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38 \title{Energy-Efficient Activity Scheduling in Heterogeneous Energy Wireless Sensor Networks}
41 % author names and affiliations
42 % use a multiple column layout for up to three different
44 \author{\IEEEauthorblockN{Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Raphael Couturier }
45 \IEEEauthorblockA{FEMTO-ST Institute, UMR CNRS, University of Franche-Comt\'e, Belfort, France \\
46 Email:$\lbrace$ali.idness, karine.deschinkel, michel.salomon,raphael.couturier$\rbrace$@femto-st.fr}
47 %\email{\{ali.idness, karine.deschinkel, michel.salomon, raphael.couturier\}@univ-fcomte.fr}
49 %\IEEEauthorblockN{Homer Simpson}
50 %\IEEEauthorblockA{FEMTO-ST Institute, UMR CNRS, University of Franche-Comte, Belfort, France}
52 %\IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
53 %\IEEEauthorblockA{FEMTO-ST Institute, UMR CNRS, University of Franche-Comte, Belfort, France}
61 One of the fundamental challenges in Wireless Sensor Networks (WSNs)
62 is coverage preservation, while extending the network lifetime
63 continuously and effectively during monitoring a certain area (or
64 region) of interest. In this paper a coverage optimization protocol to
65 improve the lifetime in heterogeneous energy wireless sensor networks
66 is proposed. The area of interest is first divided into subregions
67 using a divide-and-conquer method and then scheduling of sensor node
68 activity is planned for each subregion. The proposed scheduling
69 considers activity rounds during which a small number of nodes,
70 remaining active for sensing, is selected to ensure coverage. Each
71 round consists of four phases: (i)~Information Exchange, (ii)~Leader
72 Election, (iii)~Decision, and (iv)~Sensing. The decision process is
73 carried out by a leader node which solves an integer program.
74 Simulation results show that the proposed approach can prolong the
75 network lifetime and improve the coverage performance.
78 %\keywords{Area Coverage, Wireless Sensor Networks, lifetime Optimization, Distributed Protocol.}
80 \IEEEpeerreviewmaketitle
82 \section{Introduction}
83 \noindent Recent years have witnessed significant advances in wireless
84 communications and embedded micro-sensing MEMS technologies which have
85 made emerge wireless ensor networks as one of the most promising
86 technologies~\cite{asc02}. In fact, they present huge potential in
87 several domains ranging from health care applications to military
88 applications. A sensor network is composed of a large number of tiny
89 sensing devices deployed in a region of interest. Each device has
90 processing and wireless communication capabilities, which enable to
91 sense its environment, to compute, to store information and to deliver
92 report messages to a base station.
93 %These sensor nodes run on batteries with limited capacities. To achieve a long life of the network, it is important to conserve battery power. Therefore, lifetime optimisation is one of the most critical issues in wireless sensor networks.
94 One of the main design challenges in wireless sensor networks is to
95 prolong the network lifetime, while achieving acceptable quality of
96 service for applications. Indeed, sensor nodes have limited resources
97 in terms of memory, energy and computational power.
100 Since sensor nodes have limited battery life and without being able to replace
101 batteries, especially in remote and hostile environments,
102 it is desirable that a WSN should be deployed with
103 high density and thus redundancy can be exploited to increase
104 the lifetime of the network. In such a high density network, if all sensor nodes
105 were to be activated at the same time, the lifetime would be reduced. Consequently,
106 future software may need to adapt appropriately to achieve acceptable quality of service for applications.
107 In this paper we concentrate on area coverage problem, with the objective of maximizing the network lifetime by using an adaptive scheduling. Area of interest is divided into subregions and an activity scheduling for sensor nodes is planned for each subregion.
108 Our scheduling scheme works in round which includes a discovery phase to exchange information between sensors of the subregion, then a sensor is chosen in suitable manner to carry out a coverage strategy. This coverage strategy involves the resolution of an integer program which provides the activation of the sensors for the next round.
111 The remainder of the paper is organized as follows.
112 Section~\ref{rw} reviews the related work in the field.
113 Section \ref{pd} is devoted to the scheduling strategy for energy-efficient coverage.
114 Section \ref{cp} gives the coverage model formulation which is used to schedule the activation of sensors.
115 Section \ref{exp} shows the simulation results conducted on OMNET++, that fully demonstrate the usefulness of the proposed approach. Finally, we give concluding remarks in Section~\ref{sec:conclusion}.
117 \section{\uppercase{Related work}}
120 This section is dedicated to the various approaches proposed in the literature for the coverage lifetime maximization problem where the objective is to optimally schedule sensors'activities in order to extend network lifetime in a randomly deployed network. As this problem is subject to a wide range of interpretations, we suggest to recall main definitions and assumptions related to our work.
124 %\item Area Coverage: The main objective is to cover an area. The area coverage requires
125 %that the sensing range of working Active nodes cover the whole targeting area, which means any
126 %point in target area can be covered~\cite{Mihaela02,Raymond03}.
128 %\item Target Coverage: The objective is to cover a set of targets. Target coverage means that the discrete target points can be covered in any time. The sensing range of working Active nodes only monitors a finite number of discrete points in targeting area~\cite{Mihaela02,Raymond03}.
130 %\item Barrier Coverage An objective to determine the maximal support/breach paths that traverse a sensor field. Barrier coverage is expressed as finding one or more routes with starting position and ending position when the targets pass through the area deployed with sensor nodes~\cite{Santosh04,Ai05}.
133 The most discussed coverage problems in literature can be classified into two types \cite{} : area coverage and targets coverage. An area coverage problem is to find a minimum number of sensors to work such that each physical point in the area is monitored by at least a working sensor. Target coverage problem is to cover only a finite number of discrete points called targets.
