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39 %\title{Lifetime Coverage Optimization Protocol \\
40 % in Wireless Sensor Networks}
41 \title{Perimeter-based Coverage Optimization to Improve \\
42 Lifetime in Wireless Sensor Networks}
44 \author{Ali Kadhum Idrees,~\IEEEmembership{}
45 Karine Deschinkel,~\IEEEmembership{}
46 Michel Salomon,~\IEEEmembership{}
47 and~Rapha\"el Couturier ~\IEEEmembership{}
48 \thanks{The authors are with FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte,
49 Belfort, France. Email: ali.idness@edu.univ-fcomte.fr, $\lbrace$karine.deschinkel,
50 michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr}}
52 \markboth{IEEE Communications Letters,~Vol.~XX, No.~Y, January 2015}%
53 {Shell \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for Journals}
58 The most important problem in a Wireless Sensor Network (WSN) is to optimize the
59 use of its limited energy provision, so that it can fulfill its monitoring task
60 as long as possible. Among known available approaches that can be used to
61 improve power management, lifetime coverage optimization provides activity
62 scheduling which ensures sensing coverage while minimizing the energy cost. In
63 this paper, we propose such an approach called Perimeter-based Coverage Optimization
64 protocol (PeCO). It is a hybrid of centralized and distributed methods: the
65 region of interest is first subdivided into subregions and our protocol is then
66 distributed among sensor nodes in each subregion.
67 % A sensor node which runs LiCO protocol repeats periodically four stages:
68 %information exchange, leader election, optimization decision, and sensing.
69 %More precisely, the scheduling of nodes' activities (sleep/wake up duty cycles)
70 %is achieved in each subregion by a leader selected after cooperation between
71 %nodes within the same subregion.
72 The novelty of our approach lies essentially in the formulation of a new
73 mathematical optimization model based on the perimeter coverage level to schedule
74 sensors' activities. Extensive simulation experiments have been performed using
75 OMNeT++, the discrete event simulator, to demonstrate that PeCO can
76 offer longer lifetime coverage for WSNs in comparison with some other protocols.
79 % Note that keywords are not normally used for peerreview papers.
81 Wireless Sensor Networks, Area Coverage, Network Lifetime, Optimization, Scheduling.
84 \IEEEpeerreviewmaketitle
86 \section{Introduction}
87 \label{sec:introduction}
89 \noindent The continuous progress in Micro Electro-Mechanical Systems (MEMS) and
90 wireless communication hardware has given rise to the opportunity to use large
91 networks of tiny sensors, called Wireless Sensor Networks
92 (WSN)~\cite{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring
93 tasks. A WSN consists of small low-powered sensors working together by
94 communicating with one another through multi-hop radio communications. Each node
95 can send the data it collects in its environment, thanks to its sensor, to the
96 user by means of sink nodes. The features of a WSN made it suitable for a wide
97 range of application in areas such as business, environment, health, industry,
98 military, and so on~\cite{yick2008wireless}. Typically, a sensor node contains
99 three main components~\cite{anastasi2009energy}: a sensing unit able to measure
100 physical, chemical, or biological phenomena observed in the environment; a
101 processing unit which will process and store the collected measurements; a radio
102 communication unit for data transmission and receiving.
104 The energy needed by an active sensor node to perform sensing, processing, and
105 communication is supplied by a power supply which is a battery. This battery has
106 a limited energy provision and it may be unsuitable or impossible to replace or
107 recharge it in most applications. Therefore it is necessary to deploy WSN with
108 high density in order to increase reliability and to exploit node redundancy
109 thanks to energy-efficient activity scheduling approaches. Indeed, the overlap
110 of sensing areas can be exploited to schedule alternatively some sensors in a
111 low power sleep mode and thus save energy. Overall, the main question that must
112 be answered is: how to extend the lifetime coverage of a WSN as long as possible
113 while ensuring a high level of coverage? These past few years many
114 energy-efficient mechanisms have been suggested to retain energy and extend the
115 lifetime of the WSNs~\cite{rault2014energy}.
117 %The sensor system ought to have a lifetime long enough to satisfy the application necessities. The lifetime coverage maximization is one of the fundamental requirements of any area coverage protocol in WSN implementation~\cite{nayak2010wireless}. In order to increase the reliability and prevent the possession of coverage holes (some parts are not covered in the area of interest) in the WSN, it is necessary to deploy the WSN with high density so as to increase the reliability and to exploit redundancy by using energy-efficient activity scheduling approaches.
119 %From a certain standpoint, the high coverage ratio is required by many applications such as military and health-care. Therefore, a suitable number of sensors are being chosen so as to cover the area of interest, is the first challenge. Meanwhile, the sensor nodes have a limited capabilities in terms of memory, processing, communication, and battery power being the most important and critical one. So, the main question is: how to extend the lifetime coverage of WSN as long time as possible?. There are many energy-efficient mechanisms have been suggested to retain energy and extend the lifetime of the WSNs~\cite{rault2014energy}.
121 %\uppercase{\textbf{Our contributions.}}
123 This paper makes the following contributions.
125 \item We have devised a framework to schedule nodes to be activated alternatively such
126 that the network lifetime is prolonged while ensuring that a certain level of
127 coverage is preserved. A key idea in our framework is to exploit spatial and
128 temporal subdivision. On the one hand, the area of interest is divided into
129 several smaller subregions and, on the other hand, the time line is divided into
130 periods of equal length. In each subregion the sensor nodes will cooperatively
131 choose a leader which will schedule nodes' activities, and this grouping of
132 sensors is similar to typical cluster architecture.
133 \item We have proposed a new mathematical optimization model. Instead of trying to
134 cover a set of specified points/targets as in most of the methods proposed in
135 the literature, we formulate an integer program based on perimeter coverage of
136 each sensor. The model involves integer variables to capture the deviations
137 between the actual level of coverage and the required level. Hence, an
138 optimal scheduling will be obtained by minimizing a weighted sum of these
140 \item We have conducted extensive simulation experiments, using the discrete event
141 simulator OMNeT++, to demonstrate the efficiency of our protocol. We have compared
142 our PeCO protocol to two approaches found in the literature:
143 DESK~\cite{ChinhVu} and GAF~\cite{xu2001geography}, and also to our previous
144 work published in~\cite{Idrees2} which is based on another optimization model
145 for sensor scheduling.
148 %Two combined integrated energy-efficient techniques have been used by PeCO protocol in order to maximize the lifetime coverage in WSN: the first, by dividing the area of interest into several smaller subregions based on divide-and-conquer method and then one leader elected for each subregion in an independent, distributed, and simultaneous way by the cooperation among the sensor nodes within each subregion, and this similar to cluster architecture;
149 % the second, activity scheduling based new optimization model has been used to provide the optimal cover set that will take the mission of sensing during current period. This optimization algorithm is based on a perimeter-coverage model so as to optimize the shared perimeter among the sensors in each subregion, and this represents as a energu-efficient control topology mechanism in WSN.
