1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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 scheme 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 produce 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. Section~\ref{ch6:sec:04} presents simulation results and discusses the comparison with other approaches. Finally, concluding remarks are drawn in section~\ref{ch6:sec:05}.
27 \section{Description of the PeCO Protocol}
30 %\noindent In this section, we describe in details our Lifetime Coverage Optimization protocol.
31 First we present the assumptions we made and the models
32 we considered (in particular the perimeter coverage one), second we describe the background idea of our protocol, and third we give the outline of the algorithm executed by each node.
36 \subsection{Assumptions and Models}
38 The PeCO protocol uses the same assumptions and network model than both the DiLCO and the MuDiLCO protocols. All the hypotheses can be found in section \ref{ch4:sec:02:01}.
39 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
40 $k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).
42 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
43 its perimeter (the perimeter of the disk covered by the sensor) for each neighbor the two points resulting from intersection of the two sensing
44 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
49 \begin{tabular}{@{}cr@{}}
50 \includegraphics[width=95mm]{Figures/ch6/pcm.jpg} & \raisebox{3.25cm}{(a)} \\
51 \includegraphics[width=95mm]{Figures/ch6/twosensors.jpg} & \raisebox{2.75cm}{(b)}
53 \caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of
54 $u$'s perimeter covered by $v$.}
58 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
59 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 $v$: $Dist(u,v)=\sqrt{\vert
60 u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is obtained through the formula: $$\alpha = \arccos \left(\dfrac{Dist(u,v)}{2R_s}
61 \right).$$ The arc on the perimeter of~$u$ defined by the angular interval $[\pi
62 - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$.
64 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.
65 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
66 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,
67 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 $0$.
68 Table~\ref{my-label} summarizes for each coverage interval the maximum level of coverage and the sensor nodes covering the perimeter. The example discussed
69 above is thus given by the sixth line of the table.
74 \includegraphics[width=150.5mm]{Figures/ch6/expcm2.jpg}
75 \caption{Maximum coverage levels for perimeter of sensor node $0$.}
81 \caption{Coverage intervals and contributing sensors for sensor node 0.}
83 \begin{tabular}{|c|c|c|c|c|c|c|c|c|}
85 \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
86 0.0291 & 1L & 2L & 4 & 0 & 1 & 3 & 4 & \\ \hline
87 0.104 & 2L & 3R & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline
88 0.3168 & 3R & 4R & 4 & 0 & 1 & 4 & 2 & \\ \hline
89 0.6752 & 4R & 1R & 3 & 0 & 1 & 2 & & \\ \hline
90 1.8127 & 1R & 5L & 2 & 0 & 2 & & & \\ \hline
91 1.9228 & 5L & 6L & 3 & 0 & 2 & 5 & & \\ \hline
92 2.3959 & 6L & 2R & 4 & 0 & 2 & 5 & 6 & \\ \hline
93 2.4258 & 2R & 7L & 3 & 0 & 5 & 6 & & \\ \hline
94 2.7868 & 7L & 8L & 4 & 0 & 5 & 6 & 7 & \\ \hline
95 2.8358 & 8L & 5R & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline
96 2.9184 & 5R & 7R & 4 & 0 & 6 & 7 & 8 & \\ \hline
97 3.3301 & 7R & 9R & 3 & 0 & 6 & 8 & & \\ \hline
98 3.9464 & 9R & 6R & 4 & 0 & 6 & 8 & 9 & \\ \hline
99 4.767 & 6R & 3L & 3 & 0 & 8 & 9 & & \\ \hline
100 4.8425 & 3L & 8R & 4 & 0 & 3 & 8 & 9 & \\ \hline
101 4.9072 & 8R & 4L & 3 & 0 & 3 & 9 & & \\ \hline
102 5.3804 & 4L & 9R & 4 & 0 & 3 & 4 & 9 & \\ \hline
103 5.9157 & 9R & 1L & 3 & 0 & 3 & 4 & & \\ \hline
110 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.