134 Our work will concentrate on the area coverage by design and implement a strategy which efficiently select the active nodes that must maintain both sensing coverage and network connectivity and in the same time improve the lifetime of the wireless sensor network. But requiring that all physical points are covered may be too strict, specially where the sensor network is not dense.
135 Our approach represents an area covered by a sensor as a set of primary points and tries to maximize the total number of primary points that are covered in each round, while minimizing overcoverage (points covered by multiple active sensors simultaneously).\\
137 Various definitions exist for the lifetime of a sensor network. Main definitions proposed in the literature are related to the remaining energy of the nodes \cite{} or to the percentage of coverage \cite{}. The lifetime of the network is mainly defined as the amount of time that the network can satisfy its coverage objective (the amount of time that the network can cover a given percentage of its area or targets of interest). In our simulation we assume that the network is alive until all nodes have been drained of their energy or the sensor network disconnected and we measure the coverage ratio during the process.
139 {\bf Activity scheduling}\\
140 Activity scheduling is to schedule the activation and deactivation of nodes 'sensor units. The basic objective is to decide which sensors are in which states (active or sleeping mode) and for how long a time such that the application coverage requirement can be guaranteed and network lifetime can be prolonged. Various approaches, including centralized, distributed and localized algorithms, have been proposed for activity scheduling. In the distributed algorithms, each node in the network autonomously makes decisions on whether to turn on or turn off itself only using local neighbour information. In centralized algorithms, a central controller (node or base station) informs every sensor of the time intervals to be activated.
142 {\bf Distributed approaches}
144 Some distributed algorithms have been developed in~\cite{Gallais06,Tian02,Ye03,Zhang05,HeinzelmanCB02}. Distributed algorithms typically operate in rounds for predetermined duration. At the beginning of each round, a sensor exchange information with its neighbors and makes a decision to either turn on or go to sleep for the round. This decision is basically based on simple greedy criteria like the largest uncovered area \cite{Berman05efficientenergy}, maximum uncovered targets \cite{1240799}.
145 In \cite{Tian02}, the scheduling scheme is divided into rounds, where each round has a self-scheduling phase followed by a sensing phase. Each sensor broadcasts a message to its neighbours containing node ID and node location at the beginning of each round. Sensor determines its status by a rule named off-duty eligible rule which tells him to turn off if its sensing area is covered by its neighbours. A back-off scheme is introduced to let each sensor delay the decision process with a random period of time, in order to avoid that nodes make conflicting decisions simultaneously and that a part of the area is no longer covered.
146 \cite{Prasad:2007:DAL:1782174.1782218} propose a model for capturing the dependencies between different cover sets and propose localized heuristic based on this dependency. The algorithm consists of two phases, an initial setup phase during which each sensor calculates and prioritize the covers and a sensing phase during which each sensor first decides its on/off status and then remains on or off for the rest of the duration.
147 Authors in \cite{chin2007} propose a novel distributed heuristic named distributed Energy-efficient Scheduling for k-coverage (DESK) so that the energy consumption among all the sensors is balanced, and network lifetime is maximized while the coverage requirements being maintained. This algorithm works in round, requires only 1-sensing-hop-neighbour information, and a sensor decides its status (active/sleep) based on its perimeter coverage computed through the k-Non-Unit-disk coverage algorithm proposed in \cite{Huang:2003:CPW:941350.941367}.\\
149 Some others approaches do not consider synchronized and predetermined period of time where the sensors are active or not. Each sensor maintains its own timer and its time wake-up is randomized \cite{Ye03} or regulated \cite{cardei05} over time.
150 %A ecrire \cite{Abrams:2004:SKA:984622.984684}p33
153 %The scheduling information is disseminated throughout the network and only sensors in the active state are responsible
154 %for monitoring all targets, while all other nodes are in a low-energy sleep mode. The nodes decide cooperatively which of them will remain in sleep mode for a certain
157 %one way of increasing lifeteime is by turning off redundant nodes to sleep mode to conserve energy while active nodes provide essential coverage, which improves fault tolerance.
159 %In this paper we focus on centralized algorithms because distributed algorithms are outside the scope of our work. Note that centralized coverage algorithms have the advantage of requiring very low processing power from the sensor nodes which have usually limited processing capabilities. Moreover, a recent study conducted in \cite{pc10} concludes that there is a threshold in terms of network size to switch from a localized to a centralized algorithm. Indeed the exchange of messages in large networks may consume a considerable amount of energy in a localized approach compared to a centralized one.
161 {\bf Centralized approaches}\\
162 Power efficient centralized schemes differ according to several criteria \cite{Cardei:2006:ECP:1646656.1646898}, such as the coverage objective (target coverage or area coverage), the node deployment method (random or deterministic) and the heterogeneity of sensor nodes (common sensing range, common battery lifetime). The major approach is to divide/organize the sensors into a suitable number of set covers where each set completely covers an interest region and to activate these set covers successively.
164 First algorithms proposed in the literature consider that the cover sets are disjoint: a sensor node appears in exactly one of the generated cover sets. For instance Slijepcevic and Potkonjak \cite{Slijepcevic01powerefficient} propose an algorithm which allocates sensor nodes in mutually independent sets to monitor an area divided into several fields. Their algorithm constructs a cover set by including in priority the sensor nodes which cover critical fields, that is to say fields that are covered by the smallest number of sensors. The time complexity of their heuristic is $O(n^2)$ where $n$ is the number of sensors. ~\cite{cardei02} present
165 a graph coloring technique to achieve energy savings
166 by organizing the sensor nodes into a maximum number of disjoint
167 dominating sets which are activated successively. The dominating
168 sets do not guarantee the coverage of the whole region of interest.
