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7 \chapter{Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}
14 In this chapter, a Distributed Lifetime Coverage Optimization protocol (DiLCO) to maintain
15 the coverage and to improve the lifetime in wireless sensor networks is
16 proposed. The area of interest is first divided into subregions using a
17 divide-and-conquer method and then the DiLCO protocol is distributed on the
18 sensor nodes in each subregion. The DiLCO combines two efficient techniques:
19 leader election for each subregion, followed by an optimization-based planning
20 of activity scheduling decisions for each subregion. The proposed DiLCO works
21 into rounds during which a small number of nodes, remaining active for sensing,
22 is selected to ensure coverage so as to maximize the lifetime of wireless sensor
23 network. Each round consists of four phases: (i)~Information Exchange,
24 (ii)~Leader Election, (iii)~Decision, and (iv)~Sensing. The decision process is
25 carried out by a leader node, which solves an integer program. Compared with
26 some existing protocols, simulation results show that the proposed protocol can
27 prolong the network lifetime and improve the coverage performance effectively.
30 \section{Description of the DiLCO Protocol}
33 \noindent In this section, we introduce the DiLCO protocol which is distributed on each subregion in the area of interest. It is based on two efficient
34 techniques: network leader election and sensor activity scheduling for coverage preservation and energy conservation, applied periodically to efficiently maximize the lifetime in the network.
36 \subsection{Assumptions and Network Model}
38 \noindent We consider a sensor network composed of static nodes distributed independently and uniformly at random. A high-density deployment ensures a high coverage ratio of the interested area at the start. The nodes are supposed to have homogeneous characteristics from a communication and a processing point of view, whereas they have heterogeneous energy provisions. Each node has access to its location thanks, either to a hardware component (like a GPS unit) or a location discovery algorithm. Furthermore, we assume that sensor nodes are time synchronized in order to properly coordinate their operations to achieve complex sensing tasks~\cite{ref157}. The two sensor nodes have been supposed neighbors if the euclidean distance between them is at most equal to 2$R_s$.
41 \indent We consider a boolean disk coverage model which is the most widely used sensor coverage model in the literature. Thus, since a sensor has a constant sensing range $R_s$, every space points within a disk centered at a sensor with the radius of the sensing range is said to be covered with this sensor. We also assume that the communication range $R_c$ is at least twice the sensing range $R_s$ (i.e., $R_c \geq 2R_s$). In fact, Zhang and Hou~\cite{ref126} proved that if the transmission range fulfills the previous hypothesis, a complete coverage of a convex area implies connectivity among the working nodes in the active mode. We assume that each sensor node can directly transmit its measurements toward a mobile sink node. For example, a sink can be an unmanned aerial vehicle (UAV) is flying regularly over the sensor field to collect measurements from sensor nodes. A mobile sink node collects the measurements and transmits them to the base station.
43 During the execution of the DiLCO protocol, two kinds of packet will be used:
45 \begin{enumerate} [(i)]
46 \item \textbf{INFO packet:} sent by each sensor node to all the nodes inside a same subregion for information exchange.
47 \item \textbf{ActiveSleep packet:} sent by the leader to all the nodes in its subregion to inform them to stay Active or to go Sleep during the sensing phase.
50 There are five possible status for each sensor node in the network:
51 %and each sensor node will have five possible status in the network:
52 \begin{enumerate}[(i)]
53 \item \textbf{LISTENING:} sensor is waiting for a decision (to be active or not).
54 \item \textbf{COMPUTATION:} sensor applies the optimization process as leader.
55 \item \textbf{ACTIVE:} sensor is active.
56 \item \textbf{SLEEP:} sensor is turned off.
57 \item \textbf{COMMUNICATION:} sensor is transmitting or receiving packet.
60 \subsection{Primary Point Coverage Model}
62 \indent Instead of working with the coverage area, we consider for each sensor a set of points called primary points. We also assume that the sensing disk defined by a sensor is covered if all the primary points of this sensor are covered. By knowing the position (point center: ($p_x,p_y$)) of a wireless sensor node and it's $R_s$, we calculate the primary points directly based on the proposed model. We use these primary points (that can be increased or decreased if necessary) as references to ensure that the monitored region of interest is covered by the selected set of sensors, instead of using all the points in the area.
