called arcs.
+
+\begin{figure}[ht!]
+ \centering
+ \begin{tabular}{@{}cr@{}}
+ \includegraphics[width=75mm]{figure1a.eps} & \raisebox{3.25cm}{(a)} \\
+ \includegraphics[width=75mm]{figure1b.eps} & \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$.}
+ \label{figure1}
+\end{figure}
+
+Figure~\ref{figure1}(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~$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 the
+euclidean distance between nodes~$u$ and $v$ is computed as follows:
+$$
+ Dist(u,v)=\sqrt{(u_x - v_x)^2 + (u_y-v_y)^2},
+$$
+while the angle~$\alpha$ is obtained through the formula:
+ \[
+\alpha = \arccos \left(\frac{Dist(u,v)}{2R_s} \right).
+\]
+The arc on the perimeter of~$u$ defined by the angular interval $[\pi -
+ \alpha,\pi + \alpha]$ is then 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{figure1}(a) illustrates the arcs for the nine neighbors of
+sensor $0$ and Table~\ref{my-label} gives the position of the corresponding arcs
+in the interval $[0,2\pi)$. More precisely, 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 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{figure2}), 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.
+
+\begin{figure*}[t!]
+\centering
+\includegraphics[width=0.95\linewidth]{figure2.eps}
+\caption{Maximum coverage levels for perimeter of sensor node $0$.}
+\label{figure2}
+\end{figure*}
+
+\begin{table}
+\tbl{Coverage intervals and contributing sensors for node 0 \label{my-label}}
+{\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 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
+0.6752 & 4R & 1R & 3 & 0 & 1 & 2 & & \\ \hline
+1.8127 & 1R & 5L & 2 & 0 & 2 & & & \\ \hline
+1.9228 & 5L & 6L & 3 & 0 & 2 & 5 & & \\ \hline
+2.3959 & 6L & 2R & 4 & 0 & 2 & 5 & 6 & \\ \hline
+2.4258 & 2R & 7L & 3 & 0 & 5 & 6 & & \\ \hline
+2.7868 & 7L & 8L & 4 & 0 & 5 & 6 & 7 & \\ \hline
+2.8358 & 8L & 5R & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline
+2.9184 & 5R & 7R & 4 & 0 & 6 & 7 & 8 & \\ \hline
+3.3301 & 7R & 9R & 3 & 0 & 6 & 8 & & \\ \hline
+3.9464 & 9R & 6R & 4 & 0 & 6 & 8 & 9 & \\ \hline
+4.767 & 6R & 3L & 3 & 0 & 8 & 9 & & \\ \hline
+4.8425 & 3L & 8R & 4 & 0 & 3 & 8 & 9 & \\ \hline
+4.9072 & 8R & 4L & 3 & 0 & 3 & 9 & & \\ \hline
+5.3804 & 4L & 9R & 4 & 0 & 3 & 4 & 9 & \\ \hline
+5.9157 & 9R & 1L & 3 & 0 & 3 & 4 & & \\ \hline
+\end{tabular}}
+
+
+\end{table}
+
+In the PeCO protocol, the scheduling of the sensor nodes' activities is
+formulated with a mixed-integer program based on coverage
+intervals~\citep{doi:10.1155/2010/926075}. 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{figure3}, 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.
+
+%\newpage
+\begin{figure}[h!]
+\centering
+\includegraphics[width=57.5mm]{figure3.eps}
+\caption{Sensing range outside the WSN's area of interest.}
+\label{figure3}
+\end{figure}
+
+\vspace{-0.25cm}
+
+\subsection{Main Idea}
+
+The WSN area of interest is, in a first step, divided into regular 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. Sensor nodes are assumed to
+be deployed almost uniformly over the region. The regular subdivision is made
+such that the number of hops between any pairs of sensors inside a subregion is
+less than or equal to 3.
+
+As shown in Figure~\ref{figure4}, node activity scheduling is produced by the
+proposed 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 PeCO, are more robust against an unexpected node failure. On the one hand,
+if 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
+the next period. The energy consumption and some other constraints can easily be
+taken into account since the sensors can update and then exchange their
+information (including their residual energy) at the beginning of each period.
+However, the pre-sensing phases (INFO Exchange, Leader Election, and Decision)
+are energy consuming, even for nodes that will not join the set cover to monitor
+the area. Sensing period duration is adapted according to the QoS requirements
+of the application.
+
+\begin{figure}[t!]