169 Abrams et al.\cite{Abrams:2004:SKA:984622.984684} design three approximation algorithms for a variation of the set k-cover problem, where the objective is
170 to partition the sensors into covers such that the number of
171 covers that include an area, summed over all areas, is maximized. Their work builds upon previous work in~\cite{Slijepcevic01powerefficient} and the generated cover sets do not provide complete coverage of the monitoring zone.
174 %examine the target coverage problem by disjoint cover sets but relax the requirement that every cover set monitor all the targets and try to maximize the number of times the targets are covered by the partition. They propose various algorithms and establish approximation ratio.
176 In~\cite{Cardei:2005:IWS:1160086.1160098}, the authors propose a heuristic to
177 compute the disjoint set covers (DSC). In order to compute the maximum number of covers, they
178 first transform DSC into a maximum-flow problem ,
179 which is then formulated as a mixed integer programming problem
180 (MIP). Based on the solution of the MIP, they design a heuristic
181 to compute the final number of covers. The results show a slight performance
182 improvement in terms of the number of produced DSC in comparison to~\cite{Slijepcevic01powerefficient} but it incurs
183 higher execution time due to the complexity of the mixed integer programming resolution.
184 %Cardei and Du \cite{Cardei:2005:IWS:1160086.1160098} propose a method to efficiently compute the maximum number of disjoint set covers such that each set can monitor all targets. They first transform the problem into a maximum flow problem which is formulated as a mixed integer programming (MIP). Then their heuristic uses the output of the MIP to compute disjoint set covers. Results show that these heuristic provides a number of set covers slightly larger compared to \cite{Slijepcevic01powerefficient} but with a larger execution time due to the complexity of the mixed integer programming resolution.
185 Zorbas et al. \cite{Zorbas2007} present B\{GOP\}, a centralized coverage algorithm introducing sensor candidate categorisation depending on their coverage status and the notion of critical target to call targets that are associated with a small number of sensors. The total running time of their heuristic is $0(m n^2)$ where $n$ is the number of sensors, and $m$ the number of targets. Compared to algorithm's results of Slijepcevic and Potkonjak \cite{Slijepcevic01powerefficient}, their heuristic produces more cover sets with a slight growth rate in execution time.
186 %More recently Manju and Pujari\cite{Manju2011}
188 In the case of non-disjoint algorithms \cite{Manju2011}, sensors may participate in more than one cover set.
189 In some cases this may prolong the lifetime of the network in comparison to the disjoint cover set algorithms but designing algorithms for non-disjoint cover sets generally incurs a higher order of complexity. Moreover in case of a sensor's failure, non-disjoint scheduling policies are less resilient and less reliable because a sensor may be involved in more than one cover sets. For instance, Cardei et al.~\cite{cardei05bis} present a linear programming (LP) solution
190 and a greedy approach to extend
191 the sensor network lifetime by organizing the sensors into a
192 maximal number of non-disjoint cover sets. Simulation results show that by allowing sensors to
193 participate in multiple sets, the network lifetime
194 increases compared with related work~\cite{Cardei:2005:IWS:1160086.1160098}. In~\cite{berman04}, the authors have formulated the lifetime problem and suggested another (LP) technique to solve this problem. A centralized provably near
195 optimal solution based on the Garg-K\"{o}nemann algorithm~\cite{garg98} is also proposed.
197 {\bf Our contribution}
198 %{decoupage de la region en sous region, selection de noeud leader, formulation %et resolution du probleme de couverture, planification périodique
199 There are three main questions which should be answered to build a scheduling strategy. We give a brief answer to these three questions to describe our approach before going into details in the subsequent sections.
201 \item {\bf How must be planned the
202 phases for information exchange, decision and sensing over time?}
203 Our algorithm partitions the time line into a number of rounds. Each round contains 4 phases : information Exchange, Leader Election, Decision, and Sensing.
205 \item {\bf What are the rules to decide which node has to turn on or off?}
206 Our algorithm tends to limit the overcoverage of points of interest to avoid turning on too much sensors covering the same areas at the same time, and tries to prevent undercoverage. The decision is a good compromise between these two conflicting objectives.
208 \item {\bf Which node should make such decision ?}
209 As mentioned in \cite{pc10}, both centralized and distributed algorithms have their own advantages and disadvantages. Centralized coverage algorithms have the advantage of requiring very low processing power from the sensor nodes which have usually limited processing capabilities. Distributed algorithms are very adaptable to the dynamic and scalable nature of sensors network. Authors in \cite{pc10} concludes that there is a threshold in terms of network size to switch from a localized to a centralized algorithm. Indeed the exchange of messages in large networks may consume a considerable amount of energy in a localized approach compared to a centralized one. Our work does not consider only one leader to compute and to broadcast the schedule decision to all the sensors. When the size of network increases, the network is divided in many subregions and the decision is made by a leader in each subregion.
214 \section{\uppercase{Activity scheduling}}
216 We consider a randomly and uniformly deployed network consisting of static wireless sensors. The wireless sensors are deployed in high density to ensure initially a full coverage of the interested area. We assume that all nodes are homogeneous in terms of communication and processing capabilities and heterogeneous in term of energy. The location information is available to the sensor node either through hardware such as embedded GPS or through location discovery algorithms.
217 The area of interest can be divided using the divide-and-conquer strategy into smaller area called subregions and then our coverage protocol will be implemented in each subregion simultaneously. Our protocol works in rounds fashion as in figure \ref{fig:4}.