64 \indent We can calculate the positions of the selected primary
65 points in the circle disk of the sensing range of a wireless sensor
66 node (see figure~\ref{fig1}) as follows:\\
68 $(p_x,p_y)$ = point center of wireless sensor node\\
70 $X_2=( p_x + R_s * (1), p_y + R_s * (0) )$\\
71 $X_3=( p_x + R_s * (-1), p_y + R_s * (0)) $\\
72 $X_4=( p_x + R_s * (0), p_y + R_s * (1) )$\\
73 $X_5=( p_x + R_s * (0), p_y + R_s * (-1 )) $\\
74 $X_6= ( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (0)) $\\
75 $X_7=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (0))$\\
76 $X_8=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
77 $X_9=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
78 $X_{10}=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
79 $X_{11}=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
80 $X_{12}=( p_x + R_s * (0), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
81 $X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
82 $X_{14}=( p_x + R_s * (\frac{\sqrt{3}}{2}), p_y + R_s * (\frac{1}{2})) $\\
83 $X_{15}=( p_x + R_s * (\frac{-\sqrt{3}}{2}), p_y + R_s * (\frac{1}{2})) $\\
84 $X_{16}=( p_x + R_s * (\frac{\sqrt{3}}{2}), p_y + R_s * (\frac{- 1}{2})) $\\
85 $X_{17}=( p_x + R_s * (\frac{-\sqrt{3}}{2}), p_y + R_s * (\frac{- 1}{2})) $\\
86 $X_{18}=( p_x + R_s * (\frac{\sqrt{3}}{2}), p_y + R_s * (0) $\\
87 $X_{19}=( p_x + R_s * (\frac{-\sqrt{3}}{2}), p_y + R_s * (0) $\\
88 $X_{20}=( p_x + R_s * (0), p_y + R_s * (\frac{1}{2})) $\\
89 $X_{21}=( p_x + R_s * (0), p_y + R_s * (-\frac{1}{2})) $\\
90 $X_{22}=( p_x + R_s * (\frac{1}{2}), p_y + R_s * (\frac{\sqrt{3}}{2})) $\\
91 $X_{23}=( p_x + R_s * (\frac{- 1}{2}), p_y + R_s * (\frac{\sqrt{3}}{2})) $\\
92 $X_{24}=( p_x + R_s * (\frac{- 1}{2}), p_y + R_s * (\frac{-\sqrt{3}}{2})) $\\
93 $X_{25}=( p_x + R_s * (\frac{1}{2}), p_y + R_s * (\frac{-\sqrt{3}}{2})) $.
99 \includegraphics[scale=0.20]{Figures/ch4/fig21.pdf}\\~ ~ ~ ~ ~(a)
100 \includegraphics[scale=0.20]{Figures/ch4/fig22.pdf}\\~ ~ ~ ~ ~(b)
101 \includegraphics[scale=0.20]{Figures/ch4/principles13.pdf}\\~ ~ ~ ~ ~(c)
103 \includegraphics[scale=0.20]{Figures/ch4/fig24.pdf}\\~ ~ ~(d)
104 \includegraphics[scale=0.20]{Figures/ch4/fig25.pdf}\\~ ~ ~(e)
105 \includegraphics[scale=0.20]{Figures/ch4/fig26.pdf}\\~ ~ ~(f)
107 \caption{Wireless Sensor Node represented by (a)5, (b)9, (c)13, (d)17, (e)21 and (f)25 primary points respectively}
113 \subsection{Main Idea}
114 \label{ch4:sec:02:03}
115 \noindent We start by applying a divide-and-conquer algorithm to partition the area of interest into smaller areas called subregions and then our protocol is executed simultaneously in each subregion.
119 \includegraphics[scale=0.80]{Figures/ch4/FirstModel.pdf} % 70mm
120 \caption{DiLCO protocol}
124 As shown in Figure~\ref{FirstModel}, the proposed DiLCO protocol is a periodic protocol where each period is decomposed into 4~phases: Information Exchange, Leader Election, Decision, and Sensing. For each period, there will be exactly one cover set in charge of the sensing task. A periodic scheduling is interesting because it enhances the robustness of the network against node failures. First, a node that has not enough energy to complete a period, or which fails before the decision is taken, will be excluded from the scheduling
125 process. Second, if a node fails later, whereas it was supposed to sense the region of interest, it will only affect the quality of the coverage until the definition of a new cover set in the next period. Constraints, like energy consumption, can be easily taken into consideration since the sensors can update and exchange their information during the first phase. Let us notice that the
126 phases before the sensing one (Information Exchange, Leader Election, and Decision) are energy consuming for all the nodes, even nodes that will not be retained by the leader to keep watch over the corresponding area.
129 Below, we describe each phase in more details.
131 \subsubsection{Information Exchange Phase}
132 \label{ch4:sec:02:03:01}
133 Each sensor node $j$ sends its position, remaining energy $RE_j$, and the number
134 of neighbors $NBR_j$ to all wireless sensor nodes in its subregion by using an
135 INFO packet (containing information on position coordinates, current remaining
136 energy, sensor node ID, number of its one-hop live neighbors) and then waits for
137 packets sent by other nodes. After that, each node will have information about
138 all the sensor nodes in the subregion. In our model, the remaining energy
139 corresponds to the time that a sensor can live in the active mode.
