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11 %\jvol{00} \jnum{00} \jyear{2013} \jmonth{April}
15 \title{{\itshape Perimeter-based Coverage Optimization \\
16 to Improve Lifetime in Wireless Sensor Networks}}
18 \author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$, and Rapha\"el Couturier $^{a}$
19 $^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, \\
20 University Bourgogne Franche-Comt\'e, Belfort, France}} \\
21 $^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}}
27 The most important problem in a Wireless Sensor Network (WSN) is to optimize the
28 use of its limited energy provision, so that it can fulfill its monitoring task
29 as long as possible. Among known available approaches that can be used to
30 improve power management, lifetime coverage optimization provides activity
31 scheduling which ensures sensing coverage while minimizing the energy cost. We
32 propose such an approach called Perimeter-based Coverage Optimization protocol
33 (PeCO). It is a hybrid of centralized and distributed methods: the region of
34 interest is first subdivided into subregions and the protocol is then
35 distributed among sensor nodes in each subregion. The novelty of our approach
36 lies essentially in the formulation of a new mathematical optimization model
37 based on the perimeter coverage level to schedule sensors' activities.
38 Extensive simulation experiments demonstrate that PeCO can offer longer lifetime
39 coverage for WSNs compared to other protocols.
42 Wireless Sensor Networks, Area Coverage, Energy efficiency, Optimization, Scheduling.
47 \section{Introduction}
48 \label{sec:introduction}
50 The continuous progress in Micro Electro-Mechanical Systems (MEMS) and wireless
51 communication hardware has given rise to the opportunity of using large networks
52 of tiny sensors, called Wireless Sensor Networks
53 (WSN)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring
54 tasks. A WSN consists of small low-powered sensors working together by
55 communicating with one another through multi-hop radio communications. Each node
56 can send the data it collects in its environment, thanks to its sensor, to the
57 user by means of sink nodes. The features of a WSN makes it suitable for a wide
58 range of applications in areas such as business, environment, health, industry,
59 military, and so on~\citep{yick2008wireless}. Typically, a sensor node contains
60 three main components~\citep{anastasi2009energy}: a sensing unit able to measure
61 physical, chemical, or biological phenomena observed in the environment; a
62 processing unit which will process and store the collected measurements; a radio
63 communication unit for data transmission and reception.
65 The energy needed by an active sensor node to perform sensing, processing, and
66 communication is provided by a power supply which is a battery. This battery has
67 a limited energy provision and it may be unsuitable or impossible to replace or
68 recharge in most applications. Therefore it is necessary to deploy WSN with high
69 density in order to increase reliability and to exploit node redundancy thanks
70 to energy-efficient activity scheduling approaches. Indeed, the overlap of
71 sensing areas can be exploited to schedule alternatively some sensors in a low
72 power sleep mode and thus save energy. Overall, the main question that must be
73 answered is: how is it possible to extend the lifetime coverage of a WSN as long
74 as possible while ensuring a high level of coverage? These past few years many
75 energy-efficient mechanisms have been suggested to retain energy and extend the
76 lifetime of the WSNs~\citep{rault2014energy}.
78 This paper makes the following contributions :
80 \item A framework is devised to schedule nodes to be activated alternatively
81 such that the network lifetime is prolonged while ensuring that a certain
82 level of coverage is preserved. A key idea in the proposed framework is to
83 exploit spatial and temporal subdivision. On the one hand, the area of
84 interest is divided into several smaller subregions and, on the other hand,
85 the time line is divided into periods of equal length. In each subregion the
86 sensor nodes will cooperatively choose a leader which will schedule nodes'
87 activities, and this grouping of sensors is similar to typical cluster
89 \item A new mathematical optimization model is proposed. Instead of trying to
90 cover a set of specified points/targets as in most of the methods proposed in
91 the literature, we formulate a mixed-integer program based on the perimeter
92 coverage of each sensor. The model involves integer variables to capture the
93 deviations between the actual level of coverage and the required level.
94 Hence, an optimal schedule will be obtained by minimizing a weighted sum of
96 \item Extensive simulation experiments are conducted using the discrete event
97 simulator OMNeT++, to demonstrate the efficiency of our protocol. We have
98 compared the PeCO protocol to two approaches found in the literature:
99 DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to our previous
100 protocol DiLCO published in~\citep{Idrees2}. DiLCO uses the same framework as
101 PeCO but is based on another optimization model for sensor scheduling.
104 The rest of the paper is organized as follows. In the next section some related
105 work in the field is reviewed. Section~\ref{sec:The PeCO Protocol Description}
106 is devoted to the PeCO protocol description and Section~\ref{cp} focuses on the
107 coverage model formulation which is used to schedule the activation of sensor
108 nodes. Section~\ref{sec:Simulation Results and Analysis} presents simulations
109 results and discusses the comparison with other approaches. Finally, concluding