218 %Given the interested Area $A$, the wireless sensor nodes set $S=\lbrace s_1,\ldots,s_N \rbrace $ that are deployed randomly and uniformly in this area such that they are ensure a full coverage for A. The Area A is divided into regions $A=\lbrace A^1,\ldots,A^k,\ldots, A^{N_R} \rbrace$. We suppose that each sensor node $s_i$ know its location and its region. We will have a subset $SSET^k =\lbrace s_1,...,s_j,...,s_{N^k} \rbrace $ , where $s_N = s_{N^1} + s_{N^2} +,\ldots,+ s_{N^k} +,\ldots,+s_{N^R}$. Each sensor node $s_i$ has the same initial energy $IE_i$ in the first time and the current residual energy $RE_i$ equal to $IE_i$ in the first time for each $s_i$ in A. \\
222 \includegraphics [width=70mm]{FirstModel.eps}
223 \caption{Multi-Round Coverage Protocol}
227 Each round is divided into 4 phases : Information (INFO) Exchange, Leader Election, Decision, and Sensing. For each round there is exactly one set cover responsible for sensing task. This protocol is more reliable against the unexpectedly node failure because it works into rounds, and if the node failure is detected before taking the decision, the node will not participate in decision and if the node failure occurs after the decision, the sensing task of the network will be affected temporarily only during the period of sensing until starting new round, since a new set cover will take charge of the sensing task in the next round. The energy consumption and some other constraints can easily be taken into account since the sensors can update and then exchange the information (including their residual energy) at the beginning of each round. However, the preprocessing phase (INFO Exchange, leader Election, Decision) are energy consuming for some nodes even when they not join the network to monitor the area. We describe each phase in more detail.
229 \subsection{\textbf INFO Exchange Phase}
231 Each sensor node $j$ sends its position, remaining energy $RE_j$, number of local neighbours $NBR_j$ to all wireless sensor nodes in its subregion by using INFO packet and listen to the packets sent from other nodes. After that, each node will have information about all the sensor nodes in the subregion. In our model, the remaining energy corresponds to the time that a sensor can live in the active mode.
234 %\subsection{\textbf Working Phase:}
236 %The working phase works in rounding fashion. Each round include 3 steps described as follow :
238 \subsection{\textbf Leader Election Phase}
239 This step includes choosing the Wireless Sensor Node Leader (WSNL) which will be responsible of executing coverage algorithm to choose the list of active sensor nodes that contribute in covering the subregion.
240 All the sensor nodes cooperates to select WSNL. After the phase of information exchange , each sensor have all information about the other nodes in the same subregion, after that each node will execute the leader election procedure to determine who is the leader?(each node will know who is the leader) where all the nodes in the same subregion will select the same leader based on the received information from all other nodes in the same subregion.The leader will be selected as follow: It will select the node that have maximum number of neighbour as a leader.If there are more than one node have the same maximum number of neighbours , it will take all these nodes and then select the node that have larger remaining energy. If there are more than one node have the same maximum number of neighbours and the same remaining energy then it will select the node with larger index among them. Each subregion in the area of interest will select its own WSNL independently for each round.
242 \subsection{\textbf Decision Phase}
243 The WSNL will solve an integer program (see section \ref{cp}) to select which sensors will be activated in the next round to cover the subregion. WSNL will send Active-Sleep packet to each sensor in the subregion based on algorithm's results.
244 %The main goal in this step after choosing the WSNL is to produce the best representative active nodes set that will take the responsibility of covering the whole region $A^k$ with minimum number of sensor nodes to prolong the lifetime in the wireless sensor network. For our problem, in each round we need to select the minimum set of sensor nodes to improve the lifetime of the network and in the same time taking into account covering the region $A^k$ . We need an optimal solution with tradeoff between our two conflicting objectives.
245 %The above region coverage problem can be formulated as a Multi-objective optimization problem and we can use the Binary Particle Swarm Optimization technique to solve it.
248 \subsection{\textbf Sensing Phase}
249 Active sensors in the round will execute their sensing task to preserve maximal coverage in the region of interest. We will assume that the cost of keeping a node awake (or sleep) for sensing task is the same for all wireless sensor nodes in the network. Each sensor received Active-Sleep packet will go to awake or sleep for a time equal to the period of sensing until starting new round.
253 %\subsection{Sensing coverage model}
256 %\noindent We try to produce an adaptive scheduling which allows sensors to operate alternatively so as to prolong the network lifetime. For convenience, the notations and assumptions are described first.
257 %The wireless sensor node use the binary disk sensing model by which each sensor node will has a certain sensing range is reserved within a circular disk called radius $R_s$.
258 \noindent 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 is at least twice of the sensing range. In fact, Zhang and Zhou ~\cite{Zhang05} prove that if the transmission range is at least twice of the sensing range, a complete coverage of a convex area implies connectivity among the working nodes in the active mode.
259 %To calculate the coverage ratio for the area of interest, we can propose the following coverage model which is called Wireless Sensor Node Area Coverage Model to ensure that all the area within each node sensing range are covered. We can calculate the positions of the points in the circle disc of the sensing range of wireless sensor node based on the Unit Circle in figure~\ref{fig:cluster1}:
264 %%\includegraphics[scale=0.25]{fig1.pdf}\\ %& \includegraphics[scale=0.10]{1.pdf} \\
265 %%(A) Figure 1 & (B) Figure 2
267 %\caption{Unit Circle in radians. }
268 %\label{fig:cluster1}
271 %By using the Unit Circle in figure~\ref{fig:cluster1},
272 %We choose to representEach wireless sensor node will be represented into a selected number of primary points by which we can know if the sensor node is covered or not.
