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 framework is similar to the one described in chapter 4, 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
24 coverage model formulation which is used to schedule the activation of sensor
25 nodes based on perimeter coverage model. Section~\ref{ch6:sec:04} presents simulations
26 results and discusses the comparison with other approaches. Finally, concluding
27 remarks are drawn in section~\ref{ch6:sec:05}.
31 \section{The PeCO Protocol Description}
34 \noindent In this section, we describe in details our Lifetime Coverage
35 Optimization protocol. First we present the assumptions we made and the models
36 we considered (in particular the perimeter coverage one), second we describe the
37 background idea of our protocol, and third we give the outline of the algorithm
38 executed by each node.
42 \subsection{Assumptions and Models}
44 The PeCO protocol uses the same assumptions and network model that presented in chapter 4, section \ref{ch4:sec:02:01}.
46 The PeCO protocol uses the same perimeter-coverage model as Huang and
47 Tseng in~\cite{ref133}. It can be expressed as follows: a sensor is
48 said to be a perimeter covered if all the points on its perimeter are covered by
49 at least one sensor other than itself. They proved that a network area is
50 $k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).
52 Figure~\ref{pcm2sensors}(a) shows the coverage of sensor node~$0$. On this
53 figure, we can see that sensor~$0$ has nine neighbors and we have reported on
54 its perimeter (the perimeter of the disk covered by the sensor) for each
55 neighbor the two points resulting from intersection of the two sensing
56 areas. These points are denoted for neighbor~$i$ by $iL$ and $iR$, respectively
57 for left and right from neighbor point of view. The resulting couples of
58 intersection points subdivide the perimeter of sensor~$0$ into portions called
63 \begin{tabular}{@{}cr@{}}
64 \includegraphics[width=95mm]{Figures/ch6/pcm.jpg} & \raisebox{3.25cm}{(a)} \\
65 \includegraphics[width=95mm]{Figures/ch6/twosensors.jpg} & \raisebox{2.75cm}{(b)}
67 \caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of
68 $u$'s perimeter covered by $v$.}
72 Figure~\ref{pcm2sensors}(b) describes the geometric information used to find the
73 locations of the left and right points of an arc on the perimeter of a sensor
74 node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the
75 west side of sensor~$u$, with the following respective coordinates in the
76 sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can
77 compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert
78 u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is
79 obtained through the formula: $$\alpha = \arccos \left(\dfrac{Dist(u,v)}{2R_s}
80 \right).$$ The arc on the perimeter of~$u$ defined by the angular interval $[\pi
81 - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$.
83 Every couple of intersection points is placed on the angular interval $[0,2\pi]$
84 in a counterclockwise manner, leading to a partitioning of the interval.
85 Figure~\ref{pcm2sensors}(a) illustrates the arcs for the nine neighbors of
86 sensor $0$ and Figure~\ref{expcm} gives the position of the corresponding arcs
87 in the interval $[0,2\pi]$. More precisely, we can see that the points are
88 ordered according to the measures of the angles defined by their respective
89 positions. The intersection points are then visited one after another, starting
90 from the first intersection point after point~zero, and the maximum level of
91 coverage is determined for each interval defined by two successive points. The
92 maximum level of coverage is equal to the number of overlapping arcs. For
94 between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$
95 (the value is highlighted in yellow at the bottom of Figure~\ref{expcm}), which
96 means that at most 2~neighbors can cover the perimeter in addition to node $0$.
97 Table~\ref{my-label} summarizes for each coverage interval the maximum level of
98 coverage and the sensor nodes covering the perimeter. The example discussed
99 above is thus given by the sixth line of the table.
