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42 \title{Lifetime Coverage Optimization Protocol in Wireless Sensor Networks} %LiCO Protocol
46 \author{Ali Kadhum Idrees,~\IEEEmembership{}
47 Karine Deschinkel,~\IEEEmembership{}
48 Michel Salomon,~\IEEEmembership{}
49 and~Rapha\"el Couturier ~\IEEEmembership{}
50 \thanks{The authors are with FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comt\'e, Belfort, France. Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}}
51 %\thanks{J. Doe and J. Doe are with Anonymous University.}% <-this % stops a space
52 %\thanks{Manuscript received April 19, 2005; revised December 27, 2012.}}
54 \markboth{IEEE Communications Letters,~Vol.~11, No.~4, December~2014}%
55 {Shell \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for Journals}
64 One fundamental issue in Wireless Sensor Networks (WSNs) is the lifetime coverage optimization, which reflects how well a WSN is covered by a wireless sensors so that the network lifetime can be maximized. In this paper, a Lifetime Coverage Optimization Protocol (LiCO) in WSNs is proposed. The network is logically divided into subregions using divide-and-conquer method. LiCO protocol is distributed in each sensor node in the subregion. The lifetime coverage is divided into four stages: Information exchange, Leader Election, Optimization Decision, and Sensing. The optimization decision is made at each subregion, by a leader, who his election comes from the cooperation of the sensor nodes within the same subregion of WSN. A new mathematical optimization model is proposed to optimize the lifetime coverage in each subregion. Extensive simulation experiments have been performed using OMNeT++, the discrete event simulator, to demonstrate that LiCO is capable to extend the lifetime coverage of WSN as longer time as possible in comparison with some other protocols.
69 % Note that keywords are not normally used for peerreview papers.
71 Wireless Sensor Networks, Area Coverage, Network lifetime, Optimization, Scheduling.
75 \IEEEpeerreviewmaketitle
81 \section{\uppercase{Introduction}}
82 \label{sec:introduction}
83 \noindent The great development in Micro Electro-Mechanical Systems (MEMS) and wireless communication hardware are being led to emerge networks of tiny distributed sensors called WSN~\cite{akyildiz2002wireless,puccinelli2005wireless}. WSN comprises of small, low-powered sensors working together for perform a typical mission by communicating with one another through multihop wireless connections. They can send the sensed measurements based on local decisions to the user by means of sink nodes. WSN has been used in many applications such as Military, Habitat, Environment, Health, industrial, and Business~\cite{yick2008wireless}.Typically, a sensor node contains three main parts~\cite{anastasi2009energy}: a sensing subsystem, for sense, measure, and gather the measurements from the real environment; processing subsystem, for measurements processing and storage; a communication subsystem, for data transmission and receiving. Moreover, the energy needed by the sensor node is supplied by a power supply, to accomplish the Scheduled task. This power supply is composed of a battery with a limited lifetime. Furthermore, it maybe be unsuitable or impossible to replace or recharge the batteries, since sensor nodes may be deployed in a hostile or unpractical environment. The sensor system ought to have a lifetime long enough to satisfy the application necessities. The lifetime coverage maximization is one of the fundamental requirements of any area coverage protocol in WSN implementation~\cite{nayak2010wireless}. In order to increase the reliability and prevent the possession of coverage holes (some parts are not covered in the area of interest) in the WSN, it is necessary to deploy the WSN with high density so as to increase the reliability and to exploit redundancy by using energy-efficient activity scheduling approaches.
85 From a certain standpoint, the high coverage ratio is required by many applications such as military and health-care. Therefore, a suitable number of sensors are being chosen so as to cover the area of interest, is the first challenge. Meanwhile, the sensor nodes have a limited capabilities in terms of memory, processing, communication, and battery power being the most important and critical one. So, the main question is: how to extend the lifetime coverage of WSN as long time as possible?. There are many energy-efficient mechanisms have been suggested to retain energy and extend the lifetime of the WSNs~\cite{rault2014energy}.