151 The rest of the paper is organized as follows. In the next section we review
152 some related work in the field. Section~\ref{sec:The PeCO Protocol Description}
153 is devoted to the PeCO protocol description and Section~\ref{cp} focuses on the
154 coverage model formulation which is used to schedule the activation of sensor
155 nodes. Section~\ref{sec:Simulation Results and Analysis} presents simulations
156 results and discusses the comparison with other approaches. Finally, concluding
157 remarks are drawn and some suggestions are given for future works in
158 Section~\ref{sec:Conclusion and Future Works}.
160 % that show that our protocol outperforms others protocols.
161 \section{Related Literature}
162 \label{sec:Literature Review}
164 \noindent In this section, we summarize some related works regarding the
165 coverage problem and distinguish our PeCO protocol from the works presented in
168 The most discussed coverage problems in literature can be classified in three
169 categories~\cite{li2013survey} according to their respective monitoring
170 objective. Hence, area coverage \cite{Misra} means that every point inside a
171 fixed area must be monitored, while target coverage~\cite{yang2014novel} refers
172 to the objective of coverage for a finite number of discrete points called
173 targets, and barrier coverage~\cite{HeShibo}\cite{kim2013maximum} focuses on
174 preventing intruders from entering into the region of interest. In
175 \cite{Deng2012} authors transform the area coverage problem into the target
176 coverage one taking into account the intersection points among disks of sensors
177 nodes or between disk of sensor nodes and boundaries. In
178 \cite{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of
179 sensors are sufficiently covered it will be the case for the whole area. They
180 provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of
181 each sensor, where $d$ denotes the maximum number of sensors that are
182 neighbors to a sensor and $n$ is the total number of sensors in the
183 network. {\it In PeCO protocol, instead of determining the level of coverage of
184 a set of discrete points, our optimization model is based on checking the
185 perimeter-coverage of each sensor to activate a minimal number of sensors.}
187 The major approach to extend network lifetime while preserving coverage is to
188 divide/organize the sensors into a suitable number of set covers (disjoint or
189 non-disjoint), where each set completely covers a region of interest, and to
190 activate these set covers successively. The network activity can be planned in
191 advance and scheduled for the entire network lifetime or organized in periods,
192 and the set of active sensor nodes is decided at the beginning of each period
193 \cite{ling2009energy}. Active node selection is determined based on the problem
194 requirements (e.g. area monitoring, connectivity, or power efficiency). For
195 instance, Jaggi {\em et al.}~\cite{jaggi2006} address the problem of maximizing
196 the lifetime by dividing sensors into the maximum number of disjoint subsets
197 such that each subset can ensure both coverage and connectivity. A greedy
198 algorithm is applied once to solve this problem and the computed sets are
199 activated in succession to achieve the desired network lifetime. Vu
200 \cite{chin2007}, Padmatvathy {\em et al.}~\cite{pc10}, propose algorithms
201 working in a periodic fashion where a cover set is computed at the beginning of
202 each period. {\it Motivated by these works, PeCO protocol works in periods,
203 where each period contains a preliminary phase for information exchange and
204 decisions, followed by a sensing phase where one cover set is in charge of the
207 Various centralized and distributed approaches, or even a mixing of these two
208 concepts, have been proposed to extend the network lifetime. In distributed
209 algorithms~\cite{yangnovel,ChinhVu,qu2013distributed} each sensor decides of its
210 own activity scheduling after an information exchange with its neighbors. The
211 main interest of such an approach is to avoid long range communications and thus
212 to reduce the energy dedicated to the communications. Unfortunately, since each
213 node has only information on its immediate neighbors (usually the one-hop ones)
214 it may make a bad decision leading to a global suboptimal solution. Conversely,
216 algorithms~\cite{cardei2005improving,zorbas2010solving,pujari2011high} always
217 provide nearly or close to optimal solution since the algorithm has a global
218 view of the whole network. The disadvantage of a centralized method is obviously
219 its high cost in communications needed to transmit to a single node, the base
220 station which will globally schedule nodes' activities, data from all the other
221 sensor nodes in the area. The price in communications can be huge since
222 long range communications will be needed. In fact the larger the WNS is, the
223 higher the communication and thus the energy cost are. {\it In order to be
224 suitable for large-scale networks, in the PeCO protocol, the area of interest
225 is divided into several smaller subregions, and in each one, a node called the
226 leader is in charge of selecting the active sensors for the current
227 period. Thus our protocol is scalable and is a globally distributed method,
228 whereas it is centralized in each subregion.}
230 Various coverage scheduling algorithms have been developed these past few years.
231 Many of them, dealing with the maximization of the number of cover sets, are
232 heuristics. These heuristics involve the construction of a cover set by
233 including in priority the sensor nodes which cover critical targets, that is to
234 say targets that are covered by the smallest number of sensors
235 \cite{berman04,zorbas2010solving}. Other approaches are based on mathematical
236 programming formulations~\cite{cardei2005energy,5714480,pujari2011high,Yang2014}
237 and dedicated techniques (solving with a branch-and-bound algorithm available in
238 optimization solver). The problem is formulated as an optimization problem
239 (maximization of the lifetime or number of cover sets) under target coverage and
240 energy constraints. Column generation techniques, well-known and widely
241 practiced techniques for solving linear programs with too many variables, have
243 used~\cite{castano2013column,rossi2012exact,deschinkel2012column}. {\it In the PeCO
244 protocol, each leader, in charge of a subregion, solves an integer program
245 which has a twofold objective: minimize the overcoverage and the undercoverage
246 of the perimeter of each sensor.}
248 %\noindent Recently, the coverage problem has been received a high attention, which concentrates on how the physical space could be well monitored after the deployment. Coverage is one of the Quality of Service (QoS) parameters in WSNs, which is highly concerned with power depletion~\cite{zhu2012survey}. Most of the works about the coverage protocols have been suggested in the literature focused on three types of the coverage in WSNs~\cite{mulligan2010coverage}: the first, area coverage means that each point in the area of interest within the sensing range of at least one sensor node; the second, target coverage in which a fixed set of targets need to be monitored; the third, barrier coverage refers to detect the intruders crossing a boundary of WSN. The work in this paper emphasized on the area coverage, so, some area coverage protocols have been reviewed in this section, and the shortcomings of reviewed approaches are being summarized.
250 %The problem of k-coverage in WSNs was addressed~\cite{ammari2012centralized}. It mathematically formulated and the spacial sensor density for full k-coverage determined, where the relation between the communication range and the sensing range constructed by this work to retain the k-coverage and connectivity in WSN. After that, a four configuration protocols have proposed for treating the k-coverage in WSNs.
252 %In~\cite{rebai2014branch}, the problem of full grid coverage is formulated using two integer linear programming models: the first, a model that takes into account only the overall coverage constraint; the second, both the connectivity and the full grid coverage constraints have taken into consideration. This work did not take into account the energy constraint.
254 %Li et al.~\cite{li2011transforming} presented a framework to convert any complete coverage problem to a partial coverage one with any coverage ratio by means of executing a complete coverage algorithm to find a full coverage sets with virtual radii and transforming the coverage sets to a partial coverage sets by adjusting sensing radii. The properties of the original algorithms can be maintained by this framework and the transformation process has a low execution time.