+\centering
+\includegraphics[width=80mm]{figure4.eps}
+\caption{PeCO protocol.}
+\label{figure4}
+\end{figure}
+
+We define two types of packets to be used by the PeCO protocol:
+\begin{itemize}
+\item INFO packet: sent by each sensor node to all the nodes inside a same
+ subregion for information exchange.
+\item ActiveSleep packet: sent by the leader to all the nodes in its subregion
+ to transmit to them their respective status (stay Active or go Sleep) during
+ the sensing phase.
+\end{itemize}
+
+Five statuses are possible for a sensor node in the network:
+\begin{itemize}
+\item LISTENING: waits for a decision (to be active or not);
+\item COMPUTATION: executes the optimization algorithm as leader to
+ determine the activities scheduling;
+\item ACTIVE: node is sensing;
+\item SLEEP: node is turned off;
+\item COMMUNICATION: transmits or receives packets.
+\end{itemize}
+
+\subsection{PeCO Protocol Algorithm}
+
+The pseudocode implementing the protocol on a node is given below. More
+precisely, Algorithm~\ref{alg:PeCO} gives a brief description of the protocol
+applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
+
+
+\begin{algorithm2e}
+ % \KwIn{all the parameters related to information exchange}
+% \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
+% \BlankLine
+ %\emph{Initialize the sensor node and determine it's position and subregion} \;
+ \label{alg:PeCO}
+ \caption{PeCO pseudocode}
+ \eIf{$RE_k \geq E_{th}$}{
+ $s_k.status$ = COMMUNICATION\;
+ Send $INFO()$ packet to other nodes in subregion\;
+ Wait $INFO()$ packet from other nodes in subregion\;
+ Update K.CurrentSize\;
+ LeaderID = Leader election\;
+ \eIf{$s_k.ID = LeaderID$}{
+ $s_k.status$ = COMPUTATION\;
+ \If{$ s_k.ID $ is Not previously selected as a Leader}{
+ Execute the perimeter coverage model\;
+ }
+ \eIf{($s_k.ID $ is the same Previous Leader) {\bf and} \\
+ \indent (K.CurrentSize = K.PreviousSize)}{
+ Use the same previous cover set for current sensing stage\;
+ }{
+ Update $a^j_{ik}$; prepare data for IP~Algorithm\;
+ $\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$)\;
+ K.PreviousSize = K.CurrentSize\;
+ }
+ $s_k.status$ = COMMUNICATION\;
+ Send $ActiveSleep()$ to each node $l$ in subregion\;
+ Update $RE_k $\;
+ }{
+ $s_k.status$ = LISTENING\;
+ Wait $ActiveSleep()$ packet from the Leader\;
+ Update $RE_k $\;
+ }
+ }{
+ Exclude $s_k$ from entering in the current sensing stage\;
+ }
+\end{algorithm2e}
+
+%\begin{algorithm}
+%\noindent{\bf If} $RE_k \geq E_{th}$ {\bf then}\\
+%\hspace*{0.6cm} \emph{$s_k.status$ = COMMUNICATION;}\\
+%\hspace*{0.6cm} \emph{Send $INFO()$ packet to other nodes in subregion;}\\
+%\hspace*{0.6cm} \emph{Wait $INFO()$ packet from other nodes in subregion;}\\
+%\hspace*{0.6cm} \emph{Update K.CurrentSize;}\\
+%\hspace*{0.6cm} \emph{LeaderID = Leader election;}\\
+%\hspace*{0.6cm} {\bf If} $ s_k.ID = LeaderID $ {\bf then}\\
+%\hspace*{1.2cm} \emph{$s_k.status$ = COMPUTATION;}\\
+%\hspace*{1.2cm}{\bf If} \emph{$ s_k.ID $ is Not previously selected as a Leader} {\bf then}\\
+%\hspace*{1.8cm} \emph{ Execute the perimeter coverage model;}\\
+%\hspace*{1.2cm} {\bf end}\\
+%\hspace*{1.2cm}{\bf If} \emph{($s_k.ID $ is the same Previous Leader)~And~(K.CurrentSize = K.PreviousSize)}\\
+%\hspace*{1.8cm} \emph{ Use the same previous cover set for current sensing stage;}\\
+%\hspace*{1.2cm} {\bf end}\\
+%\hspace*{1.2cm} {\bf else}\\
+%\hspace*{1.8cm}\emph{Update $a^j_{ik}$; prepare data for IP~Algorithm;}\\
+%\hspace*{1.8cm} \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$);}\\
+%\hspace*{1.8cm} \emph{K.PreviousSize = K.CurrentSize;}\\
+%\hspace*{1.2cm} {\bf end}\\
+%\hspace*{1.2cm}\emph{$s_k.status$ = COMMUNICATION;}\\
+%\hspace*{1.2cm}\emph{Send $ActiveSleep()$ to each node $l$ in subregion;}\\
+%\hspace*{1.2cm}\emph{Update $RE_k $;}\\
+%\hspace*{0.6cm} {\bf end}\\
+%\hspace*{0.6cm} {\bf else}\\