87 \uppercase{\textbf{Our contributions.}} Two combined integrated energy-efficient techniques have been used by LiCO protocol in order to maximize the lifetime coverage in WSN: the first, by dividing the area of interest into several smaller subregions based on divide-and-conquer method and then one leader elected for each subregion in an independent, distributed, and simultaneous way by the cooperation among the sensor nodes within each subregion, and this similar to cluster architecture; the second, activity scheduling based new optimization model has been used to provide the optimal cover set that will take the mission of sensing during current period. This optimization algorithm is based on a perimeter-coverage model so as to optimize the shared perimeter among the sensors in each subregion, and this represents as a energu-efficient control topology mechanism in WSN.
90 The remainder of the paper is organized as follows. The next section reviews the related work in the field. Section~\ref{sec:The LiCO Protocol Description} is devoted to the LiCO protocol Description. Section~\ref{cp} gives the coverage model
91 formulation which is used to schedule the activation of sensors.
92 Section~\ref{sec:Simulation Results and Analysis} shows the simulation results. Finally, we give concluding remarks and some suggestions for
93 future works in Section~\ref{sec:Conclusion and Future Works}.
95 \section{\uppercase{Related Literature}}
96 \label{sec:Literature Review}
97 \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.
99 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.
101 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.
103 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.
105 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
106 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.
108 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.
110 Cho et al.~\cite{cho2007distributed} proposed a distributed node scheduling protocol, which can retain sensing coverage needed by applications
111 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.
113 In~\cite{quang2008algorithm}, the authors defined a maximum sensing coverage region problem (MSCR) in WSNs and then proposed an algorithm to solve it. The
114 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.
116 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.
117 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.
119 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.
121 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.
123 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.
125 The work that presented in~\cite{aslanyan2013optimal} solved the coverage and connectivity problem in sensor networks in
126 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
127 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.
129 Several algorithms to retain the coverage and maximize the network lifetime were proposed in~\cite{cardei2006energy,wang2011coverage}.
131 \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.
133 \uppercase{\textbf{Our Protocol}}. In this paper, a Lifetime Coverage Optimization Protocol, called (LiCO) in WSNs is suggested. The sensing field is divided into smaller subregions by means of divide-and-conquer method, and a LiCO 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. LiCO 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.
136 \section{ The LiCO Protocol Description}
137 \label{sec:The LiCO Protocol Description}
138 \noindent In this section, we describe our Lifetime Coverage Optimization Protocol which is called LiCO in more detail. 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.
139 %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.
141 \subsection{ Assumptions and Models}
142 \noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly distributed in a bounded sensor field is considered. The wireless sensors are deployed in high density to ensure initially a high coverage ratio of the interested area. We assume that all the sensor nodes are homogeneous in terms of communication, sensing, and processing capabilities and heterogeneous in term of energy supply. The location information is available to the sensor node either through hardware such as embedded GPS or through location discovery algorithms. We assume that each sensor node can directly transmit its measurements to a mobile sink node. For example, a sink can be an unmanned aerial vehicle (UAV) is flying regularly over the sensor field to collect measurements from sensor nodes. A mobile sink node collects the measurements and transmits them to the base station. We consider a boolean disk coverage model which is the most widely used sensor coverage model in the literature. Each sensor has a constant sensing range $R_s$. All space points within a disk centered at the sensor with the radius of the sensing range is said to be covered by this sensor. We also assume that the communication range $R_c \geq 2R_s$. In fact, Zhang and Zhou~\cite{Zhang05} proved that if the transmission range fulfills the previous hypothesis, a complete coverage of a convex area implies connectivity among the working nodes in the active mode.
144 \indent LiCO protocol is used the perimeter-coverage model which stated in ~\cite{huang2005coverage} as following: The sensor is said to be perimeter covered if all the points on its perimeter are covered by at least one sensor other than itself.
145 %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.
146 Figure~\ref{pcmfig} illuminates the perimeter coverage of the sensor node 0, where L refers to left point of the segment and R refers to right point of the segment.