256 %The authors in~\cite{liu2014generalized} explained that in some applications of WSNs such as structural health monitoring (SHM) and volcano monitoring, the traditional coverage model which is a geographic area defined for individual sensors is not always valid. For this reason, they define a generalized coverage model, which is not need to have the coverage area of individual nodes, but only based on a function to determine whether a set of
257 %sensor nodes is capable of satisfy the requested monitoring task for a certain area. They have proposed two approaches to divide the deployed nodes into suitable cover sets, which can be used to prolong the network lifetime.
259 %The work in~\cite{wang2010preserving} addressed the target area coverage problem by proposing a geometric-based activity scheduling scheme, named GAS, to fully cover the target area in WSNs. The authors deals with small area (target area coverage), which can be monitored by a single sensor instead of area coverage, which focuses on a large area that should be monitored by many sensors cooperatively. They explained that GAS is capable to monitor the target area by using a few sensors as possible and it can produce as many cover sets as possible.
261 %Cho et al.~\cite{cho2007distributed} proposed a distributed node scheduling protocol, which can retain sensing coverage needed by applications
262 %and increase network lifetime via putting in sleep mode some redundant nodes. In this work, the effective sensing area (ESA) concept of a sensor node is used, which refers to the sensing area that is not overlapping with another sensor's sensing area. A sensor node and by compute it's ESA can be determine whether it will be active or sleep. The suggested work permits to sensor nodes to be in sleep mode opportunistically whilst fulfill the needed sensing coverage.
264 %In~\cite{quang2008algorithm}, the authors defined a maximum sensing coverage region problem (MSCR) in WSNs and then proposed an algorithm to solve it. The
265 %maximum observed area fully covered by a minimum active sensors. In this work, the major property is to getting rid from the redundant sensors in high-density WSNs and putting them in sleep mode, and choosing a smaller number of active sensors so as to be sure that the full area is k-covered, and all events appeared in that area can be precisely and timely detected. This algorithm minimized the total energy consumption and increased the lifetime.
267 %A novel method to divide the sensors in the WSN, called node coverage grouping (NCG) suggested~\cite{lin2010partitioning}. The sensors in the connectivity group are within sensing range of each other, and the data collected by them in the same group are supposed to be similar. They are proved that dividing n sensors via NCG into connectivity groups is a NP-hard problem. So, a heuristic algorithm of NCG with time complexity of $O(n^3)$ is proposed.
268 %For some applications, such as monitoring an ecosystem with extremely diversified environment, It might be premature assumption that sensors near to each other sense similar data.
270 %In~\cite{zaidi2009minimum}, the problem of minimum cost coverage in which full coverage is performed by using the minimum number of sensors for an arbitrary geometric shape region is addressed. a geometric solution to the minimum cost coverage problem under a deterministic deployment is proposed. The probabilistic coverage solution which provides a relationship between the probability of coverage and the number of randomly deployed sensors in an arbitrarily-shaped region is suggested. The authors are clarified that with a random deployment about seven times more nodes are required to supply full coverage.
272 %A graph theoretical framework for connectivity-based coverage with configurable coverage granularity was proposed~\cite{dong2012distributed}. A new coverage criterion and scheduling approach is proposed based on cycle partition. This method is capable of build a sparse coverage set in distributed way by means of only connectivity information. This work considers only the communication range of the sensor is smaller two times the sensing range of sensor.
274 %Liu et al.~\cite{liu2010energy} formulated maximum disjoint sets problem for retaining coverage and connectivity in WSN. Two algorithms are proposed for solving this problem, heuristic algorithm and network flow algorithm. This work did not take into account the sensor node failure, which is an unpredictable event because the two solutions are full centralized algorithms.
276 %The work that presented in~\cite{aslanyan2013optimal} solved the coverage and connectivity problem in sensor networks in
277 %an integrated way. The network lifetime is divided in a fixed number of rounds. A coverage bitmap of sensors of the domain has been generated in each round and based on this bitmap, it has been decided which sensors
278 %stay active or turn it to sleep. They checked the connection of the graph via laplacian of adjancy graph of active sensors in each round. the generation of coverage bitmap by using Minkowski technique, the network is able to providing the desired ratio of coverage. They have been defined the connected coverage problem as an optimization problem and a centralized genetic algorithm is used to find the solution.
280 %Several algorithms to retain the coverage and maximize the network lifetime were proposed in~\cite{cardei2006energy,wang2011coverage}.
282 %\uppercase{\textbf{shortcomings}}. In spite of many energy-efficient protocols for maintaining the coverage and improving the network lifetime in WSNs were proposed, non of them ensure the coverage for the sensing field with optimal minimum number of active sensor nodes, and for a long time as possible. For example, in a full centralized algorithms, an optimal solutions can be given by using optimization approaches, but in the same time, a high energy is consumed for the execution time of the algorithm and the communications among the sensors in the sensing field, so, the full centralized approaches are not good candidate to use it especially in large WSNs. Whilst, a full distributed algorithms can not give optimal solutions because this algorithms use only local information of the neighboring sensors, but in the same time, the energy consumption during the communications and executing the algorithm is highly lower. Whatever the case, this would result in a shorter lifetime coverage in WSNs.
284 %\uppercase{\textbf{Our Protocol}}. In this paper, a Lifetime Coverage Optimization Protocol, called (PeCO) in WSNs is suggested. The sensing field is divided into smaller subregions by means of divide-and-conquer method, and a PeCO protocol is distributed in each sensor in the subregion. The network lifetime in each subregion is divided into periods, each period includes 4 stages: Information Exchange, Leader election, decision based activity scheduling optimization, and sensing. The leaders are elected in an independent, asynchronous, and distributed way in all the subregions of the WSN. After that, energy-efficient activity scheduling mechanism based new optimization model is performed by each leader in the subregions. This optimization model is based on the perimeter coverage model in order to producing the optimal cover set of active sensors, which are taken the responsibility of sensing during the current period. PeCO protocol merges between two energy efficient mechanisms, which are used the main advantages of the centralized and distributed approaches and avoids the most of their disadvantages.
286 \section{ The PeCO Protocol Description}
287 \label{sec:The PeCO Protocol Description}
289 \noindent In this section, we describe in details our Perimeter-based Coverage
290 Optimization protocol. First we present the assumptions we made and the models
291 we considered (in particular the perimeter coverage one), second we describe the
292 background idea of our protocol, and third we give the outline of the algorithm
293 executed by each node.
295 % It is based on two efficient-energy mechanisms: the first, is partitioning the sensing field into smaller subregions, and one leader is elected for each subregion; the second, a sensor activity scheduling based new optimization model so as to produce the optimal cover set of active sensors for the sensing stage during the period. Obviously, these two mechanisms can be contribute in extend the network lifetime coverage efficiently.
296 %Before proceeding in the presentation of the main ideas of the protocol, we will briefly describe the perimeter coverage model and give some necessary assumptions and definitions.