110 remarks are drawn and some suggestions are given for future works in
111 Section~\ref{sec:Conclusion and Future Works}.
113 \section{Related Literature}
114 \label{sec:Literature Review}
116 This section summarizes some related works regarding the coverage problem and
117 presents specific aspects of the PeCO protocol common with other literature
120 The most discussed coverage problems in literature can be classified in three
121 categories~\citep{li2013survey} according to their respective monitoring
122 objective. Hence, area coverage \citep{Misra} means that every point inside a
123 fixed area must be monitored, while target coverage~\citep{yang2014novel} refers
124 to the objective of coverage for a finite number of discrete points called
125 targets, and barrier coverage~\citep{HeShibo,kim2013maximum} focuses on
126 preventing intruders from entering into the region of interest. In
127 \citep{Deng2012} authors transform the area coverage problem into the target
128 coverage one, taking into account the intersection points among disks of sensors
129 nodes or between disks of sensor nodes and boundaries. In
130 \citep{huang2005coverage} authors prove that if the perimeters of the sensors
131 are sufficiently covered it will be the case for the whole area. They provide an
132 algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of each
133 sensor. $d$ denotes the maximum number of sensors that are neighbors to a
134 sensor, and $n$ is the total number of sensors in the network. {\it In PeCO
135 protocol, instead of determining the level of coverage of a set of discrete
136 points, our optimization model is based on checking the perimeter-coverage of
137 each sensor to activate a minimal number of sensors.}
139 The major approach to extend network lifetime while preserving coverage is to
140 divide/organize the sensors into a suitable number of set covers (disjoint or
141 non-disjoint) \citep{wang2011coverage}, where each set completely covers a
142 region of interest, and to successively activate these set covers. The network
143 activity can be planned in advance and scheduled for the entire network lifetime
144 or organized in periods, and the set of active sensor nodes decided at the
145 beginning of each period \citep{ling2009energy}. In fact, many authors propose
146 algorithms working in such a periodic fashion
147 \citep{chin2007,yan2008design,pc10}. Active node selection is determined based
148 on the problem requirements (e.g. area monitoring, connectivity, or power
149 efficiency). For instance, \citet{jaggi2006} address the problem of maximizing
150 the lifetime by dividing sensors into the maximum number of disjoint subsets
151 such that each subset can ensure both coverage and connectivity. A greedy
152 algorithm is applied once to solve this problem and the computed sets are
153 activated in succession to achieve the desired network lifetime. {\it Motivated
154 by these works, PeCO protocol works in periods, where each period contains a
155 preliminary phase for information exchange and decisions, followed by a
156 sensing phase where one cover set is in charge of the sensing task.}
158 Various centralized and distributed approaches, or even a mixing of these two
159 concepts, have been proposed to extend the network lifetime
160 \citep{zhou2009variable}. In distributed
161 algorithms~\citep{ChinhVu,qu2013distributed,yangnovel} each sensor decides of
162 its own activity scheduling after an information exchange with its neighbors.
163 The main interest of such an approach is to avoid long range communications and
164 thus to reduce the energy dedicated to the communications. Unfortunately, since
165 each node has information on its immediate neighbors only (usually the one-hop
166 ones), it may make a bad decision leading to a global suboptimal solution.
167 Conversely, centralized
168 algorithms~\citep{cardei2005improving,zorbas2010solving,pujari2011high} always
169 provide nearly optimal solutions since the algorithm has a global view of the
170 whole network. The disadvantage of a centralized method is obviously its high
171 cost in communications needed to transmit to a single node, the base station
172 which will globally schedule nodes' activities, data from all the other sensor
173 nodes in the area. The price in communications can be huge since long range
174 communications will be needed. In fact the larger the WSN, the higher the
175 communication energy cost. {\it In order to be suitable for large-scale
176 networks, in the PeCO protocol the area of interest is divided into several
177 smaller subregions, and in each one, a node called the leader is in charge of
178 selecting the active sensors for the current period. Thus the PeCO protocol
179 is scalable and a globally distributed method, whereas it is centralized in
182 Various coverage scheduling algorithms have been developed these past few years.
183 Many of them, dealing with the maximization of the number of cover sets, are
184 heuristics. These heuristics involve the construction of a cover set by
185 including in priority the sensor nodes which cover critical targets, that is to
186 say targets that are covered by the smallest number of sensors
187 \citep{berman04,zorbas2010solving}. Other approaches are based on mathematical
189 formulations~\citep{cardei2005energy,5714480,pujari2011high,Yang2014} and
190 dedicated techniques (solving with a branch-and-bound algorithm available in
191 optimization solver). The problem is formulated as an optimization problem
192 (maximization of the lifetime or number of cover sets) under target coverage and
193 energy constraints. Column generation techniques, well-known and widely
194 practiced techniques for solving linear programs with too many variables, have
196 used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012column}.
197 {\it In the PeCO protocol, each leader, in charge of a subregion, solves an
198 integer program which has a twofold objective: minimizing the overcoverage and
199 the undercoverage of the perimeter of each sensor.}
201 The authors in \citep{Idrees2} propose a Distributed Lifetime Coverage
202 Optimization (DiLCO) protocol, which maintains the coverage and improves the
203 lifetime in WSNs. It is an improved version of a research work presented
204 in~\citep{idrees2014coverage}. First, the area of interest is partitioned into
205 subregions using a divide-and-conquer method. The DiLCO protocol is then
206 distributed on the sensor nodes in each subregion in a second step. Hence this
207 protocol combines two techniques: a leader election in each subregion, followed
208 by an optimization-based node activity scheduling performed by each elected
209 leader. The proposed DiLCO protocol is a periodic protocol where each period is
210 decomposed into 4 phases: information exchange, leader election, decision, and
211 sensing. The simulations show that DiLCO is able to increase the WSN lifetime
212 and provides improved coverage performance. {\it In the PeCO protocol, a new
213 mathematical optimization model is proposed. Instead of trying to cover a set
214 of specified points/targets as in the DiLCO protocol, we formulate an integer
215 program based on the perimeter coverage of each sensor. The model involves
216 integer variables to capture the deviations between the actual level of
217 coverage and the required level. The idea is that an optimal scheduling will
218 be obtained by minimizing a weighted sum of these deviations.}
220 \section{ The P{\scshape e}CO Protocol Description}
221 \label{sec:The PeCO Protocol Description}
223 %In this section, the Perimeter-based Coverage
224 %Optimization protocol is decribed in details. First we present the assumptions we made and the models
225 %we considered (in particular the perimeter coverage one), second we describe the
226 %background idea of our protocol, and third we give the outline of the algorithm
227 %executed by each node.
230 \subsection{Assumptions and Models}
233 A WSN consisting of $J$ stationary sensor nodes randomly and uniformly
234 distributed in a bounded sensor field is considered. The wireless sensors are
235 deployed in high density to ensure initially a high coverage ratio of the area
236 of interest. All the sensor nodes are supposed to be homogeneous in terms of
237 communication, sensing, and processing capabilities and heterogeneous from the
238 energy provision point of view. The location information is available to a
239 sensor node either through hardware such as embedded GPS or location discovery
240 algorithms. A Boolean disk coverage model, which is the most widely used sensor
241 coverage model in the literature, is considered and all sensor nodes have a
242 constant sensing range $R_s$. Thus, all the space points within a disk centered
243 at a sensor with a radius equal to the sensing range are said to be covered by
244 this sensor. We also assume that the communication range $R_c$ satisfies $R_c
245 \geq 2 \cdot R_s$. In fact, \citet{Zhang05} proved that if the transmission
246 range fulfills the previous hypothesis, the complete coverage of a convex area
247 implies connectivity among active nodes.