150 \includegraphics[width=75mm]{pcm.pdf}
151 \caption{Perimeter coverage of sensor node 0}
155 In order to determine the segments of each sensor node, which are perimeter covered by the neighboring sensors, figure~\ref{twosensors} demonstrates the way of locating the left and right points of a segment of the sensor node I covered by a sensor node J. This figure supposed that the neighbor sensor node J is located on the west of a sensor I. It Supposed that the two sensor nodes I and J are located in the positions $(I_x,I_y)$ and $(J_x,J_y)$, respectively. The distance between I and J is computed by $Dist(I,J) = \sqrt{\vert I_x - J_x \vert^2 + \vert I_y - J_y \vert^2}$ . The angle $\alpha = arccos \left(\dfrac{Dist(I,J)}{2R_s} \right) $. So, the $\pi - \alpha$ and the $\pi + \alpha$ of sensor I refers to the left and right points of the segment, which is perimeter covered by sensor node J. If the arch segment of sensor I is located within the angle $[\pi - \alpha,\pi + \alpha]$, this means it is perimeter covered by sensor node J. The left and right points of each segment are put it on the line segment $[0,2\pi]$ and then are sorted in an ascending order so as to determine the level of the perimeter coverage for each left and right point of a segment.
158 \includegraphics[width=75mm]{twosensors.jpg}
159 \caption{Locating the segment of I$\rq$s perimeter covered by J.}
165 \includegraphics[width=75mm]{expcm.pdf}
166 \caption{Perimeter segment coverage levels for sensor node 0.}
170 For example, consider the sensor node 0 in figure~\ref{pcmfig}, which has 9 neighbors. Figure~\ref{expcm} shows the perimeter coverage level for all left and right points of a segments that covered by a neighboring sensor nodes. Based on the figure~\ref{expcm}, the set of sensors for each left and right point of the segments illustrated in figure~\ref{ex2pcm} for the sensor node 0.
174 \includegraphics[width=90mm]{ex2pcm.jpg}
175 \caption{The set of sensors for each left or right point of segments for sensor node 0.}
179 The optimization algorithm that used by LiCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1.
181 In the case of sensor node, which has a part of its sensing range outside the the border of the WSN sensing field as in figure~\ref{ex4pcm}, the perimeter coverage level for this segment is set to $\infty$, and the left and right points of the segments will not be taken into account by the optimization algorithm.
184 \includegraphics[width=75mm]{ex4pcm.jpg}
185 \caption{Part of sensing range outside the the border of WSN sensing field.}
188 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.
191 \includegraphics[width=75mm]{ex5pcm.jpg}
192 \caption{Perimeter coverage levels for sensor node has a part of its sensing range outside the border.}
197 \subsection{The Main Idea}
198 \noindent The area of interest can be divided using the
199 divide-and-conquer strategy into smaller areas called subregions and
200 then our protocol will be implemented in each subregion simultaneously. LiCO protocol works into periods fashion as shown in figure~\ref{fig2}.
203 \includegraphics[width=85mm]{Model.pdf}
204 \caption{LiCO protocol}
208 Each period is divided into 4 stages: Information (INFO) Exchange, Leader Election, Optimization Decision, and Sensing. For each period there is exactly one set cover responsible for the sensing task. LiCO is more powerful against an unexpected node failure because it works in periods. On the one hand, if the node failure is discovered before taking the decision of the optimization algorithm, the sensor node would not involved to current stage, and, on the other hand, if the sensor failure takes place 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 for some sensor nodes, even when they do not join the network to monitor the area.
210 We define two types of packets to be used by LiCO protocol.
211 %\begin{enumerate}[(a)]
213 \item INFO packet: sent by each sensor node to all the nodes inside a same subregion for information exchange.
214 \item ActiveSleep packet: sent by the leader to all the nodes in its subregion to inform them to be Active or Sleep during the sensing phase.
218 There are five status for each sensor node in the network :
219 %\begin{enumerate}[(a)]
221 \item LISTENING: Sensor is waiting for a decision (to be active or not)
222 \item COMPUTATION: Sensor applies the optimization process as leader
223 \item ACTIVE: Sensor is active
224 \item SLEEP: Sensor is turned off
225 \item COMMUNICATION: Sensor is transmitting or receiving packet
228 %Below, we describe each phase in more details.
230 \subsection{LiCO Protocol Algorithm}
231 The pseudo-code for LiCO Protocol is illustrated as follows:
234 \begin{algorithm}[h!]