298 \subsection{Assumptions and Models}
301 \noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly
302 distributed in a bounded sensor field is considered. The wireless sensors are
303 deployed in high density to ensure initially a high coverage ratio of the area
304 of interest. We assume that all the sensor nodes are homogeneous in terms of
305 communication, sensing, and processing capabilities and heterogeneous from
306 the energy provision point of view. The location information is available to a
307 sensor node either through hardware such as embedded GPS or location discovery
308 algorithms. We assume that each sensor node can directly transmit its
309 measurements to a mobile sink node. For example, a sink can be an unmanned
310 aerial vehicle (UAV) flying regularly over the sensor field to collect
311 measurements from sensor nodes. A mobile sink node collects the measurements and
312 transmits them to the base station. We consider a Boolean disk coverage model,
313 which is the most widely used sensor coverage model in the literature, and all
314 sensor nodes have a constant sensing range $R_s$. Thus, all the space points
315 within a disk centered at a sensor with a radius equal to the sensing range are
316 said to be covered by this sensor. We also assume that the communication range
317 $R_c$ satisfies $R_c \geq 2 \cdot R_s$. In fact, Zhang and Zhou~\cite{Zhang05}
318 proved that if the transmission range fulfills the previous hypothesis, the
319 complete coverage of a convex area implies connectivity among active nodes.
321 The PeCO protocol uses the same perimeter-coverage model as Huang and
322 Tseng in~\cite{huang2005coverage}. It can be expressed as follows: a sensor is
323 said to be perimeter covered if all the points on its perimeter are covered by
324 at least one sensor other than itself. They proved that a network area is
325 $k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).
326 %According to this model, we named the intersections among the sensor nodes in the sensing field as intersection points. Instead of working with the coverage area, we consider for each sensor a set of intersection points which are determined by using perimeter-coverage model.
327 Figure~\ref{pcm2sensors}(a) shows the coverage of sensor node~$0$. On this
328 figure, we can see that sensor~$0$ has nine neighbors and we have reported on
329 its perimeter (the perimeter of the disk covered by the sensor) for each
330 neighbor the two points resulting from the intersection of the two sensing
331 areas. These points are denoted for neighbor~$i$ by $iL$ and $iR$, respectively
332 for left and right from a neighboing point of view. The resulting couples of
333 intersection points subdivide the perimeter of sensor~$0$ into portions called
338 \begin{tabular}{@{}cr@{}}
339 \includegraphics[width=75mm]{pcm.jpg} & \raisebox{3.25cm}{(a)} \\
340 \includegraphics[width=75mm]{twosensors.jpg} & \raisebox{2.75cm}{(b)}
342 \caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of
343 $u$'s perimeter covered by $v$.}
347 Figure~\ref{pcm2sensors}(b) describes the geometric information used to find the
348 locations of the left and right points of an arc on the perimeter of a sensor
349 node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the
350 west side of sensor~$u$, with the following respective coordinates in the
351 sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can
352 compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert
353 u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is
354 obtained through the formula: $$\alpha = \arccos \left(\dfrac{Dist(u,v)}{2R_s}
355 \right).$$ The arc on the perimeter of~$u$ defined by the angular interval $[\pi
356 - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$.
358 Every couple of intersection points is placed on the angular interval $[0,2\pi]$
359 in a counterclockwise manner, leading to a partitioning of the interval.
360 Figure~\ref{pcm2sensors}(a) illustrates the arcs for the nine neighbors of
361 sensor $0$ and Figure~\ref{expcm} gives the position of the corresponding arcs
362 in the interval $[0,2\pi]$. More precisely, we can see that the points are
363 ordered according to the measures of the angles defined by their respective
364 positions. The intersection points are then visited one after another, starting
365 from the first intersection point after point~zero, and the maximum level of
366 coverage is determined for each interval defined by two successive points. The
367 maximum level of coverage is equal to the number of overlapping arcs. For
369 between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$
370 (the value is highlighted in yellow at the bottom of Figure~\ref{expcm}), which
371 means that at most 2~neighbors can cover the perimeter in addition to node $0$.
372 Table~\ref{my-label} summarizes for each coverage interval the maximum level of
373 coverage and the sensor nodes covering the perimeter. The example discussed
374 above is thus given by the sixth line of the table.
376 %The points reported on the line segment $[0,2\pi]$ separates it in intervals as shown in figure~\ref{expcm}. For example, for each neighboring sensor of sensor 0, place the points $\alpha^ 1_L$, $\alpha^ 1_R$, $\alpha^ 2_L$, $\alpha^ 2_R$, $\alpha^ 3_L$, $\alpha^ 3_R$, $\alpha^ 4_L$, $\alpha^ 4_R$, $\alpha^ 5_L$, $\alpha^ 5_R$, $\alpha^ 6_L$, $\alpha^ 6_R$, $\alpha^ 7_L$, $\alpha^ 7_R$, $\alpha^ 8_L$, $\alpha^ 8_R$, $\alpha^ 9_L$, and $\alpha^ 9_R$; on the line segment $[0,2\pi]$, and then sort all these points in an ascending order into a list. Traverse the line segment $[0,2\pi]$ by visiting each point in the sorted list from left to right and determine the coverage level of each interval of the sensor 0 (see figure \ref{expcm}). For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. Table~\ref{my-label} summarizes the level of coverage for each interval and the sensors involved in for sensor node 0 in figure~\ref{pcm2sensors}(a).
377 % to determine the level of the perimeter coverage for each left and right point of a segment.
381 \includegraphics[width=127.5mm]{expcm2.jpg}
382 \caption{Maximum coverage levels for perimeter of sensor node $0$.}
386 %For example, consider the sensor node $0$ in figure~\ref{pcmfig}, which has 9 neighbors. Figure~\ref{expcm} shows the perimeter coverage level for all left and right points of a segment that covered by a neighboring sensor nodes. Based on the figure~\ref{expcm}, the set of sensors for each left and right point of the segments illustrated in figure~\ref{ex2pcm} for the sensor node 0.
392 \includegraphics[width=90mm]{ex2pcm.jpg}
393 \caption{Coverage intervals and contributing sensors for sensor node 0.}
400 \caption{Coverage intervals and contributing sensors for sensor node 0.}
401 \begin{tabular}{|c|c|c|c|c|c|c|c|c|}
403 \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
404 0.0291 & 1L & 2L & 4 & 0 & 1 & 3 & 4 & \\ \hline
405 0.104 & 2L & 3R & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline
406 0.3168 & 3R & 4R & 4 & 0 & 1 & 4 & 2 & \\ \hline
407 0.6752 & 4R & 1R & 3 & 0 & 1 & 2 & & \\ \hline
408 1.8127 & 1R & 5L & 2 & 0 & 2 & & & \\ \hline
409 1.9228 & 5L & 6L & 3 & 0 & 2 & 5 & & \\ \hline
410 2.3959 & 6L & 2R & 4 & 0 & 2 & 5 & 6 & \\ \hline
411 2.4258 & 2R & 7L & 3 & 0 & 5 & 6 & & \\ \hline
412 2.7868 & 7L & 8L & 4 & 0 & 5 & 6 & 7 & \\ \hline
413 2.8358 & 8L & 5R & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline
414 2.9184 & 5R & 7R & 4 & 0 & 6 & 7 & 8 & \\ \hline
415 3.3301 & 7R & 9R & 3 & 0 & 6 & 8 & & \\ \hline
416 3.9464 & 9R & 6R & 4 & 0 & 6 & 8 & 9 & \\ \hline
417 4.767 & 6R & 3L & 3 & 0 & 8 & 9 & & \\ \hline
418 4.8425 & 3L & 8R & 4 & 0 & 3 & 8 & 9 & \\ \hline
419 4.9072 & 8R & 4L & 3 & 0 & 3 & 9 & & \\ \hline
420 5.3804 & 4L & 9R & 4 & 0 & 3 & 4 & 9 & \\ \hline
421 5.9157 & 9R & 1L & 3 & 0 & 3 & 4 & & \\ \hline
428 %The optimization algorithm that used by PeCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1.