141 \subsubsection{Leader Election Phase}
142 \label{ch4:sec:02:03:02}
143 This step includes choosing the Wireless Sensor Node Leader (WSNL), which will be responsible for executing the coverage algorithm. Each subregion in the area of interest will select its own WSNL independently for each round. All the sensor nodes cooperate to select WSNL. The nodes in the same subregion will select the leader based on the received information from all other nodes in the same subregion. The selection criteria are, in order of importance: larger number of neighbors, larger remaining energy, and then in case of equality, larger index. Observations on previous simulations suggest using the number of one-hop neighbors as the primary criterion to reduce energy consumption due to the communications.
146 \subsubsection{Decision phase}
147 \label{ch4:sec:02:03:03}
148 The WSNL will solve an integer program (see section~\ref{ch4:sec:03}) to select which sensors will be activated in the following sensing phase to cover the subregion. WSNL will send Active-Sleep packet to each sensor in the subregion based on the algorithm's results.
151 \subsubsection{Sensing phase}
152 \label{ch4:sec:02:03:04}
153 Active sensors in the round will execute their sensing task to
154 preserve maximal coverage in the region of interest. We will assume
155 that the cost of keeping a node awake (or asleep) for sensing task is
156 the same for all wireless sensor nodes in the network. Each sensor
157 will receive an Active-Sleep packet from WSNL informing it to stay
158 awake or to go to sleep for a time equal to the period of sensing until
159 starting a new round.
161 An outline of the protocol implementation is given by Algorithm~\ref{alg:DiLCO} which describes the execution of a period by a node (denoted by $s_j$ for a sensor node indexed by $j$). In the beginning, a node checks whether it has enough energy to stay active during the next sensing phase. If yes, it exchanges information with all the other nodes belonging to the same subregion: it collects from each node its position coordinates, remaining energy ($RE_j$), ID,
162 and the number of one-hop neighbors still alive. Once the first phase is completed, the nodes of a subregion choose a leader to take the decision based on the following criteria with decreasing importance: larger number of neighbors, larger remaining energy, and then in case of equality, larger index. After that, if the sensor node is leader, it will execute the integer program algorithm (see Section~\ref{ch4:sec:03}) which provides a set of sensors planned to be active in the next sensing phase. As leader, it will send an Active-Sleep packet to each sensor in the same subregion to indicate it if it has to be active or not. Alternately, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the coming sensing phase.
164 \begin{algorithm}[h!]
167 %\emph{Initialize the sensor node and determine it's position and subregion} \;
169 \If{ $RE_j \geq E_{th}$ }{
170 \emph{$s_j.status$ = COMMUNICATION}\;
171 \emph{Send $INFO()$ packet to other nodes in the subregion}\;
172 \emph{Wait $INFO()$ packet from other nodes in the subregion}\;
173 %\emph{UPDATE $RE_j$ for every sent or received INFO Packet}\;
174 %\emph{ Collect information and construct the list L for all nodes in the subregion}\;
176 %\If{ the received INFO Packet = No. of nodes in it's subregion -1 }{
177 \emph{LeaderID = Leader election}\;
178 \If{$ s_j.ID = LeaderID $}{
179 \emph{$s_j.status$ = COMPUTATION}\;
180 \emph{$\left\{\left(X_{1},\dots,X_{k},\dots,X_{J}\right)\right\}$ =
181 Execute Integer Program Algorithm($J$)}\;
182 \emph{$s_j.status$ = COMMUNICATION}\;
183 \emph{Send $ActiveSleep()$ to each node $k$ in subregion} \;
184 \emph{Update $RE_j $}\;
187 \emph{$s_j.status$ = LISTENING}\;
188 \emph{Wait $ActiveSleep()$ packet from the Leader}\;
190 \emph{Update $RE_j $}\;
194 \Else { Exclude $s_j$ from entering in the current sensing phase}
197 \caption{DiLCO($s_j$)}
204 \section{Primary Points based Coverage Problem Formulation}
206 \indent Our model is based on the model proposed by \cite{ref156} where the
207 objective is to find a maximum number of disjoint cover sets. To accomplish
208 this goal, the authors proposed an integer program which forces undercoverage
209 and overcoverage of targets to become minimal at the same time. They use binary
210 variables $x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our
211 model, we consider that the binary variable $X_{j}$ determines the activation of
212 sensor $j$ in the sensing phase. We also consider primary points as targets.