+%\hspace*{1.2cm}\emph{$s_k.status$ = LISTENING;}\\
+%\hspace*{1.2cm}\emph{Wait $ActiveSleep()$ packet from the Leader;}\\
+%\hspace*{1.2cm}\emph{Update $RE_k $;}\\
+%\hspace*{0.6cm} {\bf end}\\
+%{\bf end}\\
+%{\bf else}\\
+%\hspace*{0.6cm} \emph{Exclude $s_k$ from entering in the current sensing stage;}\\
+%{\bf end}\\
+%\label{alg:PeCO}
+%\end{algorithm}
+
+In this algorithm, $K.CurrentSize$ and $K.PreviousSize$ respectively represent
+the current number and the previous number of living nodes in the subnetwork of
+the subregion. At the beginning of the first period $K.PreviousSize$ is
+initialized to zero. 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. \textcolor{blue}{We suppose that both INFO packet and ActiveSleep packet contain two parts: header and data payload. The sensor id is included in the header, where the header size is 8 bits. The data part includes position coordinates (64 bits), remaining energy (32 bits), and the number of their one-hop live neighbors (8 bits). Therefore the size of the INFO packet is 112 bits. The ActiveSleep packet is 16 bits size, 8 bits for the header and 8 bits for data part that includes only sensor status (0 or 1)}
+The sensors inside a same region cooperate to elect a leader. The selection
+criteria for the leader are (in order of priority):
+\begin{enumerate}
+\item larger number of neighbors;
+\item larger remaining energy;
+\item and then, in case of equality, larger indexes.
+\end{enumerate}
+Once chosen, the leader collects information to formulate and solve the integer
+program which allows to build the set of active sensors in the sensing
+stage.
+
+\section{Perimeter-based Coverage Problem Formulation}
+\label{cp}
+
+In this section, the perimeter-based coverage problem is mathematically
+formulated. It has been proved to be a NP-hard problem
+by \citep{doi:10.1155/2010/926075}. Authors study the coverage of the perimeter
+of a large object requiring to be monitored. For the proposed formulation in
+this paper, the large object to be monitored is the sensor itself (or more
+precisely its sensing area).
+
+The following notations are used throughout the section.
+
+First, the following sets:
+\begin{itemize}
+\item $S$ represents the set of sensor nodes;
+\item $A \subseteq S $ is the subset of alive sensors;
+\item $I_j$ designates the set of coverage intervals (CI) obtained for
+ sensor~$j$.
+\end{itemize}
+$I_j$ refers to the set of coverage intervals which has 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
+in coverage interval~$i$ of sensor~$j$, that is:
+\begin{equation}
+a^j_{ik} = \left \{
+\begin{array}{lll}
+ 1 & \mbox{if sensor $k$ is involved in the } \\
+ & \mbox{coverage interval $i$ of sensor $j$}, \\
+ 0 & \mbox{otherwise.}\\
+\end{array} \right.
+\end{equation}
+Note that $a^k_{ik}=1$ by definition of the interval.
+
+Second, several variables are defined. Hence, each binary variable $X_{k}$
+determines the activation of sensor $k$ in the sensing phase ($X_k=1$ if the
+sensor $k$ is active or 0 otherwise). $M^j_i$ is a variable which measures the
+undercoverage for the coverage interval $i$ corresponding to sensor~$j$. In the
+same way, the overcoverage for the same coverage interval is given by the
+variable $V^j_i$.
+
+To sustain a level of coverage equal to $l$ all along the perimeter of sensor
+$j$, at least $l$ sensors involved in each coverage interval $i \in I_j$ of
+sensor $j$ have to be active. According to the previous notations, the number
+of active sensors in the coverage interval $i$ of sensor $j$ is given by
+$\sum_{k \in A} a^j_{ik} X_k$. 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
+variables $M^j_i$ and $V^j_i$ are introduced 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 desired coverage level,
+and if the desired level cannot be completely satisfied, to reach a coverage
+level as close as possible to the desired one.