430 In the PeCO protocol, the scheduling of the sensor nodes' activities is formulated with an
431 integer program based on coverage intervals. The formulation of the coverage
432 optimization problem is detailed in~section~\ref{cp}. Note that when a sensor
433 node has a part of its sensing range outside the WSN sensing field, as in
434 Figure~\ref{ex4pcm}, the maximum coverage level for this arc is set to $\infty$
435 and the corresponding interval will not be taken into account by the
436 optimization algorithm.
440 \includegraphics[width=62.5mm]{ex4pcm.jpg}
441 \caption{Sensing range outside the WSN's area of interest.}
444 %Figure~\ref{ex5pcm} gives an example to compute the perimeter coverage levels for the left and right points of the segments for a sensor node $0$, which has a part of its sensing range exceeding the border of the sensing field of WSN, and it has a six neighbors. In figure~\ref{ex5pcm}, the sensor node $0$ has two segments outside the border of the network sensing field, so the left and right points of the two segments called $-1L$, $-1R$, $-2L$, and $-2R$.
447 %\includegraphics[width=75mm]{ex5pcm.jpg}
448 %\caption{Coverage intervals and contributing sensors for sensor node 0 having a part of its sensing range outside the border.}
452 \subsection{The Main Idea}
454 \noindent The WSN area of interest is, in a first step, divided into regular
455 homogeneous subregions using a divide-and-conquer algorithm. In a second step
456 our protocol will be executed in a distributed way in each subregion
457 simultaneously to schedule nodes' activities for one sensing period.
459 As shown in Figure~\ref{fig2}, node activity scheduling is produced by our
460 protocol in a periodic manner. Each period is divided into 4 stages: Information
461 (INFO) Exchange, Leader Election, Decision (the result of an optimization
462 problem), and Sensing. For each period there is exactly one set cover
463 responsible for the sensing task. Protocols based on a periodic scheme, like
464 PeCO, are more robust against an unexpected node failure. On the one hand, if
465 a node failure is discovered before taking the decision, the corresponding sensor
466 node will not be considered by the optimization algorithm. On the other
467 hand, if the sensor failure happens after the decision, the sensing task of the
468 network will be temporarily affected: only during the period of sensing until a
469 new period starts, since a new set cover will take charge of the sensing task in
470 the next period. The energy consumption and some other constraints can easily be
471 taken into account since the sensors can update and then exchange their
472 information (including their residual energy) at the beginning of each period.
473 However, the pre-sensing phases (INFO Exchange, Leader Election, and Decision)
474 are energy consuming, even for nodes that will not join the set cover to monitor
479 \includegraphics[width=80mm]{Model.pdf}
480 \caption{PeCO protocol.}
484 We define two types of packets to be used by PeCO protocol:
485 %\begin{enumerate}[(a)]
487 \item INFO packet: sent by each sensor node to all the nodes inside a same
488 subregion for information exchange.
489 \item ActiveSleep packet: sent by the leader to all the nodes in its subregion
490 to transmit to them their respective status (stay Active or go Sleep) during
495 Five status are possible for a sensor node in the network:
496 %\begin{enumerate}[(a)]
498 \item LISTENING: waits for a decision (to be active or not);
499 \item COMPUTATION: executes the optimization algorithm as leader to
500 determine the activities scheduling;
501 \item ACTIVE: node is sensing;
502 \item SLEEP: node is turned off;
503 \item COMMUNICATION: transmits or receives packets.
506 %Below, we describe each phase in more details.
508 \subsection{PeCO Protocol Algorithm}
510 \noindent The pseudocode implementing the protocol on a node is given below.
511 More precisely, Algorithm~\ref{alg:PeCO} gives a brief description of the
512 protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
514 \begin{algorithm}[h!]
515 % \KwIn{all the parameters related to information exchange}
516 % \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
518 %\emph{Initialize the sensor node and determine it's position and subregion} \;
520 \If{ $RE_k \geq E_{th}$ }{
521 \emph{$s_k.status$ = COMMUNICATION}\;
522 \emph{Send $INFO()$ packet to other nodes in subregion}\;
523 \emph{Wait $INFO()$ packet from other nodes in subregion}\;
524 \emph{Update K.CurrentSize}\;
525 \emph{LeaderID = Leader election}\;
526 \If{$ s_k.ID = LeaderID $}{
527 \emph{$s_k.status$ = COMPUTATION}\;
529 \If{$ s_k.ID $ is Not previously selected as a Leader }{
530 \emph{ Execute the perimeter coverage model}\;
531 % \emph{ Determine the segment points using perimeter coverage model}\;
534 \If{$ (s_k.ID $ is the same Previous Leader) And (K.CurrentSize = K.PreviousSize)}{
536 \emph{ Use the same previous cover set for current sensing stage}\;
539 \emph{Update $a^j_{ik}$; prepare data for IP~Algorithm}\;
540 \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$)}\;
541 \emph{K.PreviousSize = K.CurrentSize}\;
544 \emph{$s_k.status$ = COMMUNICATION}\;
545 \emph{Send $ActiveSleep()$ to each node $l$ in subregion}\;
546 \emph{Update $RE_k $}\;
549 \emph{$s_k.status$ = LISTENING}\;
550 \emph{Wait $ActiveSleep()$ packet from the Leader}\;
551 \emph{Update $RE_k $}\;
554 \Else { Exclude $s_k$ from entering in the current sensing stage}
555 \caption{PeCO($s_k$)}
559 In this algorithm, K.CurrentSize and K.PreviousSize respectively represent the
560 current number and the previous number of living nodes in the subnetwork of the
561 subregion. Initially, the sensor node checks its remaining energy $RE_k$, which
562 must be greater than a threshold $E_{th}$ in order to participate in the current
563 period. Each sensor node determines its position and its subregion using an
564 embedded GPS or a location discovery algorithm. After that, all the sensors
565 collect position coordinates, remaining energy, sensor node ID, and the number
566 of their one-hop live neighbors during the information exchange. The sensors
567 inside a same region cooperate to elect a leader. The selection criteria for the
568 leader, in order of priority, are: larger numbers of neighbors, larger remaining
569 energy, and then in case of equality, larger index. Once chosen, the leader
570 collects information to formulate and solve the integer program which allows to
571 construct the set of active sensors in the sensing stage.
573 %After the cooperation among the sensor nodes in the same subregion, the leader will be elected in distributed way, where each sensor node and based on it's information decide who is the leader. The selection criteria for the leader in order of priority are: larger number of neighbors, larger remaining energy, and then in case of equality, larger index. Thereafter, if the sensor node is leader, it will execute the perimeter-coverage model for each sensor in the subregion in order to determine the segment points which would be used in the next stage by the optimization algorithm of the PeCO protocol. Every sensor node is selected as a leader, it is executed the perimeter coverage model only one time during it's life in the network.