235 % \KwIn{all the parameters related to information exchange}
236 % \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
238 %\emph{Initialize the sensor node and determine it's position and subregion} \;
240 \If{ $RE_k \geq E_{th}$ }{
241 \emph{$s_k.status$ = COMMUNICATION}\;
242 \emph{Send $INFO()$ packet to other nodes in the subregion}\;
243 \emph{Wait $INFO()$ packet from other nodes in the subregion}\;
244 \emph{Update K.CurrentSize}\;
245 \emph{LeaderID = Leader election}\;
246 \If{$ s_k.ID = LeaderID $}{
247 \emph{$s_k.status$ = COMPUTATION}\;
249 \If{$ s_k.ID $ is Not previously selected as a Leader }{
250 \emph{ Execute the perimeter coverage model}\;
251 % \emph{ Determine the segment points using perimeter coverage model}\;
254 \If{$ (s_k.ID $ is the same Previous Leader) AND (K.CurrentSize = K.PreviousSize)}{
256 \emph{ Use the same previous cover set for current sensing stage}\;
259 \emph{ Update $a^j_{ik}$ and prepare data to Algorithm}\;
260 \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$)}\;
261 \emph{K.PreviousSize = K.CurrentSize}\;
264 \emph{$s_k.status$ = COMMUNICATION}\;
265 \emph{Send $ActiveSleep()$ to each node $l$ in subregion} \;
266 \emph{Update $RE_k $}\;
269 \emph{$s_k.status$ = LISTENING}\;
270 \emph{Wait $ActiveSleep()$ packet from the Leader}\;
271 \emph{Update $RE_k $}\;
274 \Else { Exclude $s_k$ from entering in the current sensing stage}
277 \caption{LiCO($s_k$)}
282 \noindent Algorithm 1 gives a brief description of the protocol applied by each sensor node (denoted by $s_k$ for a sensor node indexed by $k$). In this algorithm, the K.CurrentSize and K.PreviousSize refer to the current size and the previous size of sensor nodes in the subregion respectively.
283 Initially, the sensor node checks its remaining energy in order to participate in the current period. Each sensor node determines its position and its subregion based Embedded GPS or Location Discovery Algorithm. After that, all the sensors collect position coordinates, remaining energy $RE_k$, sensor node id, and the number of its one-hop live neighbors during the information exchange.
284 After the cooperation among the sensor nodes in the same subregion, the leader will be elected in distributed way, where each sensor node and based on it's information decide who is the leader. The selection criteria for the leader in order of priority are: larger number of neighbors, larger remaining energy, and then in case of equality, larger index. Thereafter, if the sensor node is leader, it will execute the perimeter-coverage model for each sensor in the subregion in order to determine the segment points which would be used in the next stage by the optimization algorithm of the LiCO protocol. Every sensor node is selected as a leader, it is executed the perimeter coverage model only one time during it's life in the network. The leader has the responsibility of applying the integer program algorithm (see section~\ref{cp}), which provides a set of sensors planned to be active in the sensing stage. As leader, it will send an Active-Sleep packet to each sensor in the same subregion to inform it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing stage.
287 \section{Lifetime Coverage problem formulation}
289 In this section, the coverage model is mathematically formulated.
290 For convenience, the notations are described first.
291 %Then the lifetime problem of sensor network is formulated.
292 \noindent $S :$ the set of all sensors in the network.\\
293 \noindent $A :$ the set of alive sensors within $S$.\\
294 %\noindent $I :$ the set of segment points.\\
295 \noindent $I_j :$ the set of coverage intervals (CI) for sensor $j$.\\
297 \noindent For a coverage interval $i$, let $a^j_{ik}$ denote the indicator function of whether the sensor $k$ is involved in the coverage interval $i$ of sensor $j$, that is:
302 1 & \mbox{if the sensor $k$ is involved in the } \\
303 & \mbox{coverage interval $i$ of sensor $j$}, \\
304 0 & \mbox{Otherwise.}\\
309 %, 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.
310 %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 $k$. .
