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6 \chapter{ Perimeter-based Coverage Optimization to Improve Lifetime in WSNs}
10 \section{Introduction}
13 %The continuous progress in Micro Electro-Mechanical Systems (MEMS) and wireless communication hardware has given rise to the opportunity to use large networks of tiny sensors, called Wireless Sensor Networks (WSN)~\cite{ref1,ref223}, to fulfill monitoring tasks. The features of a WSN made it suitable for a wide range of application in areas such as business, environment, health, industry, military, and so on~\cite{ref4}. These large number of applications have led to different design, management, and operational challenges in WSNs. The challenges become harder with considering into account the main limited capabilities of the sensor nodes such memory, processing, battery life, bandwidth, and short radio ranges. One important feature that distinguish the WSN from the other types of wireless networks is the provision of the sensing capability for the sensor nodes \cite{ref224}.
15 %The sensor node consumes some energy both in performing the sensing task and in transmitting the sensed data to the sink. Therefore, it is required to activate as less number as possible of sensor nodes that can monitor the whole area of interest so as to reduce the data volume and extend the network lifetime. The sensing coverage is the most important task of the WSNs since sensing unit of the sensor node is responsible for measuring physical, chemical, or biological phenomena in the sensing field. The main challenge of any sensing coverage problem is to discover the redundant sensor node and turn off those nodes in WSN \cite{ref225}. The redundant sensor node is a node whose sensing area is covered by its active neighbors. In previous works, several approaches are used to find out the redundant node such as Voronoi diagram method, sponsored sector, crossing coverage, and perimeter coverage.
17 In this chapter, we propose an approach called Perimeter-based Coverage Optimization
19 %The 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. An energy-efficient activity scheduling mechanism based new optimization model is performed by each leader in the subregions.
20 The framework is similar to the one described in section \ref{ch4:sec:02:03}, but in this approach, the 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.
23 The rest of the chapter is organized as follows. The next section is devoted to the PeCO protocol description and section~\ref{ch6:sec:03} focuses on the coverage model formulation which is used to schedule the activation of sensor nodes based on perimeter coverage model. Section~\ref{ch6:sec:04} presents simulations results and discusses the comparison with other approaches. Finally, concluding remarks are drawn in section~\ref{ch6:sec:05}.
27 \section{The PeCO Protocol Description}
30 \noindent In this section, we describe in details our Lifetime Coverage
31 Optimization protocol. First we present the assumptions we made and the models
32 we considered (in particular the perimeter coverage one), second we describe the
33 background idea of our protocol, and third we give the outline of the algorithm
34 executed by each node.
38 \subsection{Assumptions and Models}
40 The PeCO protocol uses the same assumptions and network model that presented in section \ref{ch4:sec:02:01}.
41 The PeCO protocol uses the same perimeter-coverage model as Huang and Tseng in~\cite{ref133}. It can be expressed as follows: a sensor is said to be a perimeter covered if all the points on its perimeter are covered by at least one sensor other than itself. They proved that a network area is
42 $k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).
44 Figure~\ref{pcm2sensors}(a) shows the coverage of sensor node~$0$. On this figure, we can see that sensor~$0$ has nine neighbors and we have reported on
45 its perimeter (the perimeter of the disk covered by the sensor) for each neighbor the two points resulting from intersection of the two sensing
46 areas. These points are denoted for neighbor~$i$ by $iL$ and $iR$, respectively for left and right from neighbor point of view. The resulting couples of intersection points subdivide the perimeter of sensor~$0$ into portions called
51 \begin{tabular}{@{}cr@{}}
52 \includegraphics[width=95mm]{Figures/ch6/pcm.jpg} & \raisebox{3.25cm}{(a)} \\
53 \includegraphics[width=95mm]{Figures/ch6/twosensors.jpg} & \raisebox{2.75cm}{(b)}
55 \caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of
56 $u$'s perimeter covered by $v$.}
60 Figure~\ref{pcm2sensors}(b) describes the geometric information used to find the locations of the left and right points of an arc on the perimeter of a sensor node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the
61 west side of sensor~$u$, with the following respective coordinates in the sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert
62 u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is obtained through the formula: $$\alpha = \arccos \left(\dfrac{Dist(u,v)}{2R_s}
63 \right).$$ The arc on the perimeter of~$u$ defined by the angular interval $[\pi
64 - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$.