115 \includegraphics[width=95.5mm]{Figures/ch6/ex4pcm.jpg}
116 \caption{Sensing range outside the WSN's area of interest.}
121 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% This section deleted %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
122 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
125 \subsection{The Main Idea}
126 \label{ch6:sec:02:02}
128 \noindent The WSN area of interest is, in a first step, divided into regular
129 homogeneous subregions using a divide-and-conquer algorithm. In a second step
130 our protocol will be executed in a distributed way in each subregion
131 simultaneously to schedule nodes' activities for one sensing period.
133 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
134 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)
135 are energy consuming, even for nodes that will not join the set cover to monitor the area.
139 \includegraphics[scale=0.80]{Figures/ch6/Model.pdf}
140 \caption{PeCO protocol.}
145 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
146 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
148 \subsection{PeCO Protocol Algorithm}
149 \label{ch6:sec:02:03}
152 \noindent The pseudocode implementing the protocol on a node is given below.
153 More precisely, Algorithm~\ref{alg:PeCO} gives a brief description of the
154 protocol applied by a sensor node $s_j$ where $j$ is the node index in the WSN.
156 \begin{algorithm}[h!]
157 % \KwIn{all the parameters related to information exchange}
158 % \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
160 %\emph{Initialize the sensor node and determine it's position and subregion} \;
162 \If{ $RE_k \geq E_{th}$ }{
163 \emph{$s_j.status$ = COMMUNICATION}\;
164 \emph{Send $INFO()$ packet to other nodes in subregion}\;
165 \emph{Wait $INFO()$ packet from other nodes in subregion}\;
166 \emph{Update A.CurrentSize}\;
167 \emph{LeaderID = Leader election}\;
168 \If{$ s_j.ID = LeaderID $}{
169 \emph{$s_j.status$ = COMPUTATION}\;
171 \If{$ s_j.ID $ is Not previously selected as a Leader }{
172 \emph{ Execute the perimeter coverage model}\;
173 % \emph{ Determine the segment points using perimeter coverage model}\;
176 \If{$ (s_j.ID $ is the same Previous Leader) And (A.CurrentSize = A.PreviousSize)}{
178 \emph{ Use the same previous cover set for current sensing stage}\;
181 \emph{Update $a^j_{ik}$; prepare data for IP~Algorithm}\;
182 \emph{$\left\{\left(X_{1},\dots,X_{k},\dots,X_{A}\right)\right\}$ = Execute Integer Program Algorithm($A$)}\;
183 \emph{A.PreviousSize = A.CurrentSize}\;
186 \emph{$s_j.status$ = COMMUNICATION}\;
187 \emph{Send $ActiveSleep()$ to each node $k$ in subregion}\;
188 \emph{Update $RE_j $}\;
191 \emph{$s_j.status$ = LISTENING}\;
192 \emph{Wait $ActiveSleep()$ packet from the Leader}\;
193 \emph{Update $RE_j $}\;
196 \Else { Exclude $s_j$ from entering in the current sensing stage}
197 \caption{PeCO($s_j$)}
201 In this algorithm, A.CurrentSize and A.PreviousSize respectively represent the
202 current number and the previous number of living nodes in the subnetwork of the
203 subregion. Initially, the sensor node checks its remaining energy $RE_j$, which
204 must be greater than a threshold $E_{th}$ in order to participate in the current
205 period. Each sensor node determines its position and its subregion using an
206 embedded GPS or a location discovery algorithm. After that, all the sensors
207 collect position coordinates, remaining energy, sensor node ID, and the number
208 of their one-hop live neighbors during the information exchange. The sensors
209 inside a same region cooperate to elect a leader. The selection criteria for the
210 leader, in order of priority, are larger numbers of neighbors, larger remaining
211 energy, and then in case of equality, larger index. Once chosen, the leader
212 collects information to formulate and solve the integer program which allows to
213 construct the set of active sensors in the sensing stage.
217 \section{Perimeter-based Coverage Problem Formulation}
221 \noindent In this section, the coverage model is mathematically formulated. We
222 start with a description of the notations that will be used throughout the
225 First, we have the following sets:
227 \item $J$ represents the set of sensor nodes;
228 \item $A \subseteq J $ is the subset of alive sensors;
229 \item $I_j$ designates the set of coverage intervals (CI) obtained for
230 sensor~$j$, which have been defined according to the method introduced in section~\ref{ch6:sec:02:01}.