311 We consider binary variables $X_{k}$ ($X_k=1$ if the sensor $k$ is active or 0 otherwise), which determine the activation of sensor $k$ in the sensing phase. We define the integer variable $M^j_i$ which measures the undercoverage for the coverage interval $i$ for sensor $j$. In the same way, we define the integer variable $V^j_i$, which measures the overcoverage for the coverage interval $i$ for sensor $j$. If we decide to sustain a level of coverage equal to $l$ all along the perimeter of the sensor $j$, we have to ensure that at least $l$ sensors involved in each coverage interval $i$ ($i \in I_j$) of sensor $j$ are active. According to the previous notations, the number of active sensors in the coverage interval $i$ of sensor $j$ is given by $\sum_{k \in K} a^j_{ik} X_k$. To extend the network lifetime, the objective is to active a minimal number of sensors in each period to ensure the desired coverage level. As the number of alive sensors decreases, it becomes impossible to satisfy the level of coverage for all covergae intervals. We uses variables $M^j_i$ and $V^j_i$ as a measure of the deviation between the desired number of active sensors in a coverage interval and the effective number of active sensors. And we try to minimize these deviations, first to force the activation of a minimal number of sensors to ensure the desired coverage level, and if the desired level can not be completely satisfied, to reach a coverage level as close as possible that the desired one.
315 %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.
317 %\noindent In this paper, let us define some parameters, which are used in our protocol.
318 %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 $K$.
321 %\noindent \begin{equation}
324 % 1& \mbox{if sensor $k$ is active,} \\
325 % 0 & \mbox{otherwise.}\\
331 %\noindent $M^j_i (undercoverage): $ integer value $\in \mathbb{N}$ for segment point $i$ of sensor $j$.
333 %\noindent $V^j_i (overcoverage): $ integer value $\in \mathbb{N}$ for segment point $i$ of sensor $j$.
339 \noindent Our coverage optimization problem can be mathematically formulated as follows: \\
342 \begin{equation} \label{eq:ip2r}
345 \min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
346 \textrm{subject to :}&\\
347 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in S\\
349 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in S\\
351 % \Theta_{p}\in \mathbb{N}, &\forall p \in P\\
352 % U_{p} \in \{0,1\}, &\forall p \in P\\
353 X_{k} \in \{0,1\}, \forall k \in A
359 \noindent $\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the
360 relative importance of satisfying the associated
361 level of coverage. For example, weights associated with coverage intervals of a specified part of a region
362 may be given a relatively
363 larger magnitude than weights associated
364 with another region. This kind of integer program is inspired from the model developed for brachytherapy treatment planning for optimizing dose distribution \ref{0031-9155-44-1-012}. The integer program must be solved by the leader in each subregion at the beginning of each sensing phase, whenever the environment has changed (new leader, death of some sensors). Note that the number of constraints in the model is constant (constraints of coverage expressed for all sensors), whereas the number of variables $X_k$ decreases over periods, since we consider only alive sensors (sensors with enough energy to be alive during one sensing phase) in the model.
367 \section{\uppercase{PERFORMANCE EVALUATION AND ANALYSIS}}
368 \label{sec:Simulation Results and Analysis}
369 %\noindent \subsection{Simulation Framework}
371 \subsection{Simulation Settings}
373 In this section, we focused on the performance of LiCO protocol, which is distributed in each sensor node in the sixteen subregions of WSN. We used the same energy consumption model which are used in~\cite{Idrees2}. Table~\ref{table3} gives the chosen parameters setting.
376 \caption{Relevant parameters for network initializing.}
379 % used for centering table
381 % centered columns (4 columns)
383 Parameter & Value \\ [0.5ex]
386 % inserts single horizontal line
387 Sensing Field & $(50 \times 25)~m^2 $ \\
389 Nodes Number & 100, 150, 200, 250 and 300~nodes \\
391 Initial Energy & 500-700~joules \\
393 Sensing Period & 60 Minutes \\
394 $E_{th}$ & 36 Joules\\
397 $\alpha^j_i$ & 0.6 \\
398 % [1ex] adds vertical space
404 % is used to refer this table in the text
406 Simulations with five different node densities going from 100 to 250~nodes were
407 performed considering each time 25~randomly generated networks, to obtain
408 experimental results which are relevant. All simulations are repeated 25 times and the results are averaged. The nodes are deployed on a field of interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a high coverage ratio.