66 Every couple of intersection points is placed on the angular interval $[0,2\pi]$ in a counterclockwise manner, leading to a partitioning of the interval.
67 Figure~\ref{pcm2sensors}(a) illustrates the arcs for the nine neighbors of sensor $0$ and Figure~\ref{expcm} gives the position of the corresponding arcs in the interval $[0,2\pi]$. More precisely, we can see that the points are
68 ordered according to the measures of the angles defined by their respective positions. The intersection points are then visited one after another, starting from the first intersection point after point~zero, and the maximum level of coverage is determined for each interval defined by two successive points. The maximum level of coverage is equal to the number of overlapping arcs. For example,
69 between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$ (the value is highlighted in yellow at the bottom of Figure~\ref{expcm}), which means that at most 2~neighbors can cover the perimeter in addition to node $0$.
70 Table~\ref{my-label} summarizes for each coverage interval the maximum level of coverage and the sensor nodes covering the perimeter. The example discussed
71 above is thus given by the sixth line of the table.
76 \includegraphics[width=150.5mm]{Figures/ch6/expcm2.jpg}
77 \caption{Maximum coverage levels for perimeter of sensor node $0$.}
83 \caption{Coverage intervals and contributing sensors for sensor node 0.}
85 \begin{tabular}{|c|c|c|c|c|c|c|c|c|}
87 \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
88 0.0291 & 1L & 2L & 4 & 0 & 1 & 3 & 4 & \\ \hline
89 0.104 & 2L & 3R & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline
90 0.3168 & 3R & 4R & 4 & 0 & 1 & 4 & 2 & \\ \hline
91 0.6752 & 4R & 1R & 3 & 0 & 1 & 2 & & \\ \hline
92 1.8127 & 1R & 5L & 2 & 0 & 2 & & & \\ \hline
93 1.9228 & 5L & 6L & 3 & 0 & 2 & 5 & & \\ \hline
94 2.3959 & 6L & 2R & 4 & 0 & 2 & 5 & 6 & \\ \hline
95 2.4258 & 2R & 7L & 3 & 0 & 5 & 6 & & \\ \hline
96 2.7868 & 7L & 8L & 4 & 0 & 5 & 6 & 7 & \\ \hline
97 2.8358 & 8L & 5R & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline
98 2.9184 & 5R & 7R & 4 & 0 & 6 & 7 & 8 & \\ \hline
99 3.3301 & 7R & 9R & 3 & 0 & 6 & 8 & & \\ \hline
100 3.9464 & 9R & 6R & 4 & 0 & 6 & 8 & 9 & \\ \hline
101 4.767 & 6R & 3L & 3 & 0 & 8 & 9 & & \\ \hline
102 4.8425 & 3L & 8R & 4 & 0 & 3 & 8 & 9 & \\ \hline
103 4.9072 & 8R & 4L & 3 & 0 & 3 & 9 & & \\ \hline
104 5.3804 & 4L & 9R & 4 & 0 & 3 & 4 & 9 & \\ \hline
105 5.9157 & 9R & 1L & 3 & 0 & 3 & 4 & & \\ \hline
112 In the PeCO protocol, the scheduling of the sensor nodes' activities is formulated as an integer program based on coverage intervals. The formulation of the coverage optimization problem is detailed in~section~\ref{ch6:sec:03}. Note that when a sensor node has a part of its sensing range outside the WSN sensing field, as in Figure~\ref{ex4pcm}, the maximum coverage level for this arc is set to $\infty$ and the corresponding interval will not be taken into account by the optimization algorithm.