+
+The coverage optimization problem can then be mathematically expressed as follows:
+\begin{equation}
+ \begin{aligned}
+ \text{Minimize } & \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i ) \\
+ \text{Subject to:} & \\
+ & \sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in S \\
+ & \sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in S \\
+ & X_{k} \in \{0,1\}, \forall k \in A \\
+ & M^j_i, V^j_i \in \mathbb{R}^{+}
+ \end{aligned}
+\end{equation}
+
+%\begin{equation}
+%\left \{
+%\begin{array}{ll}
+%\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 A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in S\\
+%\sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in S\\
+%X_{k} \in \{0,1\}, \forall k \in A \\
+%M^j_i, V^j_i \in \mathbb{R}^{+}
+%\end{array}
+%\right.
+%\end{equation}
+
+If a given level of coverage $l$ is required for one sensor, the sensor is said
+to be undercovered (respectively overcovered) if the level of coverage of one of
+its CI is less (respectively greater) than $l$. If the sensor $j$ is
+undercovered, there exists at least one of its CI (say $i$) for which the number
+of active sensors (denoted by $l^{i}$) covering this part of the perimeter is
+less than $l$ and in this case : $M_{i}^{j}=l-l^{i}$, $V_{i}^{j}=0$. Conversely,
+if the sensor $j$ is overcovered, there exists at least one of its CI (say $i$)
+for which the number of active sensors (denoted by $l^{i}$) covering this part
+of the perimeter is greater than $l$ and in this case: $M_{i}^{j}=0$,
+$V_{i}^{j}=l^{i}-l$.
+
+$\alpha^j_i$ 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 the specified part of a region may
+be given by a relatively larger magnitude than weights associated with another
+region. This kind of mixed-integer program is inspired from the model developed
+for brachytherapy treatment planning to optimize dose distribution
+\citep{0031-9155-44-1-012}. The choice of the values for variables $\alpha$ and
+$\beta$ should be made according to the needs of the application. $\alpha$
+should be large enough to prevent undercoverage and so to reach the highest
+possible coverage ratio. $\beta$ should be large enough to prevent overcoverage
+and so to activate a minimum number of sensors. The mixed-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 only alive sensors (sensors with enough energy to
+be alive during one sensing phase) are considered in the model.
+
+\section{Performance Evaluation and Analysis}
+\label{sec:Simulation Results and Analysis}
+
+\subsection{Simulation Settings}
+
+The WSN area of interest is supposed to be divided into 16~regular subregions
+and we use the same energy consumption model as in our previous
+work~\citep{Idrees2}. Table~\ref{table3} gives the chosen parameters settings.
+
+\begin{table}[ht]
+\tbl{Relevant parameters for network initialization \label{table3}}{
+\centering
+\begin{tabular}{c|c}
+\hline
+Parameter & Value \\ [0.5ex]
+\hline
+% inserts single horizontal line
+Sensing field & $(50 \times 25)~m^2 $ \\
+WSN size & 100, 150, 200, 250, and 300~nodes \\
+Initial energy & in range 500-700~Joules \\
+Sensing period & duration of 60 minutes \\
+$E_{th}$ & 36~Joules \\
+$R_s$ & 5~m \\
+$R_c$ & 10~m \\
+$\alpha^j_i$ & 0.6 \\
+$\beta^j_i$ & 0.4
+\end{tabular}}
+\end{table}
+
+To obtain experimental results which are relevant, simulations with five
+different node densities going from 100 to 300~nodes were performed considering
+each time 25~randomly generated networks. 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 its energy provision reaches a
+value below the threshold $E_{th}=36$~Joules, the minimum energy needed for a
+node to stay active during one period, it will no longer participate in the
+coverage task. This value corresponds to the energy needed by the sensing phase,
+obtained by multiplying the energy consumed in the active state (9.72 mW) with
+the time in seconds for one period (3600 seconds), and adding the energy for the
+pre-sensing phases. According to the interval of initial energy, a sensor may
+be active during at most 20 periods. the information exchange to update the coverage
+is executed every hour, but the length of the sensing period could be reduced
+and adapted dynamically. On the one hand a small sensing period would allow the network to
+be more reliable but would have resulted in higher communication costs. On the
+other hand the choice of a long duration may cause problems in case of nodes
+failure during the sensing period.