213 The set of primary points is denoted by $P$ and the set of sensors by $J$.
215 \noindent Let $\alpha_{jp}$ denote the indicator function of whether the primary
216 point $p$ is covered, that is:
218 \alpha_{jp} = \left \{
220 1 & \mbox{if the primary point $p$ is covered} \\
221 & \mbox{by sensor node $j$}, \\
222 0 & \mbox{otherwise.}\\
226 The number of active sensors that cover the primary point $p$ can then be
227 computed by $\sum_{j \in J} \alpha_{jp} * X_{j}$ where:
231 1& \mbox{if sensor $j$ is active,} \\
232 0 & \mbox{otherwise.}\\
236 We define the Overcoverage variable $\Theta_{p}$ as:
238 \Theta_{p} = \left \{
240 0 & \mbox{if the primary point}\\
241 & \mbox{$p$ is not covered,}\\
242 \left( \sum_{j \in J} \alpha_{jp} * X_{j} \right)- 1 & \mbox{otherwise.}\\
246 \noindent More precisely, $\Theta_{p}$ represents the number of active sensor
247 nodes minus one that cover the primary point~$p$. The Undercoverage variable
248 $U_{p}$ of the primary point $p$ is defined by:
252 1 &\mbox{if the primary point $p$ is not covered,} \\
253 0 & \mbox{otherwise.}\\
258 \noindent Our coverage optimization problem can then be formulated as follows:
259 \begin{equation} \label{eq:ip2r}
262 \min \sum_{p \in P} (w_{\theta} \Theta_{p} + w_{U} U_{p})&\\
263 \textrm{subject to :}&\\
264 \sum_{j \in J} \alpha_{jp} X_{j} - \Theta_{p}+ U_{p} =1, &\forall p \in P\\
266 %\sum_{t \in T} X_{j,t} \leq \frac{RE_j}{e_t} &\forall j \in J \\
268 \Theta_{p}\in \mathbb{N}, &\forall p \in P\\
269 U_{p} \in \{0,1\}, &\forall p \in P \\
270 X_{j} \in \{0,1\}, &\forall j \in J
276 \item $X_{j}$ : indicates whether or not the sensor $j$ is actively sensing (1
277 if yes and 0 if not);
278 \item $\Theta_{p}$ : {\it overcoverage}, the number of sensors minus one that
279 are covering the primary point $p$;
280 \item $U_{p}$ : {\it undercoverage}, indicates whether or not the primary point
281 $p$ is being covered (1 if not covered and 0 if covered).
284 The first group of constraints indicates that some primary point $p$ should be
285 covered by at least one sensor and, if it is not always the case, overcoverage
286 and undercoverage variables help balancing the restriction equations by taking
287 positive values. Two objectives can be noticed in our model. First, we limit the
288 overcoverage of primary points to activate as few sensors as possible. Second,
289 to avoid a lack of area monitoring in a subregion we minimize the
290 undercoverage. Both weights $w_\theta$ and $w_U$ must be carefully chosen in
291 order to guarantee that the maximum number of points are covered during each
293 \section{Simulation Results and Analysis}
296 \subsection{Simulation Framework}
297 \label{ch4:sec:04:01}
299 To assess the performance of DiLCO protocol, we have used the discrete event simulator OMNeT++ \cite{ref158} to run different series of simulations. Table~\ref{tablech4} gives the chosen parameters setting.
302 \caption{Relevant parameters for network initializing.}
305 % used for centering table
307 % centered columns (4 columns)
309 %inserts double horizontal lines
310 Parameter & Value \\ [0.5ex]
314 % inserts single horizontal line
315 Sensing Field & $(50 \times 25)~m^2 $ \\
316 % inserting body of the table
318 Nodes Number & 50, 100, 150, 200 and 250~nodes \\
320 Initial Energy & 500-700~joules \\
322 Sensing Period & 60 Minutes \\
323 $E_{th}$ & 36 Joules\\
327 % [1ex] adds vertical space
333 % is used to refer this table in the text
336 Simulations with five different node densities going from 50 to 250~nodes were
337 performed considering each time 25~randomly generated networks, to obtain
338 experimental results which are relevant. The nodes are deployed on a field of
339 interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
343 \subsection{Modeling Language and Optimization Solver}
344 \label{ch4:sec:04:02}
345 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.
347 \subsection{Energy Consumption Model}
348 \label{ch4:sec:04:03}
350 \indent In this dissertation, we used an energy consumption model proposed by~\cite{DESK} and based on \cite{ref112} with slight modifications. The energy consumption for sending/receiving the packets is added, whereas the part related to the sensing range is removed because we consider a fixed sensing range.
352 \indent For our energy consumption model, we refer to the sensor node Medusa~II which uses an Atmel's AVR ATmega103L microcontroller~\cite{ref112}. The typical architecture of a sensor is composed of four subsystems: the MCU subsystem which is capable of computation, communication subsystem (radio) which is responsible for transmitting/receiving messages, the sensing subsystem that collects data, and the power supply which powers the complete sensor node \cite{ref112}. Each of the first three subsystems can be turned on or off depending on the current status of the sensor. Energy consumption (expressed in milliWatt per second) for the different status of the sensor is summarized in Table~\ref{table1}.