117 \includegraphics[width=95.5mm]{Figures/ch6/ex4pcm.jpg}
118 \caption{Sensing range outside the WSN's area of interest.}
123 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% This section deleted %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
124 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
127 \subsection{The Main Idea}
128 \label{ch6:sec:02:02}
130 \noindent The WSN area of interest is, in a first step, divided into regular
131 homogeneous subregions using a divide-and-conquer algorithm. In a second step
132 our protocol will be executed in a distributed way in each subregion
133 simultaneously to schedule nodes' activities for one sensing period.
135 As shown in Figure~\ref{fig2}, node activity scheduling is produced by our protocol in a periodic manner. Each period is divided into 4 stages: Information (INFO) Exchange, Leader Election, Decision (the result of an optimization problem), and Sensing. For each period, there is exactly one set cover responsible for the sensing task. Protocols based on a periodic scheme, like PeCO, are more robust against an unexpected node failure. On the one hand, if a node failure is discovered before taking the decision, the corresponding sensor
136 node will not be considered by the optimization algorithm. On the other hand, if the sensor failure happens after the decision, the sensing task of the network will be temporarily affected: only during the period of sensing until a new period starts, since a new set cover will take charge of the sensing task in the next period. The energy consumption and some other constraints can easily be taken into account since the sensors can update and then exchange their information (including their residual energy) at the beginning of each period. However, the pre-sensing phases (INFO Exchange, Leader Election, and Decision)
137 are energy consuming, even for nodes that will not join the set cover to monitor the area.
141 \includegraphics[scale=0.80]{Figures/ch6/Model.pdf}
142 \caption{PeCO protocol.}
147 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
148 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
150 \subsection{PeCO Protocol Algorithm}
151 \label{ch6:sec:02:03}
154 \noindent The pseudocode implementing the protocol on a node is given below.
155 More precisely, Algorithm~\ref{alg:PeCO} gives a brief description of the
156 protocol applied by a sensor node $s_j$ where $j$ is the node index in the WSN.
158 \begin{algorithm}[h!]
159 % \KwIn{all the parameters related to information exchange}
160 % \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
162 %\emph{Initialize the sensor node and determine it's position and subregion} \;
164 \If{ $RE_k \geq E_{th}$ }{
165 \emph{$s_j.status$ = COMMUNICATION}\;
166 \emph{Send $INFO()$ packet to other nodes in subregion}\;
167 \emph{Wait $INFO()$ packet from other nodes in subregion}\;
168 \emph{Update A.CurrentSize}\;
169 \emph{LeaderID = Leader election}\;
170 \If{$ s_j.ID = LeaderID $}{
171 \emph{$s_j.status$ = COMPUTATION}\;
173 \If{$ s_j.ID $ is Not previously selected as a Leader }{
174 \emph{ Execute the perimeter coverage model}\;
175 % \emph{ Determine the segment points using perimeter coverage model}\;
178 \If{$ (s_j.ID $ is the same Previous Leader) And (A.CurrentSize = A.PreviousSize)}{
180 \emph{ Use the same previous cover set for current sensing stage}\;
183 \emph{Update $a^j_{ik}$; prepare data for IP~Algorithm}\;
184 \emph{$\left\{\left(X_{1},\dots,X_{k},\dots,X_{A}\right)\right\}$ = Execute Integer Program Algorithm($A$)}\;
185 \emph{A.PreviousSize = A.CurrentSize}\;
188 \emph{$s_j.status$ = COMMUNICATION}\;
189 \emph{Send $ActiveSleep()$ to each node $k$ in subregion}\;
190 \emph{Update $RE_j $}\;
193 \emph{$s_j.status$ = LISTENING}\;
194 \emph{Wait $ActiveSleep()$ packet from the Leader}\;
195 \emph{Update $RE_j $}\;
198 \Else { Exclude $s_j$ from entering in the current sensing stage}
199 \caption{PeCO($s_j$)}
203 In this algorithm, A.CurrentSize and A.PreviousSize respectively represent the
204 current number and the previous number of living nodes in the subnetwork of the
205 subregion. Initially, the sensor node checks its remaining energy $RE_j$, which
206 must be greater than a threshold $E_{th}$ in order to participate in the current
207 period. Each sensor node determines its position and its subregion using an
208 embedded GPS or a location discovery algorithm. After that, all the sensors
209 collect position coordinates, remaining energy, sensor node ID, and the number
210 of their one-hop live neighbors during the information exchange. The sensors
211 inside a same region cooperate to elect a leader. The selection criteria for the
212 leader, in order of priority, are larger numbers of neighbors, larger remaining
213 energy, and then in case of equality, larger index. Once chosen, the leader
214 collects information to formulate and solve the integer program which allows to
215 construct the set of active sensors in the sensing stage.