232 First, for a coverage interval $i$, let $a^j_{ik}$ denotes the indicator function of whether sensor~$k$ is involved
233 in coverage interval~$i$ of sensor~$j$, that is:
237 1 & \mbox{if sensor $k$ is involved in the } \\
238 & \mbox{coverage interval $i$ of sensor $j$}, \\
239 0 & \mbox{otherwise.}\\
244 Note that $a^k_{ik}=1$ by definition of the interval.
246 Second, we define several binary and integer variables. Hence, each binary
247 variable $X_{k}$ determines the activation of sensor $k$ in the sensing phase
248 ($X_k=1$ if the sensor $k$ is active or 0 otherwise). $M^j_i$ is an integer
249 variable which measures the undercoverage for the coverage interval $i$
250 corresponding to sensor~$j$. In the same way, the overcoverage for the same
251 coverage interval is given by the variable $V^j_i$.
253 If we decide to sustain a level of coverage equal to $l$ all along the perimeter
254 of sensor $j$, we have to ensure that at least $l$ sensors involved in each
255 coverage interval $i \in I_j$ of sensor $j$ are active. According to the
256 previous notations, the number of active sensors in the coverage interval $i$ of
257 sensor $j$ is given by $\sum_{k \in A} a^j_{ik} X_k$. To extend the network
258 lifetime, the objective is to activate a minimal number of sensors in each
259 period to ensure the desired coverage level. As the number of alive sensors
260 decreases, it becomes impossible to reach the desired level of coverage for all
261 coverage intervals. Therefore, we use variables $M^j_i$ and $V^j_i$ as a measure
262 of the deviation between the desired number of active sensors in a coverage
263 interval and the effective number. And we try to minimize these deviations,
264 first to force the activation of a minimal number of sensors to ensure the
265 desired coverage level, and if the desired level cannot be completely satisfied,
266 to reach a coverage level as close as possible to the desired one.
268 Our coverage optimization problem can then be mathematically expressed as follows:
270 \begin{equation} %\label{eq:ip2r}
273 \min \sum_{j \in J} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
274 \textrm{subject to :}&\\
275 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in J\\
277 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in J\\
279 % \Theta_{p}\in \mathbb{N}, &\forall p \in P\\
280 % U_{p} \in \{0,1\}, &\forall p \in P\\
281 X_{k} \in \{0,1\}, \forall k \in A
286 $\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the
287 relative importance of satisfying the associated level of coverage. For example,
288 weights associated with coverage intervals of a specified part of a region may
289 be given by a relatively larger magnitude than weights associated with another
290 region. This kind of an integer program is inspired from the model developed for
291 brachytherapy treatment planning for optimizing dose distribution
292 \cite{0031-9155-44-1-012}. The integer program must be solved by the leader in
293 each subregion at the beginning of each sensing phase, whenever the environment
294 has changed (new leader, death of some sensors). Note that the number of
295 constraints in the model is constant (constraints of coverage expressed for all
296 sensors), whereas the number of variables $X_k$ decreases over periods, since we
297 consider only alive sensors (sensors with enough energy to be alive during one
298 sensing phase) in the model.
300 \section{Performance Evaluation and Analysis}
303 \subsection{Simulation Settings}
304 \label{ch6:sec:04:01}
306 The WSN area of interest is supposed to be divided into 16~regular subregions. The simulation parameters are summarized in Table~\ref{tablech4}.
307 %Table~\ref{table3} gives the chosen parameters settings.
309 %\caption{Relevant parameters for network initialization.}
311 %\begin{tabular}{c|c}
313 %Parameter & Value \\ [0.5ex]
315 %Sensing field & $(50 \times 25)~m^2 $ \\
316 %WSN size & 100, 150, 200, 250, and 300~nodes \\
317 %Initial energy & in range 500-700~Joules \\
318 %Sensing period & duration of 60 minutes \\
319 %$E_{th}$ & 36~Joules\\
321 %$\alpha^j_i$ & 0.6 \\
326 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
327 interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a high coverage ratio.