249 The PeCO protocol uses the same perimeter-coverage model as
250 \citet{huang2005coverage}. It can be expressed as follows: a sensor is said to
251 be perimeter covered if all the points on its perimeter are covered by at least
252 one sensor other than itself. Authors \citet{huang2005coverage} proved that a
253 network area is $k$-covered (every point in the area is covered by at least
254 $k$~sensors) if and only if each sensor in the network is $k$-perimeter-covered
255 (perimeter covered by at least $k$ sensors).
257 Figure~\ref{figure1}(a) shows the coverage of sensor node~$0$. On this figure,
258 sensor~$0$ has nine neighbors and we have reported on its perimeter (the
259 perimeter of the disk covered by the sensor) for each neighbor the two points
260 resulting from the intersection of the two sensing areas. These points are
261 denoted for neighbor~$i$ by $iL$ and $iR$, respectively for left and right from
262 a neighboring point of view. The resulting couples of intersection points
263 subdivide the perimeter of sensor~$0$ into portions called arcs.
267 \begin{tabular}{@{}cr@{}}
268 \includegraphics[width=75mm]{figure1a.eps} & \raisebox{3.25cm}{(a)} \\
269 \includegraphics[width=75mm]{figure1b.eps} & \raisebox{2.75cm}{(b)}
271 \caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of
272 $u$'s perimeter covered by $v$.}
276 Figure~\ref{figure1}(b) describes the geometric information used to find the
277 locations of the left and right points of an arc on the perimeter of a sensor
278 node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the
279 west side of sensor~$u$, with the following respective coordinates in the
280 sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates the
281 euclidean distance between nodes~$u$ and $v$ is computed as follows:
283 Dist(u,v)=\sqrt{(u_x - v_x)^2 + (u_y-v_y)^2},
285 while the angle~$\alpha$ is obtained through the formula:
287 \alpha = \arccos \left(\frac{Dist(u,v)}{2R_s} \right).
289 The arc on the perimeter of~$u$ defined by the angular interval $[\pi -
290 \alpha,\pi + \alpha]$ is then said to be perimeter-covered by sensor~$v$.
292 Every couple of intersection points is placed on the angular interval $[0,2\pi)$
293 in a counterclockwise manner, leading to a partitioning of the interval.
294 Figure~\ref{figure1}(a) illustrates the arcs for the nine neighbors of
295 sensor $0$ and Table~\ref{my-label} gives the position of the corresponding arcs
296 in the interval $[0,2\pi)$. More precisely, the points are
297 ordered according to the measures of the angles defined by their respective
298 positions. The intersection points are then visited one after another, starting
299 from the first intersection point after point~zero, and the maximum level of
300 coverage is determined for each interval defined by two successive points. The
301 maximum level of coverage is equal to the number of overlapping arcs. For
302 example, between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$
303 (the value is highlighted in yellow at the bottom of Figure~\ref{figure2}), which
304 means that at most 2~neighbors can cover the perimeter in addition to node $0$.
305 Table~\ref{my-label} summarizes for each coverage interval the maximum level of
306 coverage and the sensor nodes covering the perimeter. The example discussed
307 above is thus given by the sixth line of the table.
311 \includegraphics[width=0.95\linewidth]{figure2.eps}
312 \caption{Maximum coverage levels for perimeter of sensor node $0$.}
317 \tbl{Coverage intervals and contributing sensors for node 0 \label{my-label}}
318 {\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
320 \begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\ level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in coverage interval\end{tabular}} \\ \hline
321 0.0291 & 1L & 2L & 4 & 0 & 1 & 3 & 4 & \\ \hline
322 0.104 & 2L & 3R & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline
323 0.3168 & 3R & 4R & 4 & 0 & 1 & 4 & 2 & \\ \hline
324 0.6752 & 4R & 1R & 3 & 0 & 1 & 2 & & \\ \hline
325 1.8127 & 1R & 5L & 2 & 0 & 2 & & & \\ \hline
326 1.9228 & 5L & 6L & 3 & 0 & 2 & 5 & & \\ \hline
327 2.3959 & 6L & 2R & 4 & 0 & 2 & 5 & 6 & \\ \hline
328 2.4258 & 2R & 7L & 3 & 0 & 5 & 6 & & \\ \hline
329 2.7868 & 7L & 8L & 4 & 0 & 5 & 6 & 7 & \\ \hline
330 2.8358 & 8L & 5R & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline
331 2.9184 & 5R & 7R & 4 & 0 & 6 & 7 & 8 & \\ \hline
332 3.3301 & 7R & 9R & 3 & 0 & 6 & 8 & & \\ \hline
333 3.9464 & 9R & 6R & 4 & 0 & 6 & 8 & 9 & \\ \hline
334 4.767 & 6R & 3L & 3 & 0 & 8 & 9 & & \\ \hline
335 4.8425 & 3L & 8R & 4 & 0 & 3 & 8 & 9 & \\ \hline
336 4.9072 & 8R & 4L & 3 & 0 & 3 & 9 & & \\ \hline
337 5.3804 & 4L & 9R & 4 & 0 & 3 & 4 & 9 & \\ \hline
338 5.9157 & 9R & 1L & 3 & 0 & 3 & 4 & & \\ \hline
344 In the PeCO protocol, the scheduling of the sensor nodes' activities is
345 formulated with a mixed-integer program based on coverage
346 intervals~\citep{doi:10.1155/2010/926075}. The formulation of the coverage
347 optimization problem is detailed in~Section~\ref{cp}. Note that when a sensor
348 node has a part of its sensing range outside the WSN sensing field, as in
349 Figure~\ref{figure3}, the maximum coverage level for this arc is set to $\infty$
350 and the corresponding interval will not be taken into account by the
351 optimization algorithm.