273 % Figure ~\ref{fig:cluster2} shows the selected primary points that represents the area of the sensor node and according to the sensing range of the wireless sensor node.
275 \noindent Instead of working with area coverage, we consider for each sensor a set of points called primary points. And we assume the sensing disk defined by a sensor is covered if all primary points of this sensor are covered.
280 %%\includegraphics[scale=0.25]{fig2.pdf}\\ %& \includegraphics[scale=0.10]{1.pdf} \\
281 %%(A) Figure 1 & (B) Figure 2
283 %\caption{Wireless Sensor Node Area Coverage Model.}
284 %\label{fig:cluster2}
289 \noindent By knowing the position (point center :($p_x,p_y$) of the wireless sensor node and its $R_s$ , we calculate the primary points directly based on proposed model. We use these primary points (that can be increased or decreased as if it is necessary) as references to ensure that the monitoring area of the region is covered by the selected set of sensors instead of using the all points in the area.
293 % \begin{multicols}{6}
295 %\includegraphics[scale=0.10]{fig21.pdf}\\~ ~ ~(a)
296 %\includegraphics[scale=0.10]{fig22.pdf}\\~ ~ ~(b)
297 \includegraphics[scale=0.2]{principles13.eps}
298 %\includegraphics[scale=0.10]{fig25.pdf}\\~ ~ ~(d)
299 %\includegraphics[scale=0.10]{fig26.pdf}\\~ ~ ~(e)
300 %\includegraphics[scale=0.10]{fig27.pdf}\\~ ~ ~(f)
302 \caption{Wireless Sensor node represented by 13 primary points }
306 \noindent We can calculate the positions of the selected primary points in the circle disk of the sensing range of wireless sensor node in figure ~\ref{fig3} as follow:\\
307 $p_x,p_y$ = point center of wireless sensor node. \\
309 $X_2=( p_x + R_s * (1), p_y + R_s * (0) )$\\
310 $X_3=( p_x + R_s * (-1), p_y + R_s * (0)) $\\
311 $X_4=( p_x + R_s * (0), p_y + R_s * (1) )$\\
312 $X_5=( p_x + R_s * (0), p_y + R_s * (-1 )) $\\
313 $X_6= ( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (0)) $\\
314 $X_7=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (0))$\\
315 $X_8=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
316 $X_9=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
317 $X_{10}=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
318 $X_{11}=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
319 $X_{12}=( p_x + R_s * (0), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
320 $X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
325 \section{\uppercase{Coverage problem formulation}}
327 %We can formulate our optimization problem as energy cost minimization by minimize the number of active sensor nodes and maximizing the coverage rate at the same time in each $A^k$ . This optimization problem can be formulated as follow: Since that we use a homogeneous wireless sensor network, we will assume that the cost of keeping a node awake is the same for all wireless sensor nodes in the network. We can define the decision parameter $X_j$ as in \eqref{eq11}:\\
330 %To satisfy the coverage requirement, the set of the principal points that will represent all the sensor nodes in the monitored region as $PSET= \lbrace P_1,\ldots ,P_p, \ldots , P_{N_P^k} \rbrace $, where $N_P^k = N_{sp} * N^k $ and according to the proposed model in figure ~\ref{fig:cluster2}. These points can be used by the wireless sensor node leader which will be chosen in each region in A to build a new parameter $\alpha_{jp}$ that represents the coverage possibility for each principal point $P_p$ of each wireless sensor node $s_j$ in $A^k$ as in \eqref{eq12}:\\
333 \noindent Our model is based on the model proposed by \cite{pedraza2006} where the objective is to find a maximum number of disjoint cover sets. To accomplish this goal, authors propose a integer program which forces undercoverage and overcoverage of targets to become minimal at the same time. They use binary variables $x_{s,l}$ to indicate if the sensor $s$ belongs to cover set $l$. In our model, we consider binary variables $X_{j}$ which determine the activation of sensor $j$ in the round. We also consider primary points as targets. The set of primary points is denoted by P, and the set of sensors by J. \\
334 \noindent For a primary point $p$, let $\alpha_{jp}$ denote the indicator function of whether the point $p$ is covered, that is, \\
336 \alpha_{jp} = \left \{
338 1 & \mbox{if the primary point $p$ is covered} \\
339 & \mbox{by active sensor node $j$} \\
340 0 & \mbox{Otherwise}\\
344 The number of sensors that are covering point $p$ is equal to $\sum_{j \in J} \alpha_{jp} * X_{j}$ where :
348 1& \mbox{if sensor $j$ is active} \\
349 0 & \mbox{otherwise}\\
353 We define the Overcoverage variable $\Theta_{p}$ .\\
356 \Theta_{p} = \left \{
358 0 & \mbox{if point p is not covered}\\
359 \left( \sum_{j \in J} \alpha_{jp} * X_{j} \right)- 1 & \mbox{otherwise}\\
365 \noindent$\Theta_{p}$ represents the number of active sensor nodes minus one that cover the primary point $p$.\\
366 The Undercoverage variable $U_{p}$ of the primary point $p$ is defined as follow :\\
371 1 &\mbox{if point } $p$ \mbox{ is not covered} \\
372 0 & \mbox{otherwise}\\
377 \noindent Our coverage optimization problem can be formulated as follow.\\
378 \begin{equation} \label{eq:ip2r}
381 \min \sum_{p \in P} (w_{\theta} \Theta_{p} + w_{U} U_{p})&\\
382 \textrm{subject to :}&\\
383 \sum_{j \in J} \alpha_{jp} X_{j} - \Theta_{p}+ U_{p} =1, &\forall p \in P\\
385 %\sum_{t \in T} X_{j,t} \leq \frac{RE_j}{e_t} &\forall j \in J \\
387 \Theta_{p}\in \mathbb{N} , &\forall p \in P\\
388 U_{p} \in \{0,1\}, &\forall p \in P \\
389 X_{j} \in \{0,1\}, &\forall j \in J
394 \item $X_{j}$ : indicating whether or not sensor $j$ is active in the round (1 if yes and 0 if not)
395 \item $\Theta_{p}$ : {\it overcoverage}, the number of sensors minus one that are covering point $p$
396 \item $U_{p}$ : {\it undercoverage}, indicating whether or not point $p$ is being covered (1 if not covered and 0 if covered)
398 The first group of constraints indicates that some point $p$ should be covered by at least one sensor and, if it is not always the case, overcoverage and undercoverage variables help balance the restriction equation by taking positive values. Second group of contraints ensures for each sensor that the amount of energy consumed during its activation periods will be less than or equal to its remaining energy.