328 %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.
331 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 set the values of $\alpha^j_i$ and $\beta^j_i$ to 0.6 and 0.4 respectively. 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 sensor~$j$. On the other hand, we have assigned to
332 $\beta^j_i$ a value which is slightly lower so as to minimize the number of active sensor nodes which contribute in covering the interval.
336 \caption{The impact of $\alpha^j_i$ and $\beta^j_i$ on PeCO's performance for 200 deployed nodes}
338 \begin{tabular}{|c|c|c|c|}
340 $\alpha^j_i$ & $\beta^j_i$ & $Lifetime_{50}$ & $Lifetime_{95}$ \\ \hline
341 0.0 & 1.0 & 151 & 0 \\ \hline
342 0.1 & 0.9 & 145 & 0 \\ \hline
343 0.2 & 0.8 & 140 & 0 \\ \hline
344 0.3 & 0.7 & 134 & 0 \\ \hline
345 0.4 & 0.6 & 125 & 0 \\ \hline
346 0.5 & 0.5 & 118 & 30 \\ \hline
347 0.6 & 0.4 & 94 & 57 \\ \hline
348 0.7 & 0.3 & 97 & 49 \\ \hline
349 0.8 & 0.2 & 90 & 52 \\ \hline
350 0.9 & 0.1 & 77 & 50 \\ \hline
351 1.0 & 0.0 & 60 & 44 \\ \hline
355 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, as previously, described in section \ref{ch4:sec:04:03}.
358 \subsection{Simulation Results}
359 \label{ch6:sec:04:02}
361 In order to assess and analyze the performance of our protocol we have implemented PeCO protocol in OMNeT++~\cite{ref158} simulator.
362 %Besides PeCO, three other protocols, described in the next paragraph, will be evaluated for comparison purposes.
363 %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.
364 PeCO protocol is compared with three other approaches. DESK \cite{DESK}, GAF~\cite{GAF}, and DiLCO~\cite{Idrees2} is an improved version of a research work we presented in~\cite{ref159}, where DiLCO protocol is described in chapter 4. Let us notice that the PeCO and the 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 ($l=1$).
368 \subsubsection{Coverage Ratio}
369 \label{ch6:sec:04:02:01}
371 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
372 coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the 98.76\%
373 produced by PeCO for the first periods. This is due to the fact that at the
374 beginning the DiLCO protocol puts to sleep status more redundant sensors (which
375 slightly decreases the coverage ratio), while the three other protocols activate
376 more sensor nodes. Later, when the number of periods is beyond~70, it clearly
377 appears that PeCO provides a better coverage ratio and keeps a coverage ratio
378 greater than 50\% for longer periods (15 more compared to DiLCO, 40 more
379 compared to DESK). The energy saved by PeCO in the early periods allows later a
380 substantial increase of the coverage performance.
385 \includegraphics[scale=0.8] {Figures/ch6/R/CR.eps}
386 \caption{Coverage ratio for 200 deployed nodes.}
392 \subsubsection{Active Sensors Ratio}
393 \label{ch6:sec:04:02:02}
395 Having the less active sensor nodes in each period is essential to minimize the
396 energy consumption and thus to maximize the network lifetime. Figure~\ref{fig444}
397 shows the average active nodes ratio for 200 deployed nodes. We observe that
398 DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen
399 rounds and DiLCO and PeCO protocols compete perfectly with only 17.92 \% and
400 20.16 \% active nodes during the same time interval. As the number of periods
401 increases, PeCO protocol has a lower number of active nodes in comparison with
402 the three other approaches, while keeping a greater coverage ratio as shown in
407 \includegraphics[scale=0.8]{Figures/ch6/R/ASR.eps}
408 \caption{Active sensors ratio for 200 deployed nodes.}
412 \subsubsection{Energy Consumption}
413 \label{ch6:sec:04:02:03}
415 We studied the effect of the energy consumed by the WSN during the communication,
416 computation, listening, active, and sleep status for different network densities
417 and compared it for the four approaches. Figures~\ref{fig3EC}(a) and (b)
418 illustrate the energy consumption for different network sizes and for
419 $Lifetime95$ and $Lifetime50$. The results show that our PeCO protocol is the
420 most competitive from the energy consumption point of view. As shown in both
421 figures, PeCO consumes much less energy than the three other methods. \\ \\ \\ \\ \\ \\
423 One might think that the resolution of the integer program is too costly in energy, but the results show that it is very beneficial to lose a bit of time in the selection of sensors to activate. Indeed the optimization program allows to reduce significantly the number of active sensors and so the energy consumption while keeping a good coverage level.