410 Each node has an initial energy level, in Joules, which is randomly drawn in the
411 interval $[500-700]$. If it's energy provision reaches a value below the
412 threshold $E_{th}=36$~Joules, the minimum energy needed for a node to stay
413 active during one period, it will no more participate in the coverage task. This
414 value corresponds to the energy needed by the sensing phase, obtained by
415 multiplying the energy consumed in active state (9.72 mW) by the time in seconds
416 for one period (3600 seconds), and adding the energy for the pre-sensing phases.
417 According to the interval of initial energy, a sensor may be active during at
420 In the simulations, we introduce the following performance metrics to evaluate
421 the efficiency of our approach:
423 %\begin{enumerate}[i)]
425 \item {{\bf Network Lifetime}:} we define the network lifetime as the time until
426 the coverage ratio drops below a predefined threshold. We denote by
427 $Lifetime_{95}$ (respectively $Lifetime_{50}$) the amount of time during which
428 the network can satisfy an area coverage greater than $95\%$ (respectively
429 $50\%$). We assume that the sensor network can fulfill its task until all its
430 nodes have been drained of their energy or it becomes disconnected. Network
431 connectivity is crucial because an active sensor node without connectivity
432 towards a base station cannot transmit any information regarding an observed
433 event in the area that it monitors.
436 \item {{\bf Coverage Ratio (CR)}:} it measures how well the WSN is able to
437 observe the area of interest. In our case, we discretized the sensor field
438 as a regular grid, which yields the following equation to compute the
442 \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100.
444 where $n$ is the number of covered grid points by active sensors of every
445 subregions during the current sensing phase and $N$ is total number of grid
446 points in the sensing field. In our simulations, we have a layout of $N = 51
447 \times 26 = 1326$ grid points.
450 \item{{\bf Number of Active Sensors Ratio(ASR)}:} It is important to have as few active nodes as possible in each round,
451 in order to minimize the communication overhead and maximize the
452 network lifetime. The Active Sensors Ratio is defined as follows:
455 \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$A_r$}}{\mbox{$S$}} \times 100 .
457 Where: $A_r^t$ is the number of active sensors in the subregion $r$ in the current sensing stage, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.
461 \item {{\bf Energy Consumption}:} energy consumption (EC) can be seen as the
462 total energy consumed by the sensors during $Lifetime_{95}$ or
463 $Lifetime_{50}$, divided by the number of periods. Formally, the computation
464 of EC can be expressed as follows:
467 \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m
468 + E^{a}_m+E^{s}_m \right)}{M},
471 where $M$ corresponds to the number of periods. The total energy consumed by
472 the sensors (EC) comes through taking into consideration four main energy factors. The first one, denoted $E^{\scriptsize \mbox{com}}_m$, represent the
473 energy consumption spent by all the nodes for wireless communications during
474 period $m$. $E^{\scriptsize \mbox{list}}_m$, the next factor, corresponds to
475 the energy consumed by the sensors in LISTENING status before receiving the
476 decision to go active or sleep in period $m$. $E^{\scriptsize \mbox{comp}}_m$
477 refers to the energy needed by all the leader nodes to solve the integer program
478 during a period. Finally, $E^a_{m}$ and $E^s_{m}$ indicate the energy consumed
479 by the whole network in the sensing phase (active and sleeping nodes).
485 \subsection{Simulation Results}
486 In this section, we present the simulation results of LiCO protocol and the other protocols using a discrete event simulator OMNeT++ \cite{varga} to run different series of simulations. We implemented all protocols precisely on a laptop DELL with Intel Core~i3~2370~M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6, the original execution time on the laptop is multiplied by 2944.2 $\left(\frac{35330}{2} \times \frac{1}{6} \right)$ so as to use it by the energy consumption model especially, after the computation and listening. Employing the modeling language ????\ref{}, the associated integer program instance is generated in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method.