575 % The leader has the responsibility of applying the integer program algorithm (see section~\ref{cp}), which provides a set of sensors planned to be active in the sensing stage. As leader, it will send an Active-Sleep packet to each sensor in the same subregion to inform it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing stage.
577 \section{Perimeter-based Coverage Problem Formulation}
580 \noindent In this section, the coverage model is mathematically formulated. We
581 start with a description of the notations that will be used throughout the
584 First, we have the following sets:
586 \item $S$ represents the set of WSN sensor nodes;
587 \item $A \subseteq S $ is the subset of alive sensors;
588 \item $I_j$ designates the set of coverage intervals (CI) obtained for
591 $I_j$ refers to the set of coverage intervals which have been defined according
592 to the method introduced in subsection~\ref{CI}. For a coverage interval $i$,
593 let $a^j_{ik}$ denotes the indicator function of whether sensor~$k$ is involved
594 in coverage interval~$i$ of sensor~$j$, that is:
598 1 & \mbox{if sensor $k$ is involved in the } \\
599 & \mbox{coverage interval $i$ of sensor $j$}, \\
600 0 & \mbox{otherwise.}\\
605 Note that $a^k_{ik}=1$ by definition of the interval.
606 %, where the objective is to find the maximum number of non-disjoint sets of sensor nodes such that each set cover can assure the coverage for the whole region so as to extend the network lifetime in WSN. Our model uses the PCL~\cite{huang2005coverage} in order to optimize the lifetime coverage in each subregion.
607 %We defined some parameters, which are related to our optimization model. In our model, we consider binary variables $X_{k}$, which determine the activation of sensor $k$ in the sensing round $k$. .
608 Second, we define several binary and integer variables. Hence, each binary
609 variable $X_{k}$ determines the activation of sensor $k$ in the sensing phase
610 ($X_k=1$ if the sensor $k$ is active or 0 otherwise). $M^j_i$ is an integer
611 variable which measures the undercoverage for the coverage interval $i$
612 corresponding to sensor~$j$. In the same way, the overcoverage for the same
613 coverage interval is given by the variable $V^j_i$.
615 If we decide to sustain a level of coverage equal to $l$ all along the perimeter
616 of sensor $j$, we have to ensure that at least $l$ sensors involved in each
617 coverage interval $i \in I_j$ of sensor $j$ are active. According to the
618 previous notations, the number of active sensors in the coverage interval $i$ of
619 sensor $j$ is given by $\sum_{k \in A} a^j_{ik} X_k$. To extend the network
620 lifetime, the objective is to activate a minimal number of sensors in each
621 period to ensure the desired coverage level. As the number of alive sensors
622 decreases, it becomes impossible to reach the desired level of coverage for all
623 coverage intervals. Therefore we use variables $M^j_i$ and $V^j_i$ as a measure
624 of the deviation between the desired number of active sensors in a coverage
625 interval and the effective number. And we try to minimize these deviations,
626 first to force the activation of a minimal number of sensors to ensure the
627 desired coverage level, and if the desired level cannot be completely satisfied,
628 to reach a coverage level as close as possible to the desired one.
630 %A system of linear constraints is imposed to attempt to keep the coverage level in each coverage interval to within specified PCL. Since it is physically impossible to satisfy all constraints simultaneously, each constraint uses a variable to either record when the coverage level is achieved, or to record the deviation from the desired coverage level. These additional variables are embedded into an objective function to be minimized.
632 %\noindent In this paper, let us define some parameters, which are used in our protocol.
633 %the set of segment points is denoted by $I$, the set of all sensors in the network by $J$, and the set of alive sensors within $J$ by $K$.
636 %\noindent \begin{equation}
639 % 1& \mbox{if sensor $k$ is active,} \\
640 % 0 & \mbox{otherwise.}\\
646 %\noindent $M^j_i (undercoverage): $ integer value $\in \mathbb{N}$ for segment point $i$ of sensor $j$.
648 %\noindent $V^j_i (overcoverage): $ integer value $\in \mathbb{N}$ for segment point $i$ of sensor $j$.
650 Our coverage optimization problem can then be mathematically expressed as follows:
652 \begin{equation} %\label{eq:ip2r}
655 \min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
656 \textrm{subject to :}&\\
657 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in S\\
659 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in S\\
661 % \Theta_{p}\in \mathbb{N}, &\forall p \in P\\
662 % U_{p} \in \{0,1\}, &\forall p \in P\\
663 X_{k} \in \{0,1\}, \forall k \in A
668 $\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the
669 relative importance of satisfying the associated level of coverage. For example,
670 weights associated with coverage intervals of a specified part of a region may
671 be given by a relatively larger magnitude than weights associated with another
672 region. This kind of integer program is inspired from the model developed for
673 brachytherapy treatment planning for optimizing dose distribution
674 \cite{0031-9155-44-1-012}. The integer program must be solved by the leader in
675 each subregion at the beginning of each sensing phase, whenever the environment
676 has changed (new leader, death of some sensors). Note that the number of
677 constraints in the model is constant (constraints of coverage expressed for all
678 sensors), whereas the number of variables $X_k$ decreases over periods, since we
679 consider only alive sensors (sensors with enough energy to be alive during one
680 sensing phase) in the model.
682 \section{Performance Evaluation and Analysis}
683 \label{sec:Simulation Results and Analysis}
684 %\noindent \subsection{Simulation Framework}
686 \subsection{Simulation Settings}
689 The WSN area of interest is supposed to be divided into 16~regular subregions
690 and we use the same energy consumption than in our previous work~\cite{Idrees2}.
691 Table~\ref{table3} gives the chosen parameters settings.
694 \caption{Relevant parameters for network initialization.}
697 % used for centering table
699 % centered columns (4 columns)
701 Parameter & Value \\ [0.5ex]
704 % inserts single horizontal line
705 Sensing field & $(50 \times 25)~m^2 $ \\
707 WSN size & 100, 150, 200, 250, and 300~nodes \\
709 Initial energy & in range 500-700~Joules \\
711 Sensing period & duration of 60 minutes \\
712 $E_{th}$ & 36~Joules\\
715 $\alpha^j_i$ & 0.6 \\
716 % [1ex] adds vertical space
722 % is used to refer this table in the text
724 To obtain experimental results which are relevant, simulations with five
725 different node densities going from 100 to 300~nodes were performed considering
726 each time 25~randomly generated networks. The nodes are deployed on a field of
727 interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
728 high coverage ratio. Each node has an initial energy level, in Joules, which is
729 randomly drawn in the interval $[500-700]$. If its energy provision reaches a
730 value below the threshold $E_{th}=36$~Joules, the minimum energy needed for a
731 node to stay active during one period, it will no more participate in the
732 coverage task. This value corresponds to the energy needed by the sensing phase,
733 obtained by multiplying the energy consumed in active state (9.72 mW) with the
734 time in seconds for one period (3600 seconds), and adding the energy for the
735 pre-sensing phases. According to the interval of initial energy, a sensor may
736 be active during at most 20 periods.