104 \includegraphics[width=150.5mm]{Figures/ch6/expcm2.jpg}
105 \caption{Maximum coverage levels for perimeter of sensor node $0$.}
111 \caption{Coverage intervals and contributing sensors for sensor node 0.}
113 \begin{tabular}{|c|c|c|c|c|c|c|c|c|}
115 \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
116 0.0291 & 1L & 2L & 4 & 0 & 1 & 3 & 4 & \\ \hline
117 0.104 & 2L & 3R & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline
118 0.3168 & 3R & 4R & 4 & 0 & 1 & 4 & 2 & \\ \hline
119 0.6752 & 4R & 1R & 3 & 0 & 1 & 2 & & \\ \hline
120 1.8127 & 1R & 5L & 2 & 0 & 2 & & & \\ \hline
121 1.9228 & 5L & 6L & 3 & 0 & 2 & 5 & & \\ \hline
122 2.3959 & 6L & 2R & 4 & 0 & 2 & 5 & 6 & \\ \hline
123 2.4258 & 2R & 7L & 3 & 0 & 5 & 6 & & \\ \hline
124 2.7868 & 7L & 8L & 4 & 0 & 5 & 6 & 7 & \\ \hline
125 2.8358 & 8L & 5R & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline
126 2.9184 & 5R & 7R & 4 & 0 & 6 & 7 & 8 & \\ \hline
127 3.3301 & 7R & 9R & 3 & 0 & 6 & 8 & & \\ \hline
128 3.9464 & 9R & 6R & 4 & 0 & 6 & 8 & 9 & \\ \hline
129 4.767 & 6R & 3L & 3 & 0 & 8 & 9 & & \\ \hline
130 4.8425 & 3L & 8R & 4 & 0 & 3 & 8 & 9 & \\ \hline
131 4.9072 & 8R & 4L & 3 & 0 & 3 & 9 & & \\ \hline
132 5.3804 & 4L & 9R & 4 & 0 & 3 & 4 & 9 & \\ \hline
133 5.9157 & 9R & 1L & 3 & 0 & 3 & 4 & & \\ \hline
140 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.
145 \includegraphics[width=95.5mm]{Figures/ch6/ex4pcm.jpg}
146 \caption{Sensing range outside the WSN's area of interest.}
151 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% This section deleted %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
152 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
155 \subsection{The Main Idea}
156 \label{ch6:sec:02:02}
158 \noindent The WSN area of interest is, in a first step, divided into regular
159 homogeneous subregions using a divide-and-conquer algorithm. In a second step
160 our protocol will be executed in a distributed way in each subregion
161 simultaneously to schedule nodes' activities for one sensing period.
163 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
164 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)
165 are energy consuming, even for nodes that will not join the set cover to monitor the area.
169 \includegraphics[scale=0.80]{Figures/ch6/Model.pdf}
170 \caption{PeCO protocol.}
175 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
176 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
178 \subsection{PeCO Protocol Algorithm}
179 \label{ch6:sec:02:03}
182 \noindent The pseudocode implementing the protocol on a node is given below.
183 More precisely, Algorithm~\ref{alg:PeCO} gives a brief description of the
184 protocol applied by a sensor node $s_j$ where $j$ is the node index in the WSN.
186 \begin{algorithm}[h!]
187 % \KwIn{all the parameters related to information exchange}
188 % \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
190 %\emph{Initialize the sensor node and determine it's position and subregion} \;
192 \If{ $RE_k \geq E_{th}$ }{
193 \emph{$s_j.status$ = COMMUNICATION}\;
194 \emph{Send $INFO()$ packet to other nodes in subregion}\;
195 \emph{Wait $INFO()$ packet from other nodes in subregion}\;
196 \emph{Update A.CurrentSize}\;
197 \emph{LeaderID = Leader election}\;
198 \If{$ s_j.ID = LeaderID $}{
199 \emph{$s_j.status$ = COMPUTATION}\;
201 \If{$ s_j.ID $ is Not previously selected as a Leader }{
202 \emph{ Execute the perimeter coverage model}\;
203 % \emph{ Determine the segment points using perimeter coverage model}\;
206 \If{$ (s_j.ID $ is the same Previous Leader) And (A.CurrentSize = A.PreviousSize)}{
208 \emph{ Use the same previous cover set for current sensing stage}\;
211 \emph{Update $a^j_{ik}$; prepare data for IP~Algorithm}\;
212 \emph{$\left\{\left(X_{1},\dots,X_{k},\dots,X_{A}\right)\right\}$ = Execute Integer Program Algorithm($A$)}\;
213 \emph{A.PreviousSize = A.CurrentSize}\;
216 \emph{$s_j.status$ = COMMUNICATION}\;
217 \emph{Send $ActiveSleep()$ to each node $k$ in subregion}\;
218 \emph{Update $RE_j $}\;
221 \emph{$s_j.status$ = LISTENING}\;
222 \emph{Wait $ActiveSleep()$ packet from the Leader}\;
223 \emph{Update $RE_j $}\;
226 \Else { Exclude $s_j$ from entering in the current sensing stage}
227 \caption{PeCO($s_j$)}
231 In this algorithm, A.CurrentSize and A.PreviousSize respectively represent the
232 current number and the previous number of living nodes in the subnetwork of the
233 subregion. Initially, the sensor node checks its remaining energy $RE_j$, which
234 must be greater than a threshold $E_{th}$ in order to participate in the current
235 period. Each sensor node determines its position and its subregion using an
236 embedded GPS or a location discovery algorithm. After that, all the sensors
237 collect position coordinates, remaining energy, sensor node ID, and the number
238 of their one-hop live neighbors during the information exchange. The sensors
239 inside a same region cooperate to elect a leader. The selection criteria for the
240 leader, in order of priority, are larger numbers of neighbors, larger remaining
241 energy, and then in case of equality, larger index. Once chosen, the leader
242 collects information to formulate and solve the integer program which allows to
243 construct the set of active sensors in the sensing stage.