488 We compared LiCO protocol to three other approaches: the first, called DESK and proposed by ~\cite{ChinhVu} is a fully distributed coverage algorithm; the second, called GAF ~\cite{xu2001geography}, consists in dividing the region
489 into fixed squares. During the decision phase, in each square, one sensor is
490 chosen to remain active during the sensing phase; the third, DiLCO protocol~\cite{Idrees2} is an improved version on the work presented in ~\cite{idrees2014coverage}. DNote that the LiCO protocol is based on the same framework as that of DiLCO. For thes two protocols, the division of the region of interest in 16 subregions was chosen since it produces the best results. The difference between the two protocols relies on the use of the integer programming to provide the set of sensors that have to be actived in each sensing phase. Whereas DilCO protocol tries to satisfy the coverage of a set of primary points, LiCO protocol tries to reach a desired level of coverage $l$ for each sensor's perimeter. In the experimentations, we chose a level of coverage equal to 1 ($l=1$).
492 \subsubsection{\textbf{Coverage Ratio}}
493 Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes obtained with the four methods.
498 \includegraphics[scale=0.5] {R/CR.eps}
499 \caption{The coverage ratio for 200 deployed nodes}
503 DESK, GAF, and DiLCO provides a little better coverage ratio with 99.99\%, 99.91\%, and 99.02\% against 98.76\% produced by LiCO for the lowest number of periods. This is due to the fact that DiLCO protocol put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more active nodes in the case of others methods.
505 Moreover, when the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to LiCO protocol. This is because it optimizes the coverage and the lifetime in WSN based on the primary points by selecting the best representative sensor nodes for the sensing stage. LiCO protocol put in sleep mode a higher number of redundant sensors starting from the round 19 using the new optimization model. The coverage ratio of LiCO Protocol seems to be better than other approaches starting from the round 64 because the optimization algorithm used by LiCO has been optimized the lifetime coverage based on the perimeter coverage model, so it provided acceptable coverage for a larger number of periods and prolonging the network lifetime based on the perimeter of the sensor nodes in each subregion of WSN. Although some nodes are dead, sensor activity scheduling based optimization of LiCO selected another nodes to ensure the coverage of the area of interest. i.e. DiLCO-16 showed a good coverage in the beginning then LiCO, when the number of periods increases, the coverage ratio decreases due to died sensor nodes. Meanwhile, thanks to sensor activity scheduling based new optimization model, which is used by LiCO protocol to ensure a longer lifetime coverage in comparison with other approaches.
508 \subsubsection{\textbf{Active Sensors Ratio}}
509 It is important to have as few active nodes as possible in each period, in order to minimize the energy consumption and maximize the network lifetime. Figure~\ref{fig444} shows the average active nodes ratio for 200 deployed nodes.
513 \includegraphics[scale=0.5]{R/ASR.eps}
514 \caption{The active sensors ratio for 200 deployed nodes }
518 From figure~~\ref{fig444}, We observed that DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen rounds and DiLCO-16 and LiCO protocols competes perfectly with only 17.92 \% and 20.16 \% active nodes for the first 17 rounds. Then as the number of rounds increases our LiCO protocol has a lower number of active nodes in comparison with DiLCO-16, DESK and GAF, especially from the round $19^{th}$ because it optimizes the lifetime coverage into the subregion based on the perimeter coverage model, which made LiCO improves the coverage ratio and for a longer time in comparison with other approaches.
520 \subsubsection{\textbf{The Energy Consumption}}
521 In this experiment, we study the effect of the energy consumed by the WSN during the communication, computation, listening, active, and sleep modes for different network densities and compare it with other approaches. Figures~\ref{fig3EC95} and ~\ref{fig3EC50} illustrate the energy consumption for different network sizes for $Lifetime95$ and $Lifetime50$.
525 \includegraphics[scale=0.5]{R/EC95.eps}
526 \caption{The Energy Consumption per period with $Lifetime_{95}$}
532 \includegraphics[scale=0.5]{R/EC50.eps}
533 \caption{The Energy Consumption per period with $Lifetime_{50}$}
537 The results show that our LiCO protocol is the most competitive from the energy consumption point of view. As shown in figures Figures~\ref{fig3EC95} and ~\ref{fig3EC50}, LiCO consumes less energy especially when the network size increases because it puts in sleep mode less active sensor number as possible in most periods of the network lifetime. The optimization algorithm, which used by LiCO protocol, was improved the lifetime coverage efficiently based on the perimeter coverage model.