+
+The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good
+network coverage and a longer WSN lifetime. Higher priority is given to 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, $\beta^j_i$ is assigned to a value which is slightly lower so as
+to minimize the number of active sensor nodes which contribute in covering the
+interval. Subsection~\ref{sec:Impact} investigates more deeply how the values of
+both parameters affect the performance of the PeCO protocol.
+
+The following performance metrics are used to evaluate the efficiency of the
+approach.
+\begin{itemize}
+\item {\bf Network Lifetime}: the lifetime is defined as the time elapsed until
+ the coverage ratio falls below a fixed threshold. $Lifetime_{95}$ and
+ $Lifetime_{50}$ 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 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
+ observe the area of interest. In our case, the sensor field is discretized as
+ a regular grid, which yields the following equation:
+ \begin{equation*}
+ \scriptsize
+ \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100
+ \end{equation*}
+ where $n$ is the number of covered grid points by active sensors of every
+ subregions during the current sensing phase and $N$ is total number of grid
+ points in the sensing field. A layout of $N~=~51~\times~26~=~1326$~grid points
+ is considered in the simulations.
+\item {\bf Active Sensors Ratio (ASR)}: a major objective of our protocol is to
+ activate as few nodes as possible, in order to minimize the communication
+ overhead and maximize the WSN 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{$|J|$}} \times 100
+ \end{equation*}
+ where $|A_r^p|$ is the number of active sensors in the subregion $r$ in the
+ sensing period~$p$, $R$ is the number of subregions, and $|J|$ is the number
+ of sensors in the network.
+
+\item {\bf \textcolor{blue}{Energy Saving Ratio (ESR)}}:
+\textcolor{blue}{we consider a performance metric linked to energy. This metric, called Energy Saving Ratio (ESR), is defined by:
+\begin{equation*}
+\scriptsize
+\mbox{ESR}(\%) = \frac{\mbox{Number of alive sensors during this round}}
+{\mbox{Total number of sensors in the network}} \times 100.
+\end{equation*}
+ }
+\item {\bf Energy Consumption (EC)}: energy consumption can be seen as the total
+ energy consumed by the sensors during $Lifetime_{95}$ or $Lifetime_{50}$,
+ divided by the number of periods. The value of EC is computed according to
+ this formula:
+ \begin{equation*}
+ \scriptsize
+ \mbox{EC} = \frac{\sum\limits_{p=1}^{P} \left( E^{\mbox{com}}_p+E^{\mbox{list}}_p+E^{\mbox{comp}}_p
+ + E^{a}_p+E^{s}_p \right)}{P},
+ \end{equation*}
+ where $P$ corresponds to the number of periods. The total energy consumed by
+ the sensors comes through taking into consideration four main energy
+ factors. The first one, denoted $E^{\scriptsize \mbox{com}}_p$, represents the
+ energy consumption spent by all the nodes for wireless communications during
+ period $p$. $E^{\scriptsize \mbox{list}}_p$, the next factor, corresponds to
+ the energy consumed by the sensors in LISTENING status before receiving the
+ decision to go active or sleep in period $p$. $E^{\scriptsize \mbox{comp}}_p$
+ refers to the energy needed by all the leader nodes to solve the integer
+ program during a period (COMPUTATION status). Finally, $E^a_{p}$ and
+ $E^s_{p}$ indicate the energy consumed by the WSN during the sensing phase
+ ({\it active} and {\it sleeping} nodes).
+\end{itemize}
+
+\subsection{Simulation Results}
+
+In order to assess and analyze the performance of our protocol we have
+implemented the PeCO protocol in OMNeT++~\citep{varga} simulator. The
+simulations were run on a DELL laptop with an Intel Core~i3~2370~M (1.8~GHz)
+processor (2 cores) whose MIPS (Million Instructions Per Second) rate is equal
+to 35330. To be consistent with the use of a sensor node based on Atmels AVR
+ATmega103L microcontroller (6~MHz) having a MIPS rate equal to 6, the original
+execution time on the laptop is multiplied by 2944.2 $\left(\frac{35330}{2}
+\times \frac{1}{6} \right)$. Energy consumption is calculated according to the
+power consumption values, in milliWatt per second, given in Table~\ref{tab:EC},
+based on the energy model proposed in \citep{ChinhVu}.