247 \section{Perimeter-based Coverage Problem Formulation}
251 \noindent In this section, the coverage model is mathematically formulated. We
252 start with a description of the notations that will be used throughout the
255 First, we have the following sets:
257 \item $J$ represents the set of WSN sensor nodes;
258 \item $A \subseteq J $ is the subset of alive sensors;
259 \item $I_j$ designates the set of coverage intervals (CI) obtained for
262 $I_j$ refers to the set of coverage intervals which have been defined according
263 to the method introduced in subsection~\ref{ch6:sec:02:01}. For a coverage interval $i$,
264 let $a^j_{ik}$ denotes the indicator function of whether sensor~$k$ is involved
265 in coverage interval~$i$ of sensor~$j$, that is:
269 1 & \mbox{if sensor $k$ is involved in the } \\
270 & \mbox{coverage interval $i$ of sensor $j$}, \\
271 0 & \mbox{otherwise.}\\
276 Note that $a^k_{ik}=1$ by definition of the interval.
278 Second, we define several binary and integer variables. Hence, each binary
279 variable $X_{k}$ determines the activation of sensor $k$ in the sensing phase
280 ($X_k=1$ if the sensor $k$ is active or 0 otherwise). $M^j_i$ is an integer
281 variable which measures the undercoverage for the coverage interval $i$
282 corresponding to sensor~$j$. In the same way, the overcoverage for the same
283 coverage interval is given by the variable $V^j_i$.
285 If we decide to sustain a level of coverage equal to $l$ all along the perimeter
286 of sensor $j$, we have to ensure that at least $l$ sensors involved in each
287 coverage interval $i \in I_j$ of sensor $j$ are active. According to the
288 previous notations, the number of active sensors in the coverage interval $i$ of
289 sensor $j$ is given by $\sum_{k \in A} a^j_{ik} X_k$. To extend the network
290 lifetime, the objective is to activate a minimal number of sensors in each
291 period to ensure the desired coverage level. As the number of alive sensors
292 decreases, it becomes impossible to reach the desired level of coverage for all
293 coverage intervals. Therefore, we use variables $M^j_i$ and $V^j_i$ as a measure
294 of the deviation between the desired number of active sensors in a coverage
295 interval and the effective number. And we try to minimize these deviations,
296 first to force the activation of a minimal number of sensors to ensure the
297 desired coverage level, and if the desired level cannot be completely satisfied,
298 to reach a coverage level as close as possible to the desired one.
300 Our coverage optimization problem can then be mathematically expressed as follows:
302 \begin{equation} %\label{eq:ip2r}
305 \min \sum_{j \in J} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
306 \textrm{subject to :}&\\
307 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in J\\
309 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in J\\
311 % \Theta_{p}\in \mathbb{N}, &\forall p \in P\\
312 % U_{p} \in \{0,1\}, &\forall p \in P\\
313 X_{k} \in \{0,1\}, \forall k \in A
318 $\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the
319 relative importance of satisfying the associated level of coverage. For example,
320 weights associated with coverage intervals of a specified part of a region may
321 be given by a relatively larger magnitude than weights associated with another
322 region. This kind of an integer program is inspired from the model developed for
323 brachytherapy treatment planning for optimizing dose distribution
324 \cite{0031-9155-44-1-012}. The integer program must be solved by the leader in
325 each subregion at the beginning of each sensing phase, whenever the environment
326 has changed (new leader, death of some sensors). Note that the number of
327 constraints in the model is constant (constraints of coverage expressed for all
328 sensors), whereas the number of variables $X_k$ decreases over periods, since we
329 consider only alive sensors (sensors with enough energy to be alive during one
330 sensing phase) in the model.