219 \section{Perimeter-based Coverage Problem Formulation}
223 \noindent In this section, the coverage model is mathematically formulated. We
224 start with a description of the notations that will be used throughout the
227 First, we have the following sets:
229 \item $J$ represents the set of WSN sensor nodes;
230 \item $A \subseteq J $ is the subset of alive sensors;
231 \item $I_j$ designates the set of coverage intervals (CI) obtained for
234 $I_j$ refers to the set of coverage intervals which have been defined according
235 to the method introduced in section~\ref{ch6:sec:02:01}. For a coverage interval $i$,
236 let $a^j_{ik}$ denotes the indicator function of whether sensor~$k$ is involved
237 in coverage interval~$i$ of sensor~$j$, that is:
241 1 & \mbox{if sensor $k$ is involved in the } \\
242 & \mbox{coverage interval $i$ of sensor $j$}, \\
243 0 & \mbox{otherwise.}\\
248 Note that $a^k_{ik}=1$ by definition of the interval.
250 Second, we define several binary and integer variables. Hence, each binary
251 variable $X_{k}$ determines the activation of sensor $k$ in the sensing phase
252 ($X_k=1$ if the sensor $k$ is active or 0 otherwise). $M^j_i$ is an integer
253 variable which measures the undercoverage for the coverage interval $i$
254 corresponding to sensor~$j$. In the same way, the overcoverage for the same
255 coverage interval is given by the variable $V^j_i$.
257 If we decide to sustain a level of coverage equal to $l$ all along the perimeter
258 of sensor $j$, we have to ensure that at least $l$ sensors involved in each
259 coverage interval $i \in I_j$ of sensor $j$ are active. According to the
260 previous notations, the number of active sensors in the coverage interval $i$ of
261 sensor $j$ is given by $\sum_{k \in A} a^j_{ik} X_k$. To extend the network
262 lifetime, the objective is to activate a minimal number of sensors in each
263 period to ensure the desired coverage level. As the number of alive sensors
264 decreases, it becomes impossible to reach the desired level of coverage for all
265 coverage intervals. Therefore, we use variables $M^j_i$ and $V^j_i$ as a measure
266 of the deviation between the desired number of active sensors in a coverage
267 interval and the effective number. And we try to minimize these deviations,
268 first to force the activation of a minimal number of sensors to ensure the
269 desired coverage level, and if the desired level cannot be completely satisfied,
270 to reach a coverage level as close as possible to the desired one.
272 Our coverage optimization problem can then be mathematically expressed as follows:
274 \begin{equation} %\label{eq:ip2r}
277 \min \sum_{j \in J} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
278 \textrm{subject to :}&\\
279 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in J\\
281 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in J\\
283 % \Theta_{p}\in \mathbb{N}, &\forall p \in P\\
284 % U_{p} \in \{0,1\}, &\forall p \in P\\
285 X_{k} \in \{0,1\}, \forall k \in A
290 $\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the
291 relative importance of satisfying the associated level of coverage. For example,
292 weights associated with coverage intervals of a specified part of a region may
293 be given by a relatively larger magnitude than weights associated with another
294 region. This kind of an integer program is inspired from the model developed for
295 brachytherapy treatment planning for optimizing dose distribution
296 \cite{0031-9155-44-1-012}. The integer program must be solved by the leader in
297 each subregion at the beginning of each sensing phase, whenever the environment
298 has changed (new leader, death of some sensors). Note that the number of
299 constraints in the model is constant (constraints of coverage expressed for all
300 sensors), whereas the number of variables $X_k$ decreases over periods, since we
301 consider only alive sensors (sensors with enough energy to be alive during one
302 sensing phase) in the model.