399 There are two main objectives. We limit overcoverage of primary points in order to activate a minimum number of sensors and we prevent that parts of the subregion are not monitored by minimizing undercoverage. The weights $w_{\theta}$ and $w_{U}$ must be properly chosen so as to guarantee that the maximum number of points are covered during each round.
401 %In equation \eqref{eq15}, there are two main objectives: the first one using the Overcoverage parameter to minimize the number of active sensor nodes in the produced final solution vector $X$ which leads to improve the life time of wireless sensor network. The second goal by using the Undercoverage parameter to maximize the coverage in the region by means of covering each primary point in $SSET^k$.The two objectives are achieved at the same time. The constraint which represented in equation \eqref{eq16} refer to the coverage function for each primary point $P_p$ in $SSET^k$ , where each $P_p$ should be covered by
402 %at least one sensor node in $A^k$. The objective function in \eqref{eq15} involving two main objectives to be optimized simultaneously, where optimal decisions need to be taken in the presence of trade-offs between the two conflicting main objectives in \eqref{eq15} and this refer to that our coverage optimization problem is a multi-objective optimization problem and we can use the BPSO to solve it. The concept of Overcoverage and Undercoverage inspired from ~\cite{Fernan12} but we use it with our model as stated in subsection \ref{Sensing Coverage Model} with some modification to be applied later by BPSO.
403 %\subsection{Notations and assumptions}
406 %\item $m$ : the number of targets
407 %\item $n$ : the number of sensors
408 %\item $K$ : maximal number of cover sets
409 %\item $i$ : index of target ($i=1..m$)
410 %\item $j$ : index of sensor ($j=1..n$)
411 %\item $k$ : index of cover set ($k=1..K$)
412 %\item $T_0$ : initial set of targets
413 %\item $S_0$ : initial set of sensors
414 %\item $T $ : set of targets which are not covered by at least one cover set
415 %\item $S$ : set of available sensors
416 %\item $S_0(i)$ : set of sensors which cover the target $i$
417 %\item $T_0(j)$ : set of targets covered by sensor $j$
418 %\item $C_k$ : cover set of index $k$
419 %\item $T(C_k)$ : set of targets covered by the cover set $k$
420 %\item $NS(i)$ : set of available sensors which cover the target $i$
421 %\item $NC(i)$ : set of cover sets which do not cover the target $i$
422 %\item $|.|$ : cardinality of the set
425 \section{\uppercase{Simulation Results}}
427 In this section, we conducted a series of simulations to evaluate the efficiency of our approach
428 based on the discrete event simulator OMNeT++ (http://www.omnetpp.org/). We conduct simulations for five
429 different densities varying from 50 to 250 nodes. Experimental results were obtained from randomly generated
430 networks in which nodes are deployed over a $ 50\times25(m^2) $sensing field. For each network deployment, we
431 assume that the deployed nodes can fully cover the sensing field with the given sensing range. 10 simulation runs are performed with different network topologies. The results presented hereafter are the average of these 10 runs. Simulation ends when there all the nodes are dead or the sensor network becomes disconnected (some nodes may not be able to sent to a base station an event they sense) . Our proposed coverage protocol use the Radio energy dissipation model that defined by~\cite{HeinzelmanCB02} as energy consumption model by each wireless sensor node for transmitting and receiving the packets in the network. The energy of each node in the network is initialized randomly within the range 24-60 joules, and each sensor will consumes 0.2 watts during the sensing period of 60 seconds. Each active node will consumes 12 joules during sensing phase and each sleep node will consume 0.002 joules. Each sensor node will not participate in the next round if it's remaining energy less than 12 joules. In all experiments the parameters are given by $R_s = 5m $ , $ w_{\Theta} =1$ and $w_{U} = |P^2|$.
432 We evaluate the efficiency of our approach using some performance metrics such as : coverage ratio, number of
433 active nodes ratio, energy saving ratio, Energy Consumption,network lifetime, execution time and the number of stopped simulation runs.
434 Our approach is called Strategy (with Two Leaders) will be compared with two approaches: The first one called Strategy (with One Leader) that use the same our approach method but it implemented in $ 50\times25(m^2) $sensing field with one leader. The second method called Simple Heuristic which consists in dividing uniformly the region into squares $(5 * 5)m^2$ . During the pre-sensing phase, in each square, a sensor is chosen randomly, and will be turned on for the next round.
435 In our simulation the sensing field is subdivided into two subregions each one equal to $ 25\times25)m^2 $ of the sensing field.