+
+\begin{table}[h]
+\centering
+\caption{Power consumption values}
+\label{tab:EC}
+\begin{tabular}{|l||cccc|}
+ \hline
+ {\bf Sensor status} & MCU & Radio & Sensing & {\it Power (mW)} \\
+ \hline
+ LISTENING & On & On & On & 20.05 \\
+ ACTIVE & On & Off & On & 9.72 \\
+ SLEEP & Off & Off & Off & 0.02 \\
+ COMPUTATION & On & On & On & 26.83 \\
+ \hline
+ \multicolumn{4}{|l}{Energy needed to send or receive a 2-bit content message} & 0.515 \\
+ \hline
+\end{tabular}
+\end{table}
+
+The modeling language for Mathematical Programming (AMPL)~\citep{AMPL} is used
+to generate the integer program instance in a standard format, which is then
+read and solved by the optimization solver GLPK (GNU linear Programming Kit
+available in the public domain) \citep{glpk} through a Branch-and-Bound method.
+In practice, executing GLPK on a sensor node is obviously intractable due to the
+huge memory use. Fortunately, to solve the optimization problem we could use
+commercial solvers like CPLEX \citep{iamigo:cplex} which are less memory
+consuming and more efficient, or implement a lightweight heuristic. For example,
+for a WSN of 200 sensor nodes, a leader node has to deal with constraints
+induced by about 12 sensor nodes. In that case, to solve the optimization
+problem a memory consumption of more than 1~MB can be observed with GLPK,
+whereas less than 300~KB would be needed with CPLEX.
+
+Besides PeCO, three other protocols will be evaluated for comparison
+purposes. The first one, called DESK, is a fully distributed coverage algorithm
+proposed by \citep{ChinhVu}. The second one, called
+GAF~\citep{xu2001geography}, consists in dividing the monitoring area into fixed
+squares. Then, during the decision phase, in each square, one sensor is chosen
+to remain active during the sensing phase. The last one, the DiLCO
+protocol~\citep{Idrees2}, is an improved version of a research work we presented
+in~\citep{idrees2014coverage}. Let us notice that the PeCO and DiLCO protocols
+are based on the same framework. In particular, the choice for the simulations
+of a partitioning in 16~subregions was made because it corresponds to the
+configuration producing the best results for DiLCO. Of course, this number of
+subregions should be adapted according to the size of the area of interest and
+the number of sensors. 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. The DiLCO protocol tries to satisfy the
+coverage of a set of primary points, whereas the objective of the PeCO protocol
+is to reach a desired level of coverage for each sensor perimeter. In our
+experimentations, we chose a level of coverage equal to one ($l=1$).
+
+\subsubsection{Coverage Ratio}
+
+Figure~\ref{figure5} shows the average coverage ratio for 200 deployed nodes
+obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better
+coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the
+98.76\% produced by PeCO for the first periods. This is due to the fact that at
+the beginning the DiLCO and PeCO protocols put more redundant sensors to sleep
+status (which slightly decreases the coverage ratio), while the two other
+protocols activate more sensor nodes. Later, when the number of periods is
+beyond~70, it clearly appears that PeCO 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). The energy saved by PeCO in the early periods
+allows later a substantial increase of the coverage performance.
+
+\parskip 0pt
+\begin{figure}[h!]
+\centering
+ \includegraphics[scale=0.5] {figure5.eps}
+\caption{Coverage ratio for 200 deployed nodes.}
+\label{figure5}
+\end{figure}
+
+\subsubsection{Active Sensors Ratio}
+
+Minimizing the number of active sensor nodes in each period is essential to minimize the
+energy consumption and thus to maximize the network lifetime.
+Figure~\ref{figure6} shows the average active nodes ratio for 200 deployed
+nodes. We observe that DESK and GAF have 30.36~\% and 34.96~\% active nodes for
+the first fourteen rounds, and the DiLCO and PeCO protocols compete perfectly with
+only 17.92~\% and 20.16~\% active nodes during the same time interval. As the
+number of periods increases, the PeCO protocol has a lower number of active nodes in
+comparison with the three other approaches and exhibits a slow decrease, while
+keeping a greater coverage ratio as shown in Figure \ref{figure5}.
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.5]{figure6.eps}
+\caption{Active sensors ratio for 200 deployed nodes.}
+\label{figure6}
+\end{figure}
+
+\subsubsection{\textcolor{blue}{Energy Saving Ratio (ESR)}}
+
+\textcolor{blue}{In this experiment, we consider an Energy Saving Ratio (see Figure~\ref{fig5}) for 200 deployed nodes.
+The longer the ratio is, the more redundant sensor nodes are switched off, and consequently the longer the network may live. }
+
+\begin{figure}[h!]