356 \includegraphics[width=57.5mm]{figure3.eps}
357 \caption{Sensing range outside the WSN's area of interest.}
363 \subsection{Main Idea}
365 The WSN area of interest is, in a first step, divided into regular homogeneous
366 subregions using a divide-and-conquer algorithm. In a second step our protocol
367 will be executed in a distributed way in each subregion simultaneously to
368 schedule nodes' activities for one sensing period. Sensor nodes are assumed to
369 be deployed almost uniformly over the region. The regular subdivision is made
370 such that the number of hops between any pairs of sensors inside a subregion is
371 less than or equal to 3.
373 As shown in Figure~\ref{figure4}, node activity scheduling is produced by the
374 proposed protocol in a periodic manner. Each period is divided into 4 stages:
375 Information (INFO) Exchange, Leader Election, Decision (the result of an
376 optimization problem), and Sensing. For each period there is exactly one set
377 cover responsible for the sensing task. Protocols based on a periodic scheme,
378 like PeCO, are more robust against an unexpected node failure. On the one hand,
379 if a node failure is discovered before taking the decision, the corresponding
380 sensor node will not be considered by the optimization algorithm. On the other
381 hand, if the sensor failure happens after the decision, the sensing task of the
382 network will be temporarily affected: only during the period of sensing until a
383 new period starts, since a new set cover will take charge of the sensing task in
384 the next period. The energy consumption and some other constraints can easily be
385 taken into account since the sensors can update and then exchange their
386 information (including their residual energy) at the beginning of each period.
387 However, the pre-sensing phases (INFO Exchange, Leader Election, and Decision)
388 are energy consuming, even for nodes that will not join the set cover to monitor
389 the area. Sensing period duration is adapted according to the QoS requirements
394 \includegraphics[width=80mm]{figure4.eps}
395 \caption{PeCO protocol.}
399 We define two types of packets to be used by the PeCO protocol:
401 \item INFO packet: sent by each sensor node to all the nodes inside a same
402 subregion for information exchange.
403 \item ActiveSleep packet: sent by the leader to all the nodes in its subregion
404 to transmit to them their respective status (stay Active or go Sleep) during
408 Five statuses are possible for a sensor node in the network:
410 \item LISTENING: waits for a decision (to be active or not);
411 \item COMPUTATION: executes the optimization algorithm as leader to
412 determine the activities scheduling;
413 \item ACTIVE: node is sensing;
414 \item SLEEP: node is turned off;
415 \item COMMUNICATION: transmits or receives packets.
418 \subsection{PeCO Protocol Algorithm}
420 The pseudocode implementing the protocol on a node is given below. More
421 precisely, Algorithm~\ref{alg:PeCO} gives a brief description of the protocol
422 applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
426 % \KwIn{all the parameters related to information exchange}
427 % \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
429 %\emph{Initialize the sensor node and determine it's position and subregion} \;
431 \caption{PeCO pseudocode}
432 \eIf{$RE_k \geq E_{th}$}{
433 $s_k.status$ = COMMUNICATION\;
434 Send $INFO()$ packet to other nodes in subregion\;
435 Wait $INFO()$ packet from other nodes in subregion\;
436 Update K.CurrentSize\;
437 LeaderID = Leader election\;
438 \eIf{$s_k.ID = LeaderID$}{
439 $s_k.status$ = COMPUTATION\;
440 \If{$ s_k.ID $ is Not previously selected as a Leader}{
441 Execute the perimeter coverage model\;
443 \eIf{($s_k.ID $ is the same Previous Leader) {\bf and} \\
444 \indent (K.CurrentSize = K.PreviousSize)}{
445 Use the same previous cover set for current sensing stage\;
447 Update $a^j_{ik}$; prepare data for IP~Algorithm\;
448 $\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$)\;
449 K.PreviousSize = K.CurrentSize\;
451 $s_k.status$ = COMMUNICATION\;
452 Send $ActiveSleep()$ to each node $l$ in subregion\;
455 $s_k.status$ = LISTENING\;
456 Wait $ActiveSleep()$ packet from the Leader\;
460 Exclude $s_k$ from entering in the current sensing stage\;
465 %\noindent{\bf If} $RE_k \geq E_{th}$ {\bf then}\\
466 %\hspace*{0.6cm} \emph{$s_k.status$ = COMMUNICATION;}\\
467 %\hspace*{0.6cm} \emph{Send $INFO()$ packet to other nodes in subregion;}\\
468 %\hspace*{0.6cm} \emph{Wait $INFO()$ packet from other nodes in subregion;}\\
469 %\hspace*{0.6cm} \emph{Update K.CurrentSize;}\\
470 %\hspace*{0.6cm} \emph{LeaderID = Leader election;}\\
471 %\hspace*{0.6cm} {\bf If} $ s_k.ID = LeaderID $ {\bf then}\\
472 %\hspace*{1.2cm} \emph{$s_k.status$ = COMPUTATION;}\\
473 %\hspace*{1.2cm}{\bf If} \emph{$ s_k.ID $ is Not previously selected as a Leader} {\bf then}\\
474 %\hspace*{1.8cm} \emph{ Execute the perimeter coverage model;}\\
475 %\hspace*{1.2cm} {\bf end}\\
476 %\hspace*{1.2cm}{\bf If} \emph{($s_k.ID $ is the same Previous Leader)~And~(K.CurrentSize = K.PreviousSize)}\\
477 %\hspace*{1.8cm} \emph{ Use the same previous cover set for current sensing stage;}\\
478 %\hspace*{1.2cm} {\bf end}\\
479 %\hspace*{1.2cm} {\bf else}\\
480 %\hspace*{1.8cm}\emph{Update $a^j_{ik}$; prepare data for IP~Algorithm;}\\
481 %\hspace*{1.8cm} \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$);}\\
482 %\hspace*{1.8cm} \emph{K.PreviousSize = K.CurrentSize;}\\
483 %\hspace*{1.2cm} {\bf end}\\
484 %\hspace*{1.2cm}\emph{$s_k.status$ = COMMUNICATION;}\\
485 %\hspace*{1.2cm}\emph{Send $ActiveSleep()$ to each node $l$ in subregion;}\\
486 %\hspace*{1.2cm}\emph{Update $RE_k $;}\\
487 %\hspace*{0.6cm} {\bf end}\\
488 %\hspace*{0.6cm} {\bf else}\\
489 %\hspace*{1.2cm}\emph{$s_k.status$ = LISTENING;}\\
490 %\hspace*{1.2cm}\emph{Wait $ActiveSleep()$ packet from the Leader;}\\
491 %\hspace*{1.2cm}\emph{Update $RE_k $;}\\
492 %\hspace*{0.6cm} {\bf end}\\
495 %\hspace*{0.6cm} \emph{Exclude $s_k$ from entering in the current sensing stage;}\\
500 In this algorithm, $K.CurrentSize$ and $K.PreviousSize$ respectively represent
501 the current number and the previous number of living nodes in the subnetwork of
502 the subregion. At the beginning of the first period $K.PreviousSize$ is
503 initialized to zero. Initially, the sensor node checks its remaining energy
504 $RE_k$, which must be greater than a threshold $E_{th}$ in order to participate
505 in the current period. Each sensor node determines its position and its
506 subregion using an embedded GPS or a location discovery algorithm. After that,
507 all the sensors collect position coordinates, remaining energy, sensor node ID,
508 and the number of their one-hop live neighbors during the information exchange.