437 \subsection{The impact of the Number of Rounds on Coverage Ratio:}
438 In this experiment,the Coverage ratio measures how much area of a sensor field is covered. In our case, the coverage ratio is regarded as the number of primary points covered among the set of all primary points within the field. Fig. \ref{fig3} shows the impact of the number of rounds on the average coverage ratio for 150 deployed nodes for the three approaches.
439 The comparison shows that the Strategy (with One Leader) gives the same or better than the Strategy (with Two Leaders) for rounds from 1 to 14. after that the Strategy (with One Leader) will suffer from the sensor network becomes disconnected more than Strategy (with Two Leaders) leads to give the advantage for Strategy (with Two Leaders) that will give better coverage and more network lifetime for the rest last rounds because the Strategy (with Two Leaders) subdivide the region into 2 subregions and if on of the two subregion becomes disconnected, it not leads to stop the the responsibility of coverage optimization in the other subregion.
443 % \begin{multicols}{6}
445 \includegraphics[scale=0.5]{TheCoverageRatio150.pdf} %\\~ ~ ~(a)
447 \caption{The impact of the Number of Rounds on Coverage Ratio for 150 deployed nodes }
453 % \begin{multicols}{6}
455 %\includegraphics[scale=0.10]{fig21.pdf}\\~ ~ ~(a)
456 %\includegraphics[scale=0.10]{fig22.pdf}\\~ ~ ~(b)
457 \includegraphics[scale=0.5]{TheCoverageRatio250.pdf} %\\~ ~ ~(a)
458 %\includegraphics[scale=0.5]{CR2R2L_2.eps} %\\~ ~ ~(b)
459 %\includegraphics[scale=0.10]{fig26.pdf}\\~ ~ ~(e)
460 %\includegraphics[scale=0.10]{fig27.pdf}\\~ ~ ~(f)
462 \caption{The impact of the Number of Rounds on Coverage Ratio for 250 deployed nodes }
466 Fig. \ref{fig4} represents the average coverage ratio provided by
467 Strategy (with Two Leaders),Strategy (with One Leader) and Simple Heuristic for 250 deployed nodes while
468 varying the number of rounds. We made the same observation as in Fig. \ref{fig3}, i.e. Strategy (with One Leader) guarantee a good coverage in the beginning the same or equal to Strategy (with Two Leaders) then when the number of rounds increases, the coverage ratio decreases due to network becomes disconnected. Meanwhile,the Strategy (with Two Leaders) ensures better coverage despite the variation in rounds number.\\
470 As shown in Fig. \ref{fig3} and Fig. \ref{fig4},the Strategy (with Two Leaders) gives a full average coverage ratio or more than 90\% in the first rounds and then it decreases when the number of rounds increases due to dead nodes.Although some nodes are dead, sensor activity scheduling in each subregion choose other nodes to ensure the coverage. Moreover, when we have a dense sensor network, it leads to maintain the full coverage for larger number of rounds.\\
472 \subsection{The impact of the Number of Rounds on Active Sensor Ratio:}
473 It is important to have as few active nodes as possible in each round in order to minimize the communication
474 overhead and maximize the network lifetime. The Active Sensor Ratio(\%) = ((the no. of active sensor during this round) / (Total number of sensors in the network for the subregion)) * 100. Fig. \ref{fig5} and \ref{fig6} shows the average number of active nodes ratio versus rounds for 150 and 250 deployed nodes respectively.
478 % \begin{multicols}{6}
480 \includegraphics[scale=0.5]{TheActiveSensorRatio150.pdf} %\\~ ~ ~(a)
481 \caption{The impact of the Number of Rounds on Active Sensor Ratio for 150 deployed nodes }
486 % \begin{multicols}{6}
488 \includegraphics[scale=0.46]{TheActiveSensorRatio250.pdf} %\\~ ~ ~(a)
489 \caption{The impact of the Number of Rounds on Active Sensor Ratio for 250 deployed nodes }
493 The results in Fig. \ref{fig5} shows the superior of the Strategy (with Two Leaders) and the Strategy (with One Leader) on Simple Heuristic. The Strategy (with One Leader) uses minimum number of active nodes than the Strategy (with Two Leaders) until the last rounds because it uses central control on all the sensing field , the advantage of the Strategy (with Two Leaders) approach is that even if a network is disconnected in a one subregion the other one usually continues the optimization and this leads to extend the lifetime of the network.
494 In Fig. \ref{fig6}, we see the same observation that we saw on fig. \ref{fig5} but in the last rounds the Strategy (with Two Leaders) will be the better because the effect of disconnected network increases and it becomes near or equal to the Strategy (with One Leader) leads to give minimum average of active nodes.
496 \subsection{The impact of the Number of Rounds on Energy Saving Ratio:}
498 In this experiment, the Energy saving ratio ESR(\%) =( (No. of alive sensors in the network during this round) / (total number of sensors in the network for the subregion)) * 100. Fig. \ref{fig5} and \ref{fig6} shows the average number of active nodes ratio versus rounds for all three approach and for 150 and 250 deployed nodes respectively.
502 % \begin{multicols}{6}
504 \includegraphics[scale=0.5]{TheEnergySavingRatio150.pdf} %\\~ ~ ~(a)
505 \caption{The impact of the Number of Rounds on Energy Saving Ratio for 150 deployed nodes }
511 % \begin{multicols}{6}
513 \includegraphics[scale=0.46]{TheEnergySavingRatio250.pdf} %\\~ ~ ~(a)
514 \caption{The impact of the Number of Rounds on Energy Saving Ratio for 150 deployed nodes }
518 Simulation results explain the efficiency of the Strategy (with Two Leaders) to save the energy during larger number of rounds that seems to be very near the central approach (Strategy (with One Leader))which it be better in general.