+%\centering
+% \begin{multicols}{6}
+\centering
+\includegraphics[scale=0.5]{ESR.eps} %\\~ ~ ~(a)
+\caption{Energy Saving Ratio for 200 deployed nodes}
+\label{fig5}
+\end{figure}
+
+\textcolor{blue}{The simulation results show that our protocol PeCO allows to efficiently save energy by turning off some sensors during the sensing phase.
+As shown in Figure~\ref{fig5}, GAF provides better energy saving than PeCO for the first fifty rounds, because GAF balance the energy consumption among sensor nodes inside each small fixed grid that permits to extend the life of sensors in each grid fairly but in the same time turn on large number of sensors during sensing that lead later to quickly deplete sensor's batteries togehter. After that GAF provide less energy saving compared with other approches because of the large number of dead nodes. DESK algorithm shows less energy saving compared with other approaches due to activate a larg number of sensors during the sensing. DiLCO protocol provides less energy saving ratio commpared with PeCO because it generally activate a larger number of sensor nodes during sensing. Note that again as the number of rounds increases PeCO becomes the most performing one, since it consumes less energy compared with other approaches.}
+
+
+\subsubsection{Energy Consumption}
+
+The effect of the energy consumed by the WSN during the communication,
+computation, listening, active, and sleep status is studied for different
+network densities and the four approaches compared. Figures~\ref{figure7}(a)
+and (b) illustrate the energy consumption for different network sizes and for
+$Lifetime_{95}$ and $Lifetime_{50}$. The results show that the PeCO protocol is the most
+competitive from the energy consumption point of view. As shown by both figures,
+PeCO consumes much less energy than the 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 the optimization program allows to reduce significantly the
+number of active sensors and also the energy consumption while keeping a good
+coverage level. Let us notice that the energy overhead when increasing network
+size is the lowest with PeCO.
+
+\begin{figure}[h!]
+ \centering
+ \begin{tabular}{@{}cr@{}}
+ \includegraphics[scale=0.5]{figure7a.eps} & \raisebox{2.75cm}{(a)} \\
+ \includegraphics[scale=0.5]{figure7b.eps} & \raisebox{2.75cm}{(b)}
+ \end{tabular}
+ \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
+ \label{figure7}
+\end{figure}
+
+\subsubsection{Network Lifetime}
+
+We observe the superiority of both the PeCO and DiLCO protocols in comparison with
+the two other approaches in prolonging the network lifetime. In
+Figures~\ref{figure8}(a) and (b), $Lifetime_{95}$ and $Lifetime_{50}$ are shown for
+different network sizes. As can be seen in these figures, the lifetime
+increases with the size of the network, and it is clearly larger for the DiLCO and
+PeCO protocols. For instance, for a network of 300~sensors and coverage ratio
+greater than 50\%, we can see on Figure~\ref{figure8}(b) that the lifetime is
+about twice longer with PeCO compared to the DESK protocol. The performance
+difference is more obvious in Figure~\ref{figure8}(b) than in
+Figure~\ref{figure8}(a) because the gain induced by our protocols increases with
+time, and the lifetime with a coverage over 50\% is far longer than with 95\%.
+
+\begin{figure}[h!]
+ \centering
+ \begin{tabular}{@{}cr@{}}
+ \includegraphics[scale=0.5]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\
+ \includegraphics[scale=0.5]{figure8b.eps} & \raisebox{2.75cm}{(b)}
+ \end{tabular}
+ \caption{Network Lifetime for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
+ \label{figure8}
+\end{figure}
+
+Figure~\ref{figure9} compares the lifetime coverage of the DiLCO and PeCO protocols
+for different coverage ratios. 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, where the term Protocol refers to DiLCO or
+PeCO. \textcolor{blue}{Indeed there are applications that do not require a 100\% coverage of the
+area to be monitored. For example, forest
+fire application might require complete coverage
+in summer seasons while only requires 80$\%$ of the area to be covered in rainy seasons \cite{li2011transforming}. As another example, birds habit study requires only 70$\%$-coverage at nighttime when the birds are sleeping while requires 100$\%$-coverage at daytime when the birds are active \cite{vu2009universal}. Mudflows monitoring applications may require part of the area to be covered in sunny days. Thus, to extend network lifetime, the coverage quality can be decreased if it is acceptable\cite{wang2014keeping}}. PeCO might be an interesting method since it achieves a good balance between a high level coverage ratio and network lifetime. PeCO
+always outperforms DiLCO for the three lower coverage ratios, moreover the
+improvements grow with the network size. \textcolor{blue}{DiLCO outperforms PeCO when the coverage ratio is required to be $>90\%$, but PeCo extends the network lifetime significantly when coverage ratio can be relaxed.}
+%DiLCO is better for coverage ratios near 100\%, but in that case PeCO is not ineffective for the smallest network sizes.