509 The sensors inside a same region cooperate to elect a leader. The selection
510 criteria for the leader are (in order of priority):
512 \item larger number of neighbors;
513 \item larger remaining energy;
514 \item and then, in case of equality, larger indexes.
516 Once chosen, the leader collects information to formulate and solve the integer
517 program which allows to build the set of active sensors in the sensing
520 \section{Perimeter-based Coverage Problem Formulation}
523 In this section, the perimeter-based coverage problem is mathematically
524 formulated. It has been proved to be a NP-hard problem
525 by \citep{doi:10.1155/2010/926075}. Authors study the coverage of the perimeter
526 of a large object requiring to be monitored. For the proposed formulation in
527 this paper, the large object to be monitored is the sensor itself (or more
528 precisely its sensing area).
530 The following notations are used throughout the section.
532 First, the following sets:
534 \item $S$ represents the set of sensor nodes;
535 \item $A \subseteq S $ is the subset of alive sensors;
536 \item $I_j$ designates the set of coverage intervals (CI) obtained for
539 $I_j$ refers to the set of coverage intervals which has been defined according
540 to the method introduced in Subsection~\ref{CI}. For a coverage interval $i$,
541 let $a^j_{ik}$ denote the indicator function of whether sensor~$k$ is involved
542 in coverage interval~$i$ of sensor~$j$, that is:
546 1 & \mbox{if sensor $k$ is involved in the } \\
547 & \mbox{coverage interval $i$ of sensor $j$}, \\
548 0 & \mbox{otherwise.}\\
551 Note that $a^k_{ik}=1$ by definition of the interval.
553 Second, several variables are defined. Hence, each binary variable $X_{k}$
554 determines the activation of sensor $k$ in the sensing phase ($X_k=1$ if the
555 sensor $k$ is active or 0 otherwise). $M^j_i$ is a variable which measures the
556 undercoverage for the coverage interval $i$ corresponding to sensor~$j$. In the
557 same way, the overcoverage for the same coverage interval is given by the
560 To sustain a level of coverage equal to $l$ all along the perimeter of sensor
561 $j$, at least $l$ sensors involved in each coverage interval $i \in I_j$ of
562 sensor $j$ have to be active. According to the previous notations, the number
563 of active sensors in the coverage interval $i$ of sensor $j$ is given by
564 $\sum_{k \in A} a^j_{ik} X_k$. To extend the network lifetime, the objective is
565 to activate a minimal number of sensors in each period to ensure the desired
566 coverage level. As the number of alive sensors decreases, it becomes impossible
567 to reach the desired level of coverage for all coverage intervals. Therefore
568 variables $M^j_i$ and $V^j_i$ are introduced as a measure of the deviation
569 between the desired number of active sensors in a coverage interval and the
570 effective number. And we try to minimize these deviations, first to force the
571 activation of a minimal number of sensors to ensure the desired coverage level,
572 and if the desired level cannot be completely satisfied, to reach a coverage
573 level as close as possible to the desired one.
575 The coverage optimization problem can then be mathematically expressed as follows:
578 \text{Minimize } & \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i ) \\
579 \text{Subject to:} & \\
580 & \sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in S \\
581 & \sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in S \\
582 & X_{k} \in \{0,1\}, \forall k \in A \\
583 & M^j_i, V^j_i \in \mathbb{R}^{+}
590 %\min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i ) & \\
591 %\textrm{subject to :} &\\
592 %\sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in S\\
593 %\sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in S\\
594 %X_{k} \in \{0,1\}, \forall k \in A \\
595 %M^j_i, V^j_i \in \mathbb{R}^{+}
600 If a given level of coverage $l$ is required for one sensor, the sensor is said
601 to be undercovered (respectively overcovered) if the level of coverage of one of
602 its CI is less (respectively greater) than $l$. If the sensor $j$ is
603 undercovered, there exists at least one of its CI (say $i$) for which the number
604 of active sensors (denoted by $l^{i}$) covering this part of the perimeter is
605 less than $l$ and in this case : $M_{i}^{j}=l-l^{i}$, $V_{i}^{j}=0$. Conversely,
606 if the sensor $j$ is overcovered, there exists at least one of its CI (say $i$)
607 for which the number of active sensors (denoted by $l^{i}$) covering this part
608 of the perimeter is greater than $l$ and in this case: $M_{i}^{j}=0$,
611 $\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the
612 relative importance of satisfying the associated level of coverage. For example,
613 weights associated with coverage intervals of the specified part of a region may
614 be given by a relatively larger magnitude than weights associated with another
615 region. This kind of mixed-integer program is inspired from the model developed
616 for brachytherapy treatment planning to optimize dose distribution
617 \citep{0031-9155-44-1-012}. The choice of the values for variables $\alpha$ and
618 $\beta$ should be made according to the needs of the application. $\alpha$
619 should be large enough to prevent undercoverage and so to reach the highest
620 possible coverage ratio. $\beta$ should be large enough to prevent overcoverage
621 and so to activate a minimum number of sensors. The mixed-integer program must
622 be solved by the leader in each subregion at the beginning of each sensing
623 phase, whenever the environment has changed (new leader, death of some sensors).