355 \caption{The Energy Consumption Model}
358 % used for centering table
359 \begin{tabular}{|c|c|c|c|c|}
360 % centered columns (4 columns)
362 %inserts double horizontal lines
363 Sensor status & MCU & Radio & Sensing & Power (mW) \\ [0.5ex]
365 % inserts single horizontal line
366 LISTENING & on & on & on & 20.05 \\
367 % inserting body of the table
369 ACTIVE & on & off & on & 9.72 \\
371 SLEEP & off & off & off & 0.02 \\
373 COMPUTATION & on & on & on & 26.83 \\
375 %\multicolumn{4}{|c|}{Energy needed to send/receive a 1-bit} & 0.2575\\
380 % is used to refer this table in the text
383 \indent For the sake of simplicity we ignore the energy needed to turn on the radio, to start up the sensor node, to move from one status to another, etc. Thus, when a sensor becomes active (i.e., it has already chosen its status), it can turn its radio off to save battery. The value of energy spent to send a 1-bit-content message is obtained by using the equation in ~\cite{ref112} to calculate the energy cost for transmitting messages and we propose the same value for receiving the packets. The energy needed to send or receive a 1-bit packet is equal to $0.2575~mW$.
386 %We have used an energy consumption model, which is presented in chapter 1, section \ref{ch1:sec9:subsec2}.
388 The initial energy of each node is randomly set in the interval $[500;700]$. A sensor node will not participate in the next round if its remaining energy is less than $E_{th}=36~\mbox{Joules}$, the minimum energy needed for the node to stay alive during one round. This value has been computed by multiplying the energy consumed in the active state (9.72 mW) by the time in second for one round (3600 seconds), and adding the energy for the pre-sensing phases. According to the interval of initial energy, a sensor may be alive during at most 20 rounds.
391 \subsection{Performance Metrics}
392 \label{ch4:sec:04:04}
393 In the simulations, we introduce the following performance metrics to evaluate
394 the efficiency of our approach:
396 \begin{enumerate}[i)]
398 \item {{\bf Network Lifetime}:} we define the network lifetime as the time until
399 the coverage ratio drops below a predefined threshold. We denote by
400 $Lifetime_{95}$ (respectively $Lifetime_{50}$) the amount of time during which
401 the network can satisfy an area coverage greater than $95\%$ (respectively
402 $50\%$). We assume that the sensor network can fulfill its task until all its
403 nodes have been drained of their energy or it becomes disconnected. Network
404 connectivity is crucial because an active sensor node without connectivity
405 towards a base station cannot transmit any information regarding an observed
406 event in the area that it monitors.
408 \item {{\bf Coverage Ratio (CR)}:} it measures how well the WSN is able to
409 observe the area of interest. In our case, we discretized the sensor field
410 as a regular grid, which yields the following equation to compute the
414 \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100.
416 where $n$ is the number of covered grid points by active sensors of every
417 subregions during the current sensing phase and $N$ is the total number of grid
418 points in the sensing field. In our simulations, we have a layout of $N = 51
419 \times 26 = 1326$ grid points.
421 \item {{\bf Energy Consumption}:} energy consumption (EC) can be seen as the
422 total amount of energy consumed by the sensors during $Lifetime_{95}$
423 or $Lifetime_{50}$, divided by the number of periods. Formally, the computation
424 of EC can be expressed as follows:
427 \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m
428 + E^{a}_m+E^{s}_m \right)}{M},
431 where $M$ corresponds to the number of periods. The total amount of energy consumed by the sensors (EC) comes through taking into consideration four main energy factors. The first one, denoted $E^{\scriptsize \mbox{com}}_m$, represents the energy consumption spent by all the nodes for wireless communications during the period $m$. $E^{\scriptsize \mbox{list}}_m$, the next
432 factor, corresponds to the energy consumed by the sensors in LISTENING status before receiving the decision to go active or sleep in the period $m$. $E^{\scriptsize \mbox{comp}}_m$ refers to the energy needed for all the leader nodes to solve the integer program during a period. Finally, $E^a_{m}$ and $E^s_{m}$ indicate the energy consumed by the whole network in the sensing phase
433 (active and sleeping nodes).
435 \item{{\bf Number of Active Sensors Ratio(ASR)}:} It is important to have as few active nodes as possible in each round,
436 in order to minimize the communication overhead and maximize the
437 network lifetime. The Active Sensors Ratio is defined as follows:
440 \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$A_r$}}{\mbox{$S$}} \times 100 .
442 Where: $A_r$ is the number of active sensors in the subregion $r$ during current period, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.
444 \item {{\bf Execution Time}:} a sensor node has limited energy resources and computing power, therefore it is important that the proposed algorithm has the shortest possible execution time. The energy of a sensor node must be mainly used for the sensing phase, not for the pre-sensing ones. In this dissertation, the original execution time is computed on a laptop DELL with Intel Core~i3~2370~M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmel's AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6 to run the optimization resolution, this time is multiplied by 2944.2 $\left( \frac{35330}{2} \times \frac{1}{6} \right)$.