304 \section{Performance Evaluation and Analysis}
307 \subsection{Simulation Settings}
308 \label{ch6:sec:04:01}
310 The WSN area of interest is supposed to be divided into 16~regular subregions. The simulation parameters are summarized in Table~\ref{tablech4}.
311 %Table~\ref{table3} gives the chosen parameters settings.
313 %\caption{Relevant parameters for network initialization.}
315 %\begin{tabular}{c|c}
317 %Parameter & Value \\ [0.5ex]
319 %Sensing field & $(50 \times 25)~m^2 $ \\
320 %WSN size & 100, 150, 200, 250, and 300~nodes \\
321 %Initial energy & in range 500-700~Joules \\
322 %Sensing period & duration of 60 minutes \\
323 %$E_{th}$ & 36~Joules\\
325 %$\alpha^j_i$ & 0.6 \\
330 To obtain experimental results which are relevant, simulations with five different node densities going from 100 to 300~nodes were performed considering each time 25~randomly generated networks. The nodes are deployed on a field of
331 interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a high coverage ratio.
332 %Each node has an initial energy level, in Joules, which is randomly drawn in the interval $[500-700]$. If its energy provision reaches a value below the threshold $E_{th}=36$~Joules, the minimum energy needed for a node to stay active during one period, it will no more participate in the coverage task. This value corresponds to the energy needed by the sensing phase, obtained by multiplying the energy consumed in active state (9.72 mW) with the time in seconds for one period (3600 seconds), and adding the energy for the pre-sensing phases. According to the interval of initial energy, a sensor may be active during at most 20 periods.
335 The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good network coverage and a longer WSN lifetime as shown in Table \ref{my-beta-alfa}. We have given a higher priority to the undercoverage (by setting the $\alpha^j_i$ with a larger value than $\beta^j_i$) so as to prevent the non-coverage for the interval~$i$ of the
336 sensor~$j$. On the other hand, we have assigned to
337 $\beta^j_i$ a value which is slightly lower so as to minimize the number of active sensor nodes which contribute in covering the interval.
341 \caption{The impact of $\alpha^j_i$ and $\beta^j_i$ on PeCO's performance for 200 deployed nodes}
343 \begin{tabular}{|c|c|c|c|}
345 $\alpha^j_i$ & $\beta^j_i$ & $Lifetime_{50}$ & $Lifetime_{95}$ \\ \hline
346 0.0 & 1.0 & 151 & 0 \\ \hline
347 0.1 & 0.9 & 145 & 0 \\ \hline
348 0.2 & 0.8 & 140 & 0 \\ \hline
349 0.3 & 0.7 & 134 & 0 \\ \hline
350 0.4 & 0.6 & 125 & 0 \\ \hline
351 0.5 & 0.5 & 118 & 30 \\ \hline
352 0.6 & 0.4 & 94 & 57 \\ \hline
353 0.7 & 0.3 & 97 & 49 \\ \hline
354 0.8 & 0.2 & 90 & 52 \\ \hline
355 0.9 & 0.1 & 77 & 50 \\ \hline
356 1.0 & 0.0 & 60 & 44 \\ \hline
360 With the performance metrics, described in section \ref{ch4:sec:04:04}, we evaluate the efficiency of our approach. We use the modeling language and the optimization solver which are mentioned in section \ref{ch4:sec:04:02}. In addition, we use the same energy consumption model, presented in section \ref{ch4:sec:04:03}.