332 \section{Performance Evaluation and Analysis}
335 \subsection{Simulation Settings}
336 \label{ch6:sec:04:01}
338 The WSN area of interest is supposed to be divided into 16~regular subregions. %and we use the same energy consumption than in our previous work~\cite{Idrees2}.
339 Table~\ref{table3} gives the chosen parameters settings.
342 \caption{Relevant parameters for network initialization.}
345 % used for centering table
347 % centered columns (4 columns)
349 Parameter & Value \\ [0.5ex]
352 % inserts single horizontal line
353 Sensing field & $(50 \times 25)~m^2 $ \\
355 WSN size & 100, 150, 200, 250, and 300~nodes \\
357 Initial energy & in range 500-700~Joules \\
359 Sensing period & duration of 60 minutes \\
360 $E_{th}$ & 36~Joules\\
363 $\alpha^j_i$ & 0.6 \\
364 % [1ex] adds vertical space
370 % is used to refer this table in the text
374 To obtain experimental results which are relevant, simulations with five
375 different node densities going from 100 to 300~nodes were performed considering
376 each time 25~randomly generated networks. The nodes are deployed on a field of
377 interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
379 %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.
382 The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good
383 network coverage and a longer WSN lifetime. We have given a higher priority to
384 the undercoverage (by setting the $\alpha^j_i$ with a larger value than
385 $\beta^j_i$) so as to prevent the non-coverage for the interval~$i$ of the
386 sensor~$j$. On the other hand, we have assigned to
387 $\beta^j_i$ a value which is slightly lower so as to minimize the number of active sensor nodes which contribute in covering the interval.
389 With the performance metrics, described in chapter 4, 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 chapter 4, section \ref{ch4:sec:04:02}. In addition, we use the same energy consumption model, presented in chapter 4, section \ref{ch4:sec:04:03}.
392 \subsection{Simulation Results}
393 \label{ch6:sec:04:02}
395 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.
396 %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.
397 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 ($l=1$).
401 \subsubsection{Coverage Ratio}
402 \label{ch6:sec:04:02:01}
404 Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes
405 obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better
406 coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the 98.76\%
407 produced by PeCO for the first periods. This is due to the fact that at the
408 beginning the DiLCO protocol puts to sleep status more redundant sensors (which
409 slightly decreases the coverage ratio), while the three other protocols activate
410 more sensor nodes. Later, when the number of periods is beyond~70, it clearly
411 appears that PeCO provides a better coverage ratio and keeps a coverage ratio
412 greater than 50\% for longer periods (15 more compared to DiLCO, 40 more
413 compared to DESK). The energy saved by PeCO in the early periods allows later a
414 substantial increase of the coverage performance.
419 \includegraphics[scale=0.8] {Figures/ch6/R/CR.eps}
420 \caption{Coverage ratio for 200 deployed nodes.}
426 \subsubsection{Active Sensors Ratio}
427 \label{ch6:sec:04:02:02}
429 Having the less active sensor nodes in each period is essential to minimize the
430 energy consumption and thus to maximize the network lifetime. Figure~\ref{fig444}
431 shows the average active nodes ratio for 200 deployed nodes. We observe that
432 DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen
433 rounds and DiLCO and PeCO protocols compete perfectly with only 17.92 \% and
434 20.16 \% active nodes during the same time interval. As the number of periods
435 increases, PeCO protocol has a lower number of active nodes in comparison with
436 the three other approaches, while keeping a greater coverage ratio as shown in
441 \includegraphics[scale=0.8]{Figures/ch6/R/ASR.eps}
442 \caption{Active sensors ratio for 200 deployed nodes.}
446 \subsubsection{The Energy Consumption}
447 \label{ch6:sec:04:02:03}
449 We studied the effect of the energy consumed by the WSN during the communication,
450 computation, listening, active, and sleep status for different network densities
451 and compared it for the four approaches. Figures~\ref{fig3EC}(a) and (b)
452 illustrate the energy consumption for different network sizes and for
453 $Lifetime95$ and $Lifetime50$. The results show that our PeCO protocol is the
454 most competitive from the energy consumption point of view. As shown in both
455 figures, PeCO consumes much less energy than the three other methods. One might
456 think that the resolution of the integer program is too costly in energy, but
457 the results show that it is very beneficial to lose a bit of time in the
458 selection of sensors to activate. Indeed the optimization program allows to
459 reduce significantly the number of active sensors and so the energy consumption
460 while keeping a good coverage level.