446 \item {{\bf Stopped simulation runs}:} A simulation ends when the sensor network becomes disconnected (some nodes are dead and are not able to send information to the base station). We report the number of simulations that are stopped due to network disconnections and for which round it occurs ( in chapter 3, period consists of one round).
452 \subsection{Performance Analysis for Different Subregions}
453 \label{ch4:sec:04:05}
455 In this subsection, we are studied the performance of our DiLCO protocol for a different number of subregions (Leaders).
456 The DiLCO-1 protocol is a centralized approach to all the area of the interest, while DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 are distributed on two, four, eight, sixteen, and thirty-two subregions respectively. We did not take the DiLCO-1 protocol in our simulation results because it needs a high execution time to give the decision leading to consume all its energy before producing the solution for the optimization problem.
458 \begin{enumerate}[i)]
459 \item {{\bf Coverage Ratio}}
460 %\subsubsection{Coverage Ratio}
461 %\label{ch4:sec:04:02:01}
462 In this experiment, Figure~\ref{Figures/ch4/R1/CR} shows the average coverage ratio for 150 deployed nodes.
466 \includegraphics[scale=0.8] {Figures/ch4/R1/CR.pdf}
467 \caption{Coverage ratio for 150 deployed nodes}
468 \label{Figures/ch4/R1/CR}
470 It can be seen that DiLCO protocol (with 4, 8, 16 and 32 subregions) gives nearly similar coverage ratios during the first thirty rounds.
471 DiLCO-2 protocol gives near similar coverage ratio with other ones for first 10 rounds and then decreased until the died of the network in the round $18^{th}$ because it consumes more energy with the effect of the network disconnection.
472 As shown in the figure ~\ref{Figures/ch4/R1/CR}, as the number of subregions increases, the coverage preservation for the area of interest increases for a larger number of rounds. Coverage ratio decreases when the number of rounds increases due to dead nodes. Although some nodes are dead, thanks to DiLCO-8, DiLCO-16, and DiLCO-32 protocols, other nodes are preserved to ensure the coverage. Moreover, when we have a dense sensor network, it leads to maintain the coverage for a larger number of rounds. DiLCO-8, DiLCO-16, and DiLCO-32 protocols are slightly more efficient than other protocols, because they subdivide the area of interest into 8, 16 and 32~subregions; if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.
474 \item {{\bf Active Sensors Ratio}}
475 %\subsubsection{Active Sensors Ratio}
476 Figure~\ref{Figures/ch4/R1/ASR} shows the average active nodes ratio for 150 deployed nodes.
479 \includegraphics[scale=0.8]{Figures/ch4/R1/ASR.pdf}
480 \caption{Active sensors ratio for 150 deployed nodes }
481 \label{Figures/ch4/R1/ASR}
484 The results presented in figure~\ref{Figures/ch4/R1/ASR} show the increase in the number of subregions led to increasing in the number of active nodes. The DiLCO-16 and DiLCO-32 protocols have a larger number of active nodes, but it preserve the coverage for a larger number of rounds. The advantage of the DiLCO-16 and DiLCO-32 protocols are that even if a network is disconnected in one subregion, the other ones usually continues the optimization process, and this extends the lifetime of the network.
486 \item {{\bf The percentage of stopped simulation runs}}
487 %\subsubsection{The percentage of stopped simulation runs}
488 Figure~\ref{Figures/ch4/R1/SR} illustrates the percentage of stopped simulation runs per round for 150 deployed nodes.
491 \includegraphics[scale=0.8]{Figures/ch4/R1/SR.pdf}
492 \caption{Percentage of stopped simulation runs for 150 deployed nodes }
493 \label{Figures/ch4/R1/SR}
496 It can be observed that the DiLCO-2 is the approach which stops first because it applied the optimization on only two subregions for the area of interest that is why it is first exhibits network disconnections.
497 Thus, as explained previously, in case of the DiLCO-16 and DiLCO-32 with several subregions, the optimization effectively continues as long as a network in a subregion is still connected. This longer partial coverage optimization participates in extending the network lifetime.
499 \item {{\bf The Energy Consumption}}
500 %\subsubsection{The Energy Consumption}
501 We measure the energy consumed by the sensors during the communication, listening, computation, active, and sleep modes for different network densities and compare it for different subregions. Figures~\ref{Figures/ch4/R1/EC95} and ~\ref{Figures/ch4/R1/EC50} illustrate the energy consumption for different network sizes for $Lifetime95$ and $Lifetime50$.