363 \subsection{Simulation Results}
364 \label{ch6:sec:04:02}
366 In order to assess and analyze the performance of our protocol we have implemented PeCO protocol in OMNeT++~\cite{ref158} simulator. Besides PeCO, three other protocols, described in the next paragraph, will be evaluated for comparison purposes.
367 %The simulations were run on a laptop DELL with an Intel Core~i3~2370~M (2.4~GHz) processor (2 cores) whose MIPS (Million Instructions Per Second) rate is equal to 35330. To be consistent with the use of a sensor node based on Atmels AVR ATmega103L microcontroller (6~MHz) having a MIPS rate equal to 6, the original execution time on the laptop is multiplied by 2944.2 $\left(\frac{35330}{2} \times \frac{1}{6} \right)$. The modeling language for Mathematical Programming (AMPL)~\cite{AMPL} is employed to generate the integer program instance in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method.
368 As said previously, the PeCO is compared with three other approaches. The first one, called DESK, is a fully distributed coverage algorithm proposed by \cite{DESK}. The second one, called GAF~\cite{GAF}, consists in dividing the monitoring area into fixed squares. Then, during the decision phase, in each square, one sensor is chosen to remain active during the sensing phase. The last one, the DiLCO protocol~\cite{Idrees2}, is an improved version of a research work we presented in~\cite{ref159}. Let us notice that PeCO and DiLCO protocols are based on the same framework. In particular, the choice for the simulations of a partitioning in 16~subregions was chosen because it corresponds to the configuration producing the better results for DiLCO. The protocols are distinguished from one another by the formulation of the integer program providing the set of sensors which have to be activated in each sensing phase. DiLCO protocol tries to satisfy the coverage of a set of primary points, whereas PeCO protocol objective is to reach a desired level of coverage for each sensor perimeter. In our experimentations, we chose a level of coverage equal to one ($l=1$).
372 \subsubsection{Coverage Ratio}
373 \label{ch6:sec:04:02:01}
375 Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better
376 coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the 98.76\%
377 produced by PeCO for the first periods. This is due to the fact that at the
378 beginning the DiLCO protocol puts to sleep status more redundant sensors (which
379 slightly decreases the coverage ratio), while the three other protocols activate
380 more sensor nodes. Later, when the number of periods is beyond~70, it clearly
381 appears that PeCO provides a better coverage ratio and keeps a coverage ratio
382 greater than 50\% for longer periods (15 more compared to DiLCO, 40 more
383 compared to DESK). The energy saved by PeCO in the early periods allows later a
384 substantial increase of the coverage performance.
389 \includegraphics[scale=0.8] {Figures/ch6/R/CR.eps}
390 \caption{Coverage ratio for 200 deployed nodes.}
396 \subsubsection{Active Sensors Ratio}
397 \label{ch6:sec:04:02:02}
399 Having the less active sensor nodes in each period is essential to minimize the
400 energy consumption and thus to maximize the network lifetime. Figure~\ref{fig444}
401 shows the average active nodes ratio for 200 deployed nodes. We observe that
402 DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen
403 rounds and DiLCO and PeCO protocols compete perfectly with only 17.92 \% and
404 20.16 \% active nodes during the same time interval. As the number of periods
405 increases, PeCO protocol has a lower number of active nodes in comparison with
406 the three other approaches, while keeping a greater coverage ratio as shown in
411 \includegraphics[scale=0.8]{Figures/ch6/R/ASR.eps}
412 \caption{Active sensors ratio for 200 deployed nodes.}
416 \subsubsection{The Energy Consumption}
417 \label{ch6:sec:04:02:03}
419 We studied the effect of the energy consumed by the WSN during the communication,
420 computation, listening, active, and sleep status for different network densities
421 and compared it for the four approaches. Figures~\ref{fig3EC}(a) and (b)
422 illustrate the energy consumption for different network sizes and for
423 $Lifetime95$ and $Lifetime50$. The results show that our PeCO protocol is the
424 most competitive from the energy consumption point of view. As shown in both
425 figures, PeCO consumes much less energy than the three other methods. One might
426 think that the resolution of the integer program is too costly in energy, but
427 the results show that it is very beneficial to lose a bit of time in the
428 selection of sensors to activate. Indeed the optimization program allows to
429 reduce significantly the number of active sensors and so the energy consumption
430 while keeping a good coverage level.