464 \begin{tabular}{@{}cr@{}}
465 \includegraphics[scale=0.8]{Figures/ch6/R/EC95.eps} & \raisebox{4cm}{(a)} \\
466 \includegraphics[scale=0.8]{Figures/ch6/R/EC50.eps} & \raisebox{4cm}{(b)}
468 \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
474 \subsubsection{The Network Lifetime}
475 \label{ch6:sec:04:02:04}
477 We observe the superiority of PeCO and DiLCO protocols in comparison with the
478 two other approaches in prolonging the network lifetime. In
479 Figures~\ref{fig3LT}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for
480 different network sizes. As highlighted by these figures, the lifetime
481 increases with the size of the network, and it is clearly largest for DiLCO
482 and PeCO protocols. For instance, for a network of 300~sensors and coverage
483 ratio greater than 50\%, we can see on Figure~\ref{fig3LT}(b) that the lifetime
484 is about twice longer with PeCO compared to DESK protocol. The performance
485 difference is more obvious in Figure~\ref{fig3LT}(b) than in
486 Figure~\ref{fig3LT}(a) because the gain induced by our protocols increases with
487 time, and the lifetime with a coverage of 50\% is far longer than with
492 \begin{tabular}{@{}cr@{}}
493 \includegraphics[scale=0.8]{Figures/ch6/R/LT95.eps} & \raisebox{4cm}{(a)} \\
494 \includegraphics[scale=0.8]{Figures/ch6/R/LT50.eps} & \raisebox{4cm}{(b)}
496 \caption{Network Lifetime for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
500 Figure~\ref{figLTALL} compares the lifetime coverage of our protocols for
501 different coverage ratios. We denote by Protocol/50, Protocol/80, Protocol/85,
502 Protocol/90, and Protocol/95 the amount of time during which the network can
503 satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$
504 respectively, where the term Protocol refers to DiLCO or PeCO. Indeed there are applications
505 that do not require a 100\% coverage of the area to be monitored. PeCO might be
506 an interesting method since it achieves a good balance between a high level
507 coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three
508 lower coverage ratios, moreover the improvements grow with the network
509 size. DiLCO is better for coverage ratios near 100\%, but in that case PeCO is
510 not ineffective for the smallest network sizes.
513 \centering \includegraphics[scale=0.8]{Figures/ch6/R/LTa.eps}
514 \caption{Network lifetime for different coverage ratios.}
523 In this chapter, we have studied the problem of Perimeter-based Coverage Optimization in
524 WSNs. We have designed a new protocol, called Perimeter-based Coverage Optimization, which
525 schedules nodes' activities (wake up and sleep stages) with the objective of
526 maintaining a good coverage ratio while maximizing the network lifetime. This
527 protocol is applied in a distributed way in regular subregions obtained after
528 partitioning the area of interest in a preliminary step. It works in periods and
529 is based on the resolution of an integer program to select the subset of sensors
530 operating in active status for each period. Our work is original in so far as it
531 proposes for the first time an integer program scheduling the activation of
532 sensors based on their perimeter coverage level, instead of using a set of
533 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
536 We plan to extend our framework so that the schedules are planned for multiple
538 %in order to compute all active sensor schedules in only one step for many periods;
539 We also want to improve our integer program to take into account heterogeneous
540 sensors from both energy and node characteristics point of views.
541 %the third, we are investigating new optimization model based on the sensing range so as to maximize the lifetime coverage in WSN;
542 Finally, it would be interesting to implement our protocol using a
543 sensor-testbed to evaluate it in real world applications.