505 \includegraphics[scale=0.8]{Figures/ch4/R1/EC95.pdf}
506 \caption{Energy Consumption for Lifetime95}
507 \label{Figures/ch4/R1/EC95}
510 The results show that DiLCO-16 and DiLCO-32 are the most competitive from the energy consumption point of view but as the network size increase the energy consumption increase compared with DiLCO-2, DiLCO-4, and DiLCO-8. The other approaches have a high energy consumption due to the energy consumed during the different modes of the sensor node.\\
512 As shown in Figures~\ref{Figures/ch4/R1/EC95} and ~\ref{Figures/ch4/R1/EC50}, DiLCO-2 consumes more energy than the other versions of DiLCO, especially for large sizes of network. This is easy to understand since the bigger the number of sensors involved in the integer program, the larger the time computation to solve the optimization problem, as well as the higher energy consumed during the communication.
515 \includegraphics[scale=0.8]{Figures/ch4/R1/EC50.pdf}
516 \caption{Energy Consumption for Lifetime50}
517 \label{Figures/ch4/R1/EC50}
519 In fact, a distributed method on the subregions greatly reduces the number of communications, the time of listening and computation so thanks to the partitioning of the initial network in several independent subnetworks.
521 \item {{\bf Execution Time}}
522 %\subsubsection{Execution Time}
523 In this experiment, the execution time of the our distributed optimization approach has been studied. Figure~\ref{Figures/ch4/R1/T} gives the average execution times in seconds for the decision phase (solving of the optimization problem) during one round. They are given for the different approaches and various numbers of sensors. The original execution time is computed as described in section \ref{ch4:sec:04:02}.
524 %The original execution time is computed on a laptop DELL with intel Core i3 2370 M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6 to run the optimization resolution, this time is multiplied by 2944.2 $\left( \frac{35330}{2} \times 6\right)$ and reported on Figure~\ref{fig8} for different network sizes.
528 \includegraphics[scale=0.8]{Figures/ch4/R1/T.pdf}
529 \caption{Execution Time (in seconds)}
530 \label{Figures/ch4/R1/T}
533 We can see from figure~\ref{Figures/ch4/R1/T}, that the DiLCO-32 has very low execution times in comparison with other DiLCO versions because it distributed on larger number of small subregions. Conversely, DiLCO-2 requires to solve an optimization problem considering half the nodes in each subregion presents high execution times.
535 The DiLCO-32 protocol has more suitable times at the same time it turns on redundant nodes more. We think that in distributed fashion the solving of the optimization problem in a subregion can be tackled by sensor nodes. Overall, to be able to deal with very large networks, a distributed method is clearly required.
537 \item {{\bf The Network Lifetime}}
538 %\subsubsection{The Network Lifetime}
539 In figure~\ref{Figures/ch4/R1/LT95} and \ref{Figures/ch4/R1/LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes.
543 \includegraphics[scale=0.8]{Figures/ch4/R1/LT95.pdf}
544 \caption{Network Lifetime for $Lifetime95$}
545 \label{Figures/ch4/R1/LT95}
547 We see that DiLCO-2 protocol results in execution times that quickly become unsuitable for a sensor network, as well as the energy consumed during the communication, seems to be huge because it is distributed over only two subregions.
549 As highlighted by figures~\ref{Figures/ch4/R1/LT95} and \ref{Figures/ch4/R1/LT50}, the network lifetime obviously increases when the size of the network increases, with DiLCO-16 protocol that leads to the larger lifetime improvement. By choosing the best-suited nodes, for each round, to cover the area of interest and by
550 letting the other ones sleep in order to be used later in next rounds, DiLCO-16 protocol efficiently extends the network lifetime because the benefit from the optimization with 16 subregions is better than DiLCO-32 protocol with 32 subregions. DilCO-32 protocol puts in active mode a larger number of sensor nodes especially near the borders of the subdivisions.
552 Comparison shows that DiLCO-16 protocol, which uses 16 leaders, is the best one because it is used less number of active nodes during the network lifetime compared with DiLCO-32 protocol. It also means that distributing the protocol 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.
556 \includegraphics[scale=0.8]{Figures/ch4/R1/LT50.pdf}
557 \caption{Network Lifetime for $Lifetime50$}
558 \label{Figures/ch4/R1/LT50}
563 \subsection{Performance Analysis for Primary Point Models}
564 \label{ch4:sec:04:06}
566 In this section, we are studied the performance of DiLCO~16 approach for a different primary point models. The objective of this comparison is to select the suitable primary point model to be used by DiLCO protocol.
568 In this comparisons, DiLCO-16 protocol are used with five models which are called Model~1( With 5 Primary Points), Model~2 ( With 9 Primary Points), Model~3 ( With 13 Primary Points), Model~4 ( With 17 Primary Points), and Model~5 ( With 21 Primary Points).