434 \begin{tabular}{@{}cr@{}}
435 \includegraphics[scale=0.8]{Figures/ch6/R/EC95.eps} & \raisebox{4cm}{(a)} \\
436 \includegraphics[scale=0.8]{Figures/ch6/R/EC50.eps} & \raisebox{4cm}{(b)}
438 \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
444 \subsubsection{The Network Lifetime}
445 \label{ch6:sec:04:02:04}
447 We observe the superiority of PeCO and DiLCO protocols in comparison with the
448 two other approaches in prolonging the network lifetime. In
449 Figures~\ref{fig3LT}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for
450 different network sizes. As highlighted by these figures, the lifetime
451 increases with the size of the network, and it is clearly largest for DiLCO
452 and PeCO protocols. For instance, for a network of 300~sensors and coverage
453 ratio greater than 50\%, we can see on Figure~\ref{fig3LT}(b) that the lifetime
454 is about twice longer with PeCO compared to DESK protocol. The performance
455 difference is more obvious in Figure~\ref{fig3LT}(b) than in
456 Figure~\ref{fig3LT}(a) because the gain induced by our protocols increases with
457 time, and the lifetime with a coverage of 50\% is far longer than with
462 \begin{tabular}{@{}cr@{}}
463 \includegraphics[scale=0.8]{Figures/ch6/R/LT95.eps} & \raisebox{4cm}{(a)} \\
464 \includegraphics[scale=0.8]{Figures/ch6/R/LT50.eps} & \raisebox{4cm}{(b)}
466 \caption{Network Lifetime for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
470 Figure~\ref{figLTALL} compares the lifetime coverage of our protocols for
471 different coverage ratios. We denote by Protocol/50, Protocol/80, Protocol/85,
472 Protocol/90, and Protocol/95 the amount of time during which the network can
473 satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$
474 respectively, where the term Protocol refers to DiLCO or PeCO. Indeed there are applications
475 that do not require a 100\% coverage of the area to be monitored. PeCO might be
476 an interesting method since it achieves a good balance between a high level
477 coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three
478 lower coverage ratios, moreover the improvements grow with the network
479 size. DiLCO is better for coverage ratios near 100\%, but in that case PeCO is
480 not ineffective for the smallest network sizes.
483 \centering \includegraphics[scale=0.8]{Figures/ch6/R/LTa.eps}
484 \caption{Network lifetime for different coverage ratios.}
493 In this chapter, we have studied the problem of Perimeter-based Coverage Optimization in
494 WSNs. We have designed a new protocol, called Perimeter-based Coverage Optimization, which
495 schedules nodes' activities (wake up and sleep stages) with the objective of
496 maintaining a good coverage ratio while maximizing the network lifetime. This
497 protocol is applied in a distributed way in regular subregions obtained after
498 partitioning the area of interest in a preliminary step. It works in periods and
499 is based on the resolution of an integer program to select the subset of sensors
500 operating in active status for each period. Our work is original in so far as it
501 proposes for the first time an integer program scheduling the activation of
502 sensors based on their perimeter coverage level, instead of using a set of
503 targets/points to be covered. We have carried out several simulations to evaluate the proposed protocol. The simulation results show that PeCO is more energy-efficient than other approaches, with respect to lifetime, coverage ratio, active sensors ratio, and
506 We plan to extend our framework so that the schedules are planned for multiple
508 %in order to compute all active sensor schedules in only one step for many periods;
509 We also want to improve our integer program to take into account heterogeneous
510 sensors from both energy and node characteristics point of views.
511 %the third, we are investigating new optimization model based on the sensing range so as to maximize the lifetime coverage in WSN;
512 Finally, it would be interesting to implement our protocol using a
513 sensor-testbed to evaluate it in real world applications.