+
+\begin{figure}[h!]
+\centering \includegraphics[scale=0.55]{figure9.eps}
+\caption{Network lifetime for different coverage ratios.}
+\label{figure9}
+\end{figure}
+
+\subsubsection{Impact of $\alpha$ and $\beta$ on PeCO's performance}
+\label{sec:Impact}
+
+Table~\ref{my-labelx} shows network lifetime results for different values of
+$\alpha$ and $\beta$, and a network size equal to 200 sensor nodes. On the one
+hand, the choice of $\beta \gg \alpha$ prevents the overcoverage, and also
+limits the activation of a large number of sensors, but as $\alpha$ is low, some
+areas may be poorly covered. This explains the results obtained for
+$Lifetime_{50}$ with $\beta \gg \alpha$: a large number of periods with low
+coverage ratio. On the other hand, when we choose $\alpha \gg \beta$, we favor
+the coverage even if some areas may be overcovered, so a high coverage ratio is
+reached, but a large number of sensors are activated to achieve this goal.
+Therefore the network lifetime is reduced. The choice $\alpha=0.6$ and
+$\beta=0.4$ seems to achieve the best compromise between lifetime and coverage
+ratio. That explains why we have chosen this setting for the experiments
+presented in the previous subsections.
+
+%As can be seen in Table~\ref{my-labelx}, it is obvious and clear that when $\alpha$ decreased and $\beta$ increased by any step, the network lifetime for $Lifetime_{50}$ increased and the $Lifetime_{95}$ decreased. Therefore, selecting the values of $\alpha$ and $\beta$ depend on the application type used in the sensor nework. In PeCO protocol, $\alpha$ and $\beta$ are chosen based on the largest value of network lifetime for $Lifetime_{95}$.
+
+\begin{table}[h]
+\centering
+\caption{The impact of $\alpha$ and $\beta$ on PeCO's performance}
+\label{my-labelx}
+\begin{tabular}{|c|c|c|c|}
+\hline
+$\alpha$ & $\beta$ & $Lifetime_{50}$ & $Lifetime_{95}$ \\ \hline
+0.0 & 1.0 & 151 & 0 \\ \hline
+0.1 & 0.9 & 145 & 0 \\ \hline
+0.2 & 0.8 & 140 & 0 \\ \hline
+0.3 & 0.7 & 134 & 0 \\ \hline
+0.4 & 0.6 & 125 & 0 \\ \hline
+0.5 & 0.5 & 118 & 30 \\ \hline
+{\bf 0.6} & {\bf 0.4} & {\bf 94} & {\bf 57} \\ \hline
+0.7 & 0.3 & 97 & 49 \\ \hline
+0.8 & 0.2 & 90 & 52 \\ \hline
+0.9 & 0.1 & 77 & 50 \\ \hline
+1.0 & 0.0 & 60 & 44 \\ \hline
+\end{tabular}
+\end{table}
+
+
+\section{Conclusion and Future Works}
+\label{sec:Conclusion and Future Works}
+
+In this paper we have studied the problem of perimeter coverage optimization in
+WSNs. We have designed a new protocol, called Perimeter-based Coverage
+Optimization, which 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 is based on the resolution of an integer program to select the
+subset of sensors operating in active status 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. Several simulations have
+been carried out to evaluate the proposed protocol. The simulation results show
+that PeCO is more energy-efficient than other approaches, with respect to
+lifetime, coverage ratio, active sensors ratio, and energy consumption.
+
+We plan to extend our framework so that the schedules are planned for multiple
+sensing periods. We also want to improve the integer program to take into
+account heterogeneous sensors from both energy and node characteristics point of
+views. Finally, it would be interesting to implement the PeCO protocol using a
+sensor-testbed to evaluate it in real world applications.
+
+\subsection*{Acknowledgments}
+The authors are deeply grateful to the anonymous reviewers for their
+constructive advice, which improved the technical quality of the paper. As a
+Ph.D. student, Ali Kadhum Idrees would like to gratefully acknowledge the
+University of Babylon - Iraq for financial support and Campus France for the
+received support. This work is also partially funded by the Labex ACTION program
+(contract ANR-11-LABX-01-01).
+
+\bibliographystyle{gENO}
+\bibliography{biblio} %articleeo
+
+\end{document}