624 Note that the number of constraints in the model is constant (constraints of
625 coverage expressed for all sensors), whereas the number of variables $X_k$
626 decreases over periods, since only alive sensors (sensors with enough energy to
627 be alive during one sensing phase) are considered in the model.
629 \section{Performance Evaluation and Analysis}
630 \label{sec:Simulation Results and Analysis}
632 \subsection{Simulation Settings}
634 The WSN area of interest is supposed to be divided into 16~regular subregions
635 and we use the same energy consumption model as in our previous
636 work~\citep{Idrees2}. Table~\ref{table3} gives the chosen parameters settings.
639 \tbl{Relevant parameters for network initialization \label{table3}}{
643 Parameter & Value \\ [0.5ex]
645 % inserts single horizontal line
646 Sensing field & $(50 \times 25)~m^2 $ \\
647 WSN size & 100, 150, 200, 250, and 300~nodes \\
648 Initial energy & in range 500-700~Joules \\
649 Sensing period & duration of 60 minutes \\
650 $E_{th}$ & 36~Joules \\
653 $\alpha^j_i$ & 0.6 \\
658 To obtain experimental results which are relevant, simulations with five
659 different node densities going from 100 to 300~nodes were performed considering
660 each time 25~randomly generated networks. The nodes are deployed on a field of
661 interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
662 high coverage ratio. Each node has an initial energy level, in Joules, which is
663 randomly drawn in the interval $[500-700]$. If its energy provision reaches a
664 value below the threshold $E_{th}=36$~Joules, the minimum energy needed for a
665 node to stay active during one period, it will no longer participate in the
666 coverage task. This value corresponds to the energy needed by the sensing phase,
667 obtained by multiplying the energy consumed in the active state (9.72 mW) with
668 the time in seconds for one period (3600 seconds), and adding the energy for the
669 pre-sensing phases. According to the interval of initial energy, a sensor may
670 be active during at most 20 periods. the information exchange to update the coverage
671 is executed every hour, but the length of the sensing period could be reduced
672 and adapted dynamically. On the one hand a small sensing period would allow the network to
673 be more reliable but would have resulted in higher communication costs. On the
674 other hand the choice of a long duration may cause problems in case of nodes
675 failure during the sensing period.
677 The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good
678 network coverage and a longer WSN lifetime. Higher priority is given to the
679 undercoverage (by setting the $\alpha^j_i$ with a larger value than $\beta^j_i$)
680 so as to prevent the non-coverage for the interval~$i$ of the sensor~$j$. On
681 the other hand, $\beta^j_i$ is assigned to a value which is slightly lower so as
682 to minimize the number of active sensor nodes which contribute in covering the
683 interval. Subsection~\ref{sec:Impact} investigates more deeply how the values of
684 both parameters affect the performance of the PeCO protocol.
686 The following performance metrics are used to evaluate the efficiency of the
689 \item {\bf Network Lifetime}: the lifetime is defined as the time elapsed until
690 the coverage ratio falls below a fixed threshold. $Lifetime_{95}$ and
691 $Lifetime_{50}$ denote, respectively, the amount of time during which is
692 guaranteed a level of coverage greater than $95\%$ and $50\%$. The WSN can
693 fulfill the expected monitoring task until all its nodes have depleted their
694 energy or if the network is no more connected. This last condition is crucial
695 because without network connectivity a sensor may not be able to send to a
696 base station an event it has sensed.
697 \item {\bf Coverage Ratio (CR)} : it measures how well the WSN is able to
698 observe the area of interest. In our case, the sensor field is discretized as
699 a regular grid, which yields the following equation:
702 \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100
704 where $n$ is the number of covered grid points by active sensors of every
705 subregions during the current sensing phase and $N$ is total number of grid
706 points in the sensing field. A layout of $N~=~51~\times~26~=~1326$~grid points
707 is considered in the simulations.
708 \item {\bf Active Sensors Ratio (ASR)}: a major objective of our protocol is to
709 activate as few nodes as possible, in order to minimize the communication
710 overhead and maximize the WSN lifetime. The active sensors ratio is defined as
714 \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|J|$}} \times 100
716 where $|A_r^p|$ is the number of active sensors in the subregion $r$ in the
717 sensing period~$p$, $R$ is the number of subregions, and $|J|$ is the number
718 of sensors in the network.
719 \item {\bf Energy Consumption (EC)}: energy consumption can be seen as the total
720 energy consumed by the sensors during $Lifetime_{95}$ or $Lifetime_{50}$,
721 divided by the number of periods. The value of EC is computed according to
725 \mbox{EC} = \frac{\sum\limits_{p=1}^{P} \left( E^{\mbox{com}}_p+E^{\mbox{list}}_p+E^{\mbox{comp}}_p
726 + E^{a}_p+E^{s}_p \right)}{P},
728 where $P$ corresponds to the number of periods. The total energy consumed by
729 the sensors comes through taking into consideration four main energy
730 factors. The first one, denoted $E^{\scriptsize \mbox{com}}_p$, represents the
731 energy consumption spent by all the nodes for wireless communications during
732 period $p$. $E^{\scriptsize \mbox{list}}_p$, the next factor, corresponds to
733 the energy consumed by the sensors in LISTENING status before receiving the
734 decision to go active or sleep in period $p$. $E^{\scriptsize \mbox{comp}}_p$
735 refers to the energy needed by all the leader nodes to solve the integer
736 program during a period (COMPUTATION status). Finally, $E^a_{p}$ and
737 $E^s_{p}$ indicate the energy consumed by the WSN during the sensing phase
738 ({\it active} and {\it sleeping} nodes).
741 \subsection{Simulation Results}
743 In order to assess and analyze the performance of our protocol we have
744 implemented the PeCO protocol in OMNeT++~\citep{varga} simulator. The
745 simulations were run on a DELL laptop with an Intel Core~i3~2370~M (1.8~GHz)
746 processor (2 cores) whose MIPS (Million Instructions Per Second) rate is equal
747 to 35330. To be consistent with the use of a sensor node based on Atmels AVR
748 ATmega103L microcontroller (6~MHz) having a MIPS rate equal to 6, the original
749 execution time on the laptop is multiplied by 2944.2 $\left(\frac{35330}{2}
750 \times \frac{1}{6} \right)$. Energy consumption is calculated according to the
751 power consumption values, in milliWatt per second, given in Table~\ref{tab:EC},
752 based on the energy model proposed in \citep{ChinhVu}.