738 The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good
739 network coverage and a longer WSN lifetime. We have given a higher priority to
740 the undercoverage (by setting the $\alpha^j_i$ with a larger value than
741 $\beta^j_i$) so as to prevent the non-coverage for the interval~$i$ of the
742 sensor~$j$. On the other hand, we have assigned to
743 $\beta^j_i$ a value which is slightly lower so as to minimize the number of active sensor nodes which contribute
744 in covering the interval.
746 We introduce the following performance metrics to evaluate the efficiency of our
749 %\begin{enumerate}[i)]
751 \item {\bf Network Lifetime}: the lifetime is defined as the time elapsed until
752 the coverage ratio falls below a fixed threshold. $Lifetime_{95}$ and
753 $Lifetime_{50}$ denote, respectively, the amount of time during which is
754 guaranteed a level of coverage greater than $95\%$ and $50\%$. The WSN can
755 fulfill the expected monitoring task until all its nodes have depleted their
756 energy or if the network is no more connected. This last condition is crucial
757 because without network connectivity a sensor may not be able to send to a
758 base station an event it has sensed.
759 \item {\bf Coverage Ratio (CR)} : it measures how well the WSN is able to
760 observe the area of interest. In our case, we discretized the sensor field as
761 a regular grid, which yields the following equation:
764 \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100
766 where $n$ is the number of covered grid points by active sensors of every
767 subregions during the current sensing phase and $N$ is total number of grid
768 points in the sensing field. In our simulations we have set a layout of
769 $N~=~51~\times~26~=~1326$~grid points.
770 \item {\bf Active Sensors Ratio (ASR)}: a major objective of our protocol is to
771 activate as few nodes as possible, in order to minimize the communication
772 overhead and maximize the WSN lifetime. The active sensors ratio is defined as
776 \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|S|$}} \times 100
778 where $|A_r^p|$ is the number of active sensors in the subregion $r$ in the
779 current sensing period~$p$, $|S|$ is the number of sensors in the network, and
780 $R$ is the number of subregions.
781 \item {\bf Energy Consumption (EC)}: energy consumption can be seen as the total
782 energy consumed by the sensors during $Lifetime_{95}$ or $Lifetime_{50}$,
783 divided by the number of periods. The value of EC is computed according to
787 \mbox{EC} = \frac{\sum\limits_{p=1}^{P} \left( E^{\mbox{com}}_p+E^{\mbox{list}}_p+E^{\mbox{comp}}_p
788 + E^{a}_p+E^{s}_p \right)}{P},
790 where $P$ corresponds to the number of periods. The total energy consumed by
791 the sensors comes through taking into consideration four main energy
792 factors. The first one, denoted $E^{\scriptsize \mbox{com}}_p$, represents the
793 energy consumption spent by all the nodes for wireless communications during
794 period $p$. $E^{\scriptsize \mbox{list}}_p$, the next factor, corresponds to
795 the energy consumed by the sensors in LISTENING status before receiving the
796 decision to go active or sleep in period $p$. $E^{\scriptsize \mbox{comp}}_p$
797 refers to the energy needed by all the leader nodes to solve the integer
798 program during a period. Finally, $E^a_{p}$ and $E^s_{p}$ indicate the energy
799 consumed by the WSN during the sensing phase (active and sleeping nodes).
803 \subsection{Simulation Results}
805 In order to assess and analyze the performance of our protocol we have
806 implemented PeCO protocol in OMNeT++~\cite{varga} simulator. Besides PeCO, two
807 other protocols, described in the next paragraph, will be evaluated for
808 comparison purposes. The simulations were run on a DELL laptop with an Intel
809 Core~i3~2370~M (2.4~GHz) processor (2 cores) whose MIPS (Million Instructions
810 Per Second) rate is equal to 35330. To be consistent with the use of a sensor
811 node based on Atmels AVR ATmega103L microcontroller (6~MHz) having a MIPS rate
812 equal to 6, the original execution time on the laptop is multiplied by 2944.2
813 $\left(\frac{35330}{2} \times \frac{1}{6} \right)$. The modeling language for
814 Mathematical Programming (AMPL)~\cite{AMPL} is employed to generate the integer
815 program instance in a standard format, which is then read and solved by the
816 optimization solver GLPK (GNU linear Programming Kit available in the public
817 domain) \cite{glpk} through a Branch-and-Bound method.
819 As said previously, the PeCO is compared to three other approaches. The first
820 one, called DESK, is a fully distributed coverage algorithm proposed by
821 \cite{ChinhVu}. The second one, called GAF~\cite{xu2001geography}, consists in
822 dividing the monitoring area into fixed squares. Then, during the decision
823 phase, in each square, one sensor is chosen to remain active during the sensing
824 phase. The last one, the DiLCO protocol~\cite{Idrees2}, is an improved version
825 of a research work we presented in~\cite{idrees2014coverage}. Let us notice that
826 PeCO and DiLCO protocols are based on the same framework. In particular, the
827 choice for the simulations of a partitioning in 16~subregions was made because
828 it corresponds to the configuration producing the best results for DiLCO. The
829 protocols are distinguished from one another by the formulation of the integer
830 program providing the set of sensors which have to be activated in each sensing
831 phase. DiLCO protocol tries to satisfy the coverage of a set of primary points,
832 whereas the PeCO protocol objective is to reach a desired level of coverage for each
833 sensor perimeter. In our experimentations, we chose a level of coverage equal to
836 \subsubsection{\bf Coverage Ratio}
838 Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes
839 obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better
840 coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the 98.76\%
841 produced by PeCO for the first periods. This is due to the fact that at the
842 beginning the DiLCO protocol puts to sleep status more redundant sensors (which
843 slightly decreases the coverage ratio), while the three other protocols activate
844 more sensor nodes. Later, when the number of periods is beyond~70, it clearly
845 appears that PeCO provides a better coverage ratio and keeps a coverage ratio
846 greater than 50\% for longer periods (15 more compared to DiLCO, 40 more
847 compared to DESK). The energy saved by PeCO in the early periods allows later a
848 substantial increase of the coverage performance.
853 \includegraphics[scale=0.5] {R/CR.eps}
854 \caption{Coverage ratio for 200 deployed nodes.}
858 %When the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to PeCO protocol. The coverage ratio of PeCO protocol is better than other approaches from the period 64.
860 %because the optimization algorithm used by PeCO has been optimized the lifetime coverage based on the perimeter coverage model, so it provided acceptable coverage for a larger number of periods and prolonging the network lifetime based on the perimeter of the sensor nodes in each subregion of WSN. Although some nodes are dead, sensor activity scheduling based optimization of PeCO selected another nodes to ensure the coverage of the area of interest. i.e. DiLCO-16 showed a good coverage in the beginning then PeCO, when the number of periods increases, the coverage ratio decreases due to died sensor nodes. Meanwhile, thanks to sensor activity scheduling based new optimization model, which is used by PeCO protocol to ensure a longer lifetime coverage in comparison with other approaches.