427 \begin{tabular}{@{}cr@{}}
428 \includegraphics[scale=0.8]{Figures/ch6/R/EC95.eps} & \raisebox{4cm}{(a)} \\
429 \includegraphics[scale=0.8]{Figures/ch6/R/EC50.eps} & \raisebox{4cm}{(b)}
431 \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
437 \subsubsection{Network Lifetime}
438 \label{ch6:sec:04:02:04}
440 We observe the superiority of PeCO and DiLCO protocols in comparison with the two other approaches in prolonging the network lifetime. In
441 Figures~\ref{fig3LT}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for different network sizes. As highlighted by these figures, the lifetime increases with the size of the network, and it is clearly largest for the DiLCO and the PeCO protocols. For instance, for a network of 300~sensors and coverage ratio greater than 50\%, we can see on Figure~\ref{fig3LT}(b) that the lifetime is about twice longer with the PeCO compared to the DESK protocol. The performance difference is more obvious in Figure~\ref{fig3LT}(b) than in Figure~\ref{fig3LT}(a) because the gain induced by our protocols increases with time, and the lifetime with a coverage of 50\% is far longer than with
446 \begin{tabular}{@{}cr@{}}
447 \includegraphics[scale=0.8]{Figures/ch6/R/LT95.eps} & \raisebox{4cm}{(a)} \\
448 \includegraphics[scale=0.8]{Figures/ch6/R/LT50.eps} & \raisebox{4cm}{(b)}
450 \caption{Network Lifetime for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
454 Figure~\ref{figLTALL} compares the lifetime coverage of our protocols for
455 different coverage ratios. We denote by Protocol/50, Protocol/80, Protocol/85,
456 Protocol/90, and Protocol/95 the amount of time during which the network can
457 satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$
458 respectively, where the term Protocol refers to DiLCO or PeCO. Indeed there are applications that do not require a 100\% coverage of the area to be monitored. PeCO might be an interesting method since it achieves a good balance between a high level coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three lower coverage ratios, moreover the improvements grow with the network size. DiLCO is better for coverage ratios near 100\%, but in that case PeCO is not ineffective for the smallest network sizes.
461 \centering \includegraphics[scale=0.8]{Figures/ch6/R/LTa.eps}
462 \caption{Network lifetime for different coverage ratios.}
471 In this chapter, we have studied the problem of Perimeter-based Coverage Optimization in WSNs. We have designed a new protocol, called Perimeter-based Coverage Optimization, which schedules nodes' activities (wake up and sleep stages) with the objective of maintaining a good coverage ratio while maximizing the network lifetime. This protocol is applied in a distributed way in regular subregions obtained after partitioning the area of interest in a preliminary step. It works in periods and
472 is based on the resolution of an integer program to select the subset of sensors operating in active status for each period. Our work is original because it proposes for the first time an integer program scheduling the activation of sensors based on their perimeter coverage level, instead of using a set of 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 energy consumption.
474 %We plan to extend our framework so that the schedules are planned for multiple sensing periods. We also want to improve our integer program to take into account heterogeneous sensors from both energy and node characteristics point of views. Finally, it would be interesting to implement our protocol using a sensor-testbed to evaluate it in real world applications.
477 %in order to compute all active sensor schedules in only one step for many periods;
478 %the third, we are investigating new optimization model based on the sensing range so as to maximize the lifetime coverage in WSN;