756 \caption{Power consumption values}
758 \begin{tabular}{|l||cccc|}
760 {\bf Sensor status} & MCU & Radio & Sensing & {\it Power (mW)} \\
762 LISTENING & On & On & On & 20.05 \\
763 ACTIVE & On & Off & On & 9.72 \\
764 SLEEP & Off & Off & Off & 0.02 \\
765 COMPUTATION & On & On & On & 26.83 \\
767 \multicolumn{4}{|l}{Energy needed to send or receive a 2-bit content message} & 0.515 \\
772 The modeling language for Mathematical Programming (AMPL)~\citep{AMPL} is used
773 to generate the integer program instance in a standard format, which is then
774 read and solved by the optimization solver GLPK (GNU linear Programming Kit
775 available in the public domain) \citep{glpk} through a Branch-and-Bound method.
776 In practice, executing GLPK on a sensor node is obviously intractable due to the
777 huge memory use. Fortunately, to solve the optimization problem we could use
778 commercial solvers like CPLEX \citep{iamigo:cplex} which are less memory
779 consuming and more efficient, or implement a lightweight heuristic. For example,
780 for a WSN of 200 sensor nodes, a leader node has to deal with constraints
781 induced by about 12 sensor nodes. In that case, to solve the optimization
782 problem a memory consumption of more than 1~MB can be observed with GLPK,
783 whereas less than 300~KB would be needed with CPLEX.
785 Besides PeCO, three other protocols will be evaluated for comparison
786 purposes. The first one, called DESK, is a fully distributed coverage algorithm
787 proposed by \citep{ChinhVu}. The second one, called
788 GAF~\citep{xu2001geography}, consists in dividing the monitoring area into fixed
789 squares. Then, during the decision phase, in each square, one sensor is chosen
790 to remain active during the sensing phase. The last one, the DiLCO
791 protocol~\citep{Idrees2}, is an improved version of a research work we presented
792 in~\citep{idrees2014coverage}. Let us notice that the PeCO and DiLCO protocols
793 are based on the same framework. In particular, the choice for the simulations
794 of a partitioning in 16~subregions was made because it corresponds to the
795 configuration producing the best results for DiLCO. Of course, this number of
796 subregions should be adapted according to the size of the area of interest and
797 the number of sensors. The protocols are distinguished from one another by the
798 formulation of the integer program providing the set of sensors which have to be
799 activated in each sensing phase. The DiLCO protocol tries to satisfy the
800 coverage of a set of primary points, whereas the objective of the PeCO protocol
801 is to reach a desired level of coverage for each sensor perimeter. In our
802 experimentations, we chose a level of coverage equal to one ($l=1$).
804 \subsubsection{Coverage Ratio}
806 Figure~\ref{figure5} shows the average coverage ratio for 200 deployed nodes
807 obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better
808 coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the
809 98.76\% produced by PeCO for the first periods. This is due to the fact that at
810 the beginning the DiLCO and PeCO protocols put more redundant sensors to sleep
811 status (which slightly decreases the coverage ratio), while the two other
812 protocols activate more sensor nodes. Later, when the number of periods is
813 beyond~70, it clearly appears that PeCO provides a better coverage ratio and
814 keeps a coverage ratio greater than 50\% for longer periods (15 more compared to
815 DiLCO, 40 more compared to DESK). The energy saved by PeCO in the early periods
816 allows later a substantial increase of the coverage performance.
821 \includegraphics[scale=0.5] {figure5.eps}
822 \caption{Coverage ratio for 200 deployed nodes.}
826 \subsubsection{Active Sensors Ratio}
828 Minimizing the number of active sensor nodes in each period is essential to minimize the
829 energy consumption and thus to maximize the network lifetime.
830 Figure~\ref{figure6} shows the average active nodes ratio for 200 deployed
831 nodes. We observe that DESK and GAF have 30.36~\% and 34.96~\% active nodes for
832 the first fourteen rounds, and the DiLCO and PeCO protocols compete perfectly with
833 only 17.92~\% and 20.16~\% active nodes during the same time interval. As the
834 number of periods increases, the PeCO protocol has a lower number of active nodes in
835 comparison with the three other approaches and exhibits a slow decrease, while
836 keeping a greater coverage ratio as shown in Figure \ref{figure5}.
840 \includegraphics[scale=0.5]{figure6.eps}
841 \caption{Active sensors ratio for 200 deployed nodes.}
845 \subsubsection{Energy Consumption}
847 The effect of the energy consumed by the WSN during the communication,
848 computation, listening, active, and sleep status is studied for different
849 network densities and the four approaches compared. Figures~\ref{figure7}(a)
850 and (b) illustrate the energy consumption for different network sizes and for
851 $Lifetime_{95}$ and $Lifetime_{50}$. The results show that the PeCO protocol is the most
852 competitive from the energy consumption point of view. As shown by both figures,
853 PeCO consumes much less energy than the other methods. One might think that the
854 resolution of the integer program is too costly in energy, but the results show
855 that it is very beneficial to lose a bit of time in the selection of sensors to
856 activate. Indeed the optimization program allows to reduce significantly the
857 number of active sensors and also the energy consumption while keeping a good
858 coverage level. Let us notice that the energy overhead when increasing network
859 size is the lowest with PeCO.
863 \begin{tabular}{@{}cr@{}}
864 \includegraphics[scale=0.5]{figure7a.eps} & \raisebox{2.75cm}{(a)} \\
865 \includegraphics[scale=0.5]{figure7b.eps} & \raisebox{2.75cm}{(b)}
867 \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
871 \subsubsection{Network Lifetime}
873 We observe the superiority of both the PeCO and DiLCO protocols in comparison with
874 the two other approaches in prolonging the network lifetime. In
875 Figures~\ref{figure8}(a) and (b), $Lifetime_{95}$ and $Lifetime_{50}$ are shown for
876 different network sizes. As can be seen in these figures, the lifetime
877 increases with the size of the network, and it is clearly larger for the DiLCO and
878 PeCO protocols. For instance, for a network of 300~sensors and coverage ratio
879 greater than 50\%, we can see on Figure~\ref{figure8}(b) that the lifetime is
880 about twice longer with PeCO compared to the DESK protocol. The performance
881 difference is more obvious in Figure~\ref{figure8}(b) than in
882 Figure~\ref{figure8}(a) because the gain induced by our protocols increases with
883 time, and the lifetime with a coverage over 50\% is far longer than with 95\%.