539 The other approaches have a high energy consumption due to activating a larger number of redundant nodes as well as the energy consumed during the different modes of sensor nodes. In fact, a distributed method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks.
542 %\subsubsection{Execution Time}
544 \subsubsection{\textbf{The Network Lifetime}}
545 In this experiment, we are observed the superiority of LiCO and DiLCO-16 protocols against other two approaches in prolonging the network lifetime. In figures~\ref{fig3LT95} and \ref{fig3LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes.
549 \includegraphics[scale=0.5]{R/LT95.eps}
550 \caption{The Network Lifetime for $Lifetime_{95}$}
557 \includegraphics[scale=0.5]{R/LT50.eps}
558 \caption{The Network Lifetime for $Lifetime_{50}$}
562 As highlighted by figures~\ref{fig3LT95} and \ref{fig3LT50}, the network lifetime obviously increases when the size of the network increases, with our LiCO and DiLCO-16 protocols that leads to maximize the lifetime of the network compared with other approaches.
564 By choosing the best suited nodes, for each round, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next rounds, LiCO protocol efficiently prolonged the network lifetime especially for a coverage ratio greater than $50 \%$, whilst it stayed very near to DiLCO-16 protocol for $95 \%$. Figure~\ref{figLTALL} introduces the comparisons of the lifetime coverage for different coverage ratios between LiCO and DiLCO-16 protocols.
565 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.
569 \includegraphics[scale=0.5]{R/LTa.eps}
570 \caption{The Network Lifetime for different coverage ratios}
574 Comparison shows that LiCO protocol, which are used distributed optimization over the subregions, is the more relevance one for most coverage ratios and WSN sizes because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. LiCO protocol gave acceptable coverage ratio for a larger number of periods using new optimization algorithm that based on a perimeter coverage model. It also means that distributing the algorithm in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
577 \section{\uppercase{Conclusion and Future Works}}
578 \label{sec:Conclusion and Future Works}
579 In this paper, we have studied the problem of lifetime coverage optimization in
580 WSNs. To cope with this problem, the area of interest is divided into a smaller subregions using divide-and-conquer method, and then a LiCO protocol for optimizing the lifetime coverage in each subregion. LiCO protocol combines two efficient techniques: the first, network
581 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
582 in the subregion. The network lifetime coverage in each subregion is divided into
583 periods, each period consists of four stages: (i) Information Exchange,
584 (ii) Leader Election, (iii) a Decision based new optimization model in order to
585 select the nodes remaining active for the last stage, and (iv) Sensing.
586 The simulation results show that LiCO is is more energy-efficient than other approaches, with respect to lifetime, coverage ratio, active sensors ratio, and energy consumption. Indeed, when dealing with large and dense WSNs, a distributed optimization approach on the subregions of WSN like the one we are proposed allows to reduce the difficulty of a single global optimization problem by partitioning it in many smaller problems, one per subregion, that can be solved more easily.
588 Our future work is four-fold: the first, we plan to extend a lifetime coverage optimization problem in order to computes all active sensor schedules in only one step for many periods;
589 the second, we focus on extend our protocol and optimization algorithm to take into account the heterogeneous sensors, which do not have the same energy, processing, sensing and communication capabilities;
590 the third, we are investigating new optimization model based on the sensing range so as to maximize the lifetime coverage in WSN;
591 Finally, our final goal is to implement our protocol using a sensor-testbed to evaluate their performance in real world applications.
593 \section*{\uppercase{Acknowledgements}}
594 \noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully acknowledge the University of Babylon - IRAQ for the financial support and Campus France for the received support.
599 \ifCLASSOPTIONcaptionsoff
604 \bibliographystyle{IEEEtran}
605 %\bibliographystyle{IEEEbiographynophoto}
606 \bibliography{LiCO_Journal}
610 %\begin{IEEEbiographynophoto}{Jane Doe}