863 \subsubsection{\bf Active Sensors Ratio}
865 Having the less active sensor nodes in each period is essential to minimize the
866 energy consumption and thus to maximize the network lifetime. Figure~\ref{fig444}
867 shows the average active nodes ratio for 200 deployed nodes. We observe that
868 DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen
869 rounds and DiLCO and PeCO protocols compete perfectly with only 17.92 \% and
870 20.16 \% active nodes during the same time interval. As the number of periods
871 increases, PeCO protocol has a lower number of active nodes in comparison with
872 the three other approaches, while keeping a greater coverage ratio as shown in
877 \includegraphics[scale=0.5]{R/ASR.eps}
878 \caption{Active sensors ratio for 200 deployed nodes.}
882 \subsubsection{\bf Energy Consumption}
884 We studied the effect of the energy consumed by the WSN during the communication,
885 computation, listening, active, and sleep status for different network densities
886 and compared it for the four approaches. Figures~\ref{fig3EC}(a) and (b)
887 illustrate the energy consumption for different network sizes and for
888 $Lifetime95$ and $Lifetime50$. The results show that our PeCO protocol is the
889 most competitive from the energy consumption point of view. As shown in both
890 figures, PeCO consumes much less energy than the three other methods. One might
891 think that the resolution of the integer program is too costly in energy, but
892 the results show that it is very beneficial to lose a bit of time in the
893 selection of sensors to activate. Indeed the optimization program allows to
894 reduce significantly the number of active sensors and so the energy consumption
895 while keeping a good coverage level.
899 \begin{tabular}{@{}cr@{}}
900 \includegraphics[scale=0.475]{R/EC95.eps} & \raisebox{2.75cm}{(a)} \\
901 \includegraphics[scale=0.475]{R/EC50.eps} & \raisebox{2.75cm}{(b)}
903 \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
907 %The optimization algorithm, which used by PeCO protocol, was improved the lifetime coverage efficiently based on the perimeter coverage model.
909 %The other approaches have a high energy consumption due to activating a larger number of sensors. In fact, a distributed method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks.
912 %\subsubsection{Execution Time}
914 \subsubsection{\bf Network Lifetime}
916 We observe the superiority of PeCO and DiLCO protocols in comparison with the
917 two other approaches in prolonging the network lifetime. In
918 Figures~\ref{fig3LT}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for
919 different network sizes. As highlighted by these figures, the lifetime
920 increases with the size of the network, and it is clearly largest for DiLCO
921 and PeCO protocols. For instance, for a network of 300~sensors and coverage
922 ratio greater than 50\%, we can see on Figure~\ref{fig3LT}(b) that the lifetime
923 is about twice longer with PeCO compared to DESK protocol. The performance
924 difference is more obvious in Figure~\ref{fig3LT}(b) than in
925 Figure~\ref{fig3LT}(a) because the gain induced by our protocols increases with
926 time, and the lifetime with a coverage of 50\% is far longer than with
931 \begin{tabular}{@{}cr@{}}
932 \includegraphics[scale=0.475]{R/LT95.eps} & \raisebox{2.75cm}{(a)} \\
933 \includegraphics[scale=0.475]{R/LT50.eps} & \raisebox{2.75cm}{(b)}
935 \caption{Network Lifetime for (a)~$Lifetime_{95}$ \\
936 and (b)~$Lifetime_{50}$.}
940 %By choosing the best suited nodes, for each period, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next rounds, PeCO protocol efficiently prolonged the network lifetime especially for a coverage ratio greater than $50 \%$, whilst it stayed very near to DiLCO-16 protocol for $95 \%$.
942 Figure~\ref{figLTALL} compares the lifetime coverage of our protocols for
943 different coverage ratios. We denote by Protocol/50, Protocol/80, Protocol/85,
944 Protocol/90, and Protocol/95 the amount of time during which the network can
945 satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$
946 respectively, where the term Protocol refers to DiLCO or PeCO. Indeed there are applications
947 that do not require a 100\% coverage of the area to be monitored. PeCO might be
948 an interesting method since it achieves a good balance between a high level
949 coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three
950 lower coverage ratios, moreover the improvements grow with the network
951 size. DiLCO is better for coverage ratios near 100\%, but in that case PeCO is
952 not ineffective for the smallest network sizes.
955 \centering \includegraphics[scale=0.5]{R/LTa.eps}
956 \caption{Network lifetime for different coverage ratios.}
960 %Comparison shows that PeCO protocol, which are used distributed optimization over the subregions, is the more relevance one for most coverage ratios and WSN sizes because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. PeCO protocol gave acceptable coverage ratio for a larger number of periods using new optimization algorithm that based on a perimeter coverage model. It also means that distributing the algorithm in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
963 \section{Conclusion and Future Works}
964 \label{sec:Conclusion and Future Works}
966 In this paper we have studied the problem of Perimeter-based Coverage Optimization in
967 WSNs. We have designed a new protocol, called Perimeter-based Coverage Optimization, which
968 schedules nodes' activities (wake up and sleep stages) with the objective of
969 maintaining a good coverage ratio while maximizing the network lifetime. This
970 protocol is applied in a distributed way in regular subregions obtained after
971 partitioning the area of interest in a preliminary step. It works in periods and
972 is based on the resolution of an integer program to select the subset of sensors
973 operating in active status for each period. Our work is original in so far as it
974 proposes for the first time an integer program scheduling the activation of
975 sensors based on their perimeter coverage level, instead of using a set of
976 targets/points to be covered.
978 %To cope with this problem, the area of interest is divided into a smaller subregions using divide-and-conquer method, and then a PeCO protocol for optimizing the lifetime coverage in each subregion. PeCO protocol combines two efficient techniques: network
979 %leader election, which executes the perimeter coverage model (only one time), the optimization algorithm, and sending the schedule produced by the optimization algorithm to other nodes in the subregion ; the second, sensor activity scheduling based optimization in which a new lifetime coverage optimization model is proposed. The main challenges include how to select the most efficient leader in each subregion and the best schedule of sensor nodes that will optimize the network lifetime coverage
981 %The network lifetime coverage in each subregion is divided into
982 %periods, each period consists of four stages: (i) Information Exchange,
983 %(ii) Leader Election, (iii) a Decision based new optimization model in order to
984 %select the nodes remaining active for the last stage, and (iv) Sensing.
985 We have carried out several simulations to evaluate the proposed protocol. The
986 simulation results show that PeCO is more energy-efficient than other
987 approaches, with respect to lifetime, coverage ratio, active sensors ratio, and
989 %Indeed, when dealing with large and dense WSNs, a distributed optimization approach on the subregions of WSN like the one we are proposed allows to reduce the difficulty of a single global optimization problem by partitioning it in many smaller problems, one per subregion, that can be solved more easily. We have identified different research directions that arise out of the work presented here.
990 We plan to extend our framework so that the schedules are planned for multiple
992 %in order to compute all active sensor schedules in only one step for many periods;
993 We also want to improve our integer program to take into account heterogeneous
994 sensors from both energy and node characteristics point of views.
995 %the third, we are investigating new optimization model based on the sensing range so as to maximize the lifetime coverage in WSN;
996 Finally, it would be interesting to implement our protocol using a
997 sensor-testbed to evaluate it in real world applications.
999 \section*{Acknowledgments}
1001 \noindent As a Ph.D. student, Ali Kadhum IDREES would like to gratefully
1002 acknowledge the University of Babylon - IRAQ for financial support and Campus
1003 France for the received support. This work is also partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).
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