887 \begin{tabular}{@{}cr@{}}
888 \includegraphics[scale=0.5]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\
889 \includegraphics[scale=0.5]{figure8b.eps} & \raisebox{2.75cm}{(b)}
891 \caption{Network Lifetime for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
895 Figure~\ref{figure9} compares the lifetime coverage of the DiLCO and PeCO protocols
896 for different coverage ratios. We denote by Protocol/50, Protocol/80,
897 Protocol/85, Protocol/90, and Protocol/95 the amount of time during which the
898 network can satisfy an area coverage greater than $50\%$, $80\%$, $85\%$,
899 $90\%$, and $95\%$ respectively, where the term Protocol refers to DiLCO or
900 PeCO. Indeed there are applications that do not require a 100\% coverage of the
901 area to be monitored. PeCO might be an interesting method since it achieves a
902 good balance between a high level coverage ratio and network lifetime. PeCO
903 always outperforms DiLCO for the three lower coverage ratios, moreover the
904 improvements grow with the network size. DiLCO is better for coverage ratios
905 near 100\%, but in that case PeCO is not ineffective for the smallest network
909 \centering \includegraphics[scale=0.55]{figure9.eps}
910 \caption{Network lifetime for different coverage ratios.}
914 \subsubsection{Impact of $\alpha$ and $\beta$ on PeCO's performance}
917 Table~\ref{my-labelx} shows network lifetime results for different values of
918 $\alpha$ and $\beta$, and a network size equal to 200 sensor nodes. On the one
919 hand, the choice of $\beta \gg \alpha$ prevents the overcoverage, and also
920 limits the activation of a large number of sensors, but as $\alpha$ is low, some
921 areas may be poorly covered. This explains the results obtained for
922 $Lifetime_{50}$ with $\beta \gg \alpha$: a large number of periods with low
923 coverage ratio. On the other hand, when we choose $\alpha \gg \beta$, we favor
924 the coverage even if some areas may be overcovered, so a high coverage ratio is
925 reached, but a large number of sensors are activated to achieve this goal.
926 Therefore the network lifetime is reduced. The choice $\alpha=0.6$ and
927 $\beta=0.4$ seems to achieve the best compromise between lifetime and coverage
928 ratio. That explains why we have chosen this setting for the experiments
929 presented in the previous subsections.
931 %As can be seen in Table~\ref{my-labelx}, it is obvious and clear that when $\alpha$ decreased and $\beta$ increased by any step, the network lifetime for $Lifetime_{50}$ increased and the $Lifetime_{95}$ decreased. Therefore, selecting the values of $\alpha$ and $\beta$ depend on the application type used in the sensor nework. In PeCO protocol, $\alpha$ and $\beta$ are chosen based on the largest value of network lifetime for $Lifetime_{95}$.
935 \caption{The impact of $\alpha$ and $\beta$ on PeCO's performance}
937 \begin{tabular}{|c|c|c|c|}
939 $\alpha$ & $\beta$ & $Lifetime_{50}$ & $Lifetime_{95}$ \\ \hline
940 0.0 & 1.0 & 151 & 0 \\ \hline
941 0.1 & 0.9 & 145 & 0 \\ \hline
942 0.2 & 0.8 & 140 & 0 \\ \hline
943 0.3 & 0.7 & 134 & 0 \\ \hline
944 0.4 & 0.6 & 125 & 0 \\ \hline
945 0.5 & 0.5 & 118 & 30 \\ \hline
946 {\bf 0.6} & {\bf 0.4} & {\bf 94} & {\bf 57} \\ \hline
947 0.7 & 0.3 & 97 & 49 \\ \hline
948 0.8 & 0.2 & 90 & 52 \\ \hline
949 0.9 & 0.1 & 77 & 50 \\ \hline
950 1.0 & 0.0 & 60 & 44 \\ \hline
955 \section{Conclusion and Future Works}
956 \label{sec:Conclusion and Future Works}
958 In this paper we have studied the problem of perimeter coverage optimization in
959 WSNs. We have designed a new protocol, called Perimeter-based Coverage
960 Optimization, which schedules nodes' activities (wake up and sleep stages) with
961 the objective of maintaining a good coverage ratio while maximizing the network
962 lifetime. This protocol is applied in a distributed way in regular subregions
963 obtained after partitioning the area of interest in a preliminary step. It works
964 in periods and is based on the resolution of an integer program to select the
965 subset of sensors operating in active status for each period. Our work is
966 original in so far as it proposes for the first time an integer program
967 scheduling the activation of sensors based on their perimeter coverage level,
968 instead of using a set of targets/points to be covered. Several simulations have
969 been carried out to evaluate the proposed protocol. The simulation results show
970 that PeCO is more energy-efficient than other approaches, with respect to
971 lifetime, coverage ratio, active sensors ratio, and energy consumption.
973 We plan to extend our framework so that the schedules are planned for multiple
974 sensing periods. We also want to improve the integer program to take into
975 account heterogeneous sensors from both energy and node characteristics point of
976 views. Finally, it would be interesting to implement the PeCO protocol using a
977 sensor-testbed to evaluate it in real world applications.
979 \subsection*{Acknowledgments}
980 The authors are deeply grateful to the anonymous reviewers for their
981 constructive advice, which improved the technical quality of the paper. As a
982 Ph.D. student, Ali Kadhum Idrees would like to gratefully acknowledge the
983 University of Babylon - Iraq for financial support and Campus France for the
984 received support. This work is also partially funded by the Labex ACTION program
985 (contract ANR-11-LABX-01-01).
987 \bibliographystyle{gENO}
988 \bibliography{biblio} %articleeo