520 \subsection{The Network Lifetime:}
521 we can define the network lifetime as the time until all nodes have been drained of their energy or the sensor network disconnected. In Fig. \ref{fig7}, the network lifetime for different network sizes and for the three approaches is illustrated.
525 % \begin{multicols}{6}
527 \includegraphics[scale=0.46]{TheNetworkLifetime.pdf} %\\~ ~ ~(a)
528 \caption{The Network Lifetime }
532 As shown in fig. \ref{fig7}, the network lifetime increase when the size of the network increase because the efficient of our approach in choosing the best representative nodes that will cover all the subregion and let the others nodes to sleep to be used later in the next rounds. Comparison shows that our approach is better than the other two methods in improving the network lifetime and this shows us by distributing the algorithm in each node in the network and subdivide the sensing field into many subregions to be managed independently and simultaneously can be more powerful against the sensor network disconnected in some subregions leads to maximize the lifetime of the network obviously.
534 \subsection{The Energy Consumption:}
535 In this experiment, we study the effect of the multi-hop communication protocol on the performance of our approach and compare it with other two approaches. The average energy consumption calculated based only on the energy consumed by transmitting and receiving packets by all sensor nodes in the network and during the lifetime of the network for 10 simulation runs divided by the average number of rounds and for different sizes of the network.We took the total energy consumption in both subregions for Strategy (with Two Leaders) and Simple heuristic. Fig. \ref{fig8} illustrates the Energy Consumption for different network sizes and for the three approaches.
539 \includegraphics[scale=0.46]{TheEnergyConsumption.pdf}
540 \caption{The Energy Consumption }
544 The results show that our approach consume less energy during the lifetime of the network by using multi-hop communication protocol in comparison with other two approaches especially Strategy (with One Leader) in spite of our approach make the network live for a longer time.
546 \subsection{The impact of Number of Sensors on Execution Time:}
547 It is important to have time efficient algorithm to be executed in sensor node because the limited resources in the sensor node. We took the total Execution Time of algorithms in both subregions for Strategy (with Two Leaders) and Simple heuristic. Table \ref{table1} exhibits the execution time for three approaches using different number of sensors.
550 \caption{The Execution Time(s) vs The Number of Sensors }
554 % used for centering table
555 \begin{tabular}{|c| c| c| c |}
556 % centered columns (4 columns)
558 %inserts double horizontal lines
559 Sensors Number & Strategy & Strategy & Simple Heuristic \\ [0.5ex]
560 & (with Two Leaders) & (with One Leader) \\ [0.5ex]
561 %Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
565 % inserts single horizontal line
566 50 & 0.097 & 0.189 & 0.001 \\
567 % inserting body of the table
569 100 & 0.419 & 1.972 & 0.0032 \\
571 150 & 1.295 & 13.098 & 0.0032 \\
573 200 & 4.54 & 169.469 & 0.0046 \\
575 250 & 12.252 & 1581.163 & 0.0056 \\ [1ex]
577 % [1ex] adds vertical space
582 % is used to refer this table in the text
585 Table \ref{table1} shows the efficiency of our algorithm to produce the solution with good execution time though the Simple Heuristic gives the solution in less time but our approach ensure a better coverage for the region with energy saving and less energy consumption led to extend the lifetime of the network.
587 \subsection{The Number of Stopped Simulation Runs :}
588 In this study, we will shows the number of stopped simulation runs (the disconnected network) per round for 150 and 250 deployed nodes and for three approaches. Fig. \ref{fig9} and \ref{fig10} illustrate the number of stopped simulation runs per round for 150 and 250 deployed nodes respectively.
592 \includegraphics[scale=0.50]{TheNumberofStoppedSimulationRuns150.pdf}
593 \caption{The Number of Stopped Simulation Runs against Rounds for 150 deployed nodes }
599 \includegraphics[scale=0.50]{TheNumberofStoppedSimulationRuns250.pdf}
600 \caption{The Number of Stopped Simulation Runs against Rounds for 250 deployed nodes }
604 The results explain the powerful of our approach against the Stopped Simulation Runs in comparison with other two approaches especially in the last rounds from the network lifetime and this will participate in extending the life time of the network.
606 \label{Simulation Results}
609 \section{\uppercase{Conclusions and Future Works}}
610 \label{sec:conclusion}
611 In this paper, we have addressed the problem of lifetime optimization in wireless sensor networks. This is a very natural and important problem, as sensor nodes have limited resources in terms of memory, energy and computational power. To cope with this problem, The field of sensing divided into smaller subregion using the concept of divide-and-conquer method and then multi-rounds coverage protocol will optimize the lifetime in each subregion.The suggested protocol joins two efficient techniques: network Leader Election and sensor activity scheduling where the challenges include how to select the most efficient Leader in each subregion and the best representative active nodes that will optimize the lifetime and take the responsibility of covering the subregion. The network lifetime in each subregion is divided into rounds, each round consists of four phases information exchange, Leader Election, Decision with optimization, and sensing.Our simulation results show that the proposed protocol outperforms or very near some other methods in terms of lifetime, coverage ratio, Active sensor Ratio, energy saving , energy consumption, execution time, and the number of stopped simulation runs. In future, we will study and prepare the one round coverage protocol by which all active sensor schedules will be prepared in one round using intelligent optimization methods such as swarms optimization or Evolutionary algorithms.
614 % use section* for acknowledgement
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