571 \begin{enumerate}[i)]
573 \item {{\bf Coverage Ratio}}
574 %\subsubsection{Coverage Ratio}
575 In this experiment, we Figure~\ref{Figures/ch4/R2/CR} shows the average coverage ratio for 150 deployed nodes.
579 \includegraphics[scale=0.8] {Figures/ch4/R2/CR.pdf}
580 \caption{Coverage ratio for 150 deployed nodes}
581 \label{Figures/ch4/R2/CR}
584 It is shown that all models provide a very near coverage ratios during the network lifetime, with very small superiority for the models with higher number of primary points. Moreover, when the number of rounds increases, coverage ratio produced by Model~3, Model~4, and Model~5 decreases in comparison with Model~1 and Model~2 due to the high energy consumption during the listening to take the decision after finishing optimization process for larger number of primary points. As shown in figure ~\ref{Figures/ch4/R2/CR}, Coverage ratio decreases when the number of rounds increases due to dead nodes. Although some nodes are dead,
585 thanks to Model~2, which is slightly more efficient than other Models, because it is balanced between the number of rounds and the better coverage ratio in comparison with other Models.
587 \item {{\bf Active Sensors Ratio}}
588 %\subsubsection{Active Sensors Ratio}
589 Figure~\ref{Figures/ch4/R2/ASR} shows the average active nodes ratio for 150 deployed nodes.
592 \includegraphics[scale=0.8]{Figures/ch4/R2/ASR.pdf}
593 \caption{Active sensors ratio for 150 deployed nodes }
594 \label{Figures/ch4/R2/ASR}
597 The results presented in figure~\ref{Figures/ch4/R2/ASR} show the superiority of the proposed Model 1, in comparison with the other Models. The model with fewer number of primary points uses fewer active nodes than the other models, which uses larger number of primary points to represent the area of the sensor. According to the results that presented in figure~\ref{Figures/ch4/R2/CR}, we observe that although the Model~1 continue to a larger number of rounds, but it has less coverage ratio compared with other models. The advantage of the Model~2 approach is to use fewer number of active nodes for each round compared with Model~3, Model~4, and Model~5. This led to continuing for a larger number of rounds with extending the network lifetime. Model~2 has a better coverage ratio compared to Model~1 and acceptable number of rounds.
600 \item {{\bf he percentage of stopped simulation runs}}
601 %\subsubsection{The percentage of stopped simulation runs}
602 In this study, we want to show the effect of increasing the primary points on the number of stopped simulation runs for each round. Figure~\ref{Figures/ch4/R2/SR} illustrates the percentage of stopped simulation runs per round for 150 deployed nodes.
606 \includegraphics[scale=0.8]{Figures/ch4/R2/SR.pdf}
607 \caption{Percentage of stopped simulation runs for 150 deployed nodes }
608 \label{Figures/ch4/R2/SR}
611 As shown in Figure~\ref{Figures/ch4/R2/SR}, when the number of primary points is increased, the percentage of the stopped simulation runs per round is increased. The reason behind the increase is the increase in the sensors dead when the primary points increase. We are observed that the Model~1 is a better than other models because it conserve more energy by turn on less number of sensors during the sensing phase, but in the same time it preserve the coverage with a less coverage ratio in comparison with other models. Model~2 seems to be more suitable to be used in wireless sensor networks.
614 \item {{\bf The Energy Consumption}}
615 %\subsubsection{The Energy Consumption}
616 In this experiment, we study the effect of increasing the primary points to represent the area of the sensor on the energy consumed by the wireless sensor network for different network densities. Figures~\ref{Figures/ch4/R2/EC95} and ~\ref{Figures/ch4/R2/EC50} illustrate the energy consumption for different network sizes for $Lifetime95$ and $Lifetime50$.
619 \includegraphics[scale=0.8]{Figures/ch4/R2/EC95.pdf}
620 \caption{Energy Consumption with $95\%-Lifetime$}
621 \label{Figures/ch4/R2/EC95}
626 \includegraphics[scale=0.8]{Figures/ch4/R2/EC50.pdf}
627 \caption{Energy Consumption with $Lifetime50$}
628 \label{Figures/ch4/R2/EC50}
631 We see from the results presented in Figures~\ref{Figures/ch4/R2/EC95} and \ref{Figures/ch4/R2/EC50}, The energy consumed by the network for each round increases when the primary points increases, because the decision for the optimization process requires more time, which leads to consuming more energy during the listening mode. The results show that Model~1 is the most competitive from the energy consumption point of view, but the worst one from coverage ratio point of view. The other Models have a high energy consumption due to the increase in the primary points, which are led to increase the energy consumption during the listening mode before producing the solution by solving the optimization process. In fact, we see that Model~2 is a good candidate to be used by wireless sensor network because it preserves a good coverage ratio with a suitable energy consumption in comparison with other models.
633 \item {{\bf Execution Time}}
634 %\subsubsection{Execution Time}
635 In this experiment, we have studied the impact of the increase in primary points on the execution time of DiLCO protocol. Figure~\ref{Figures/ch4/R2/T} gives the average execution times in seconds for the decision phase (solving of the optimization problem) during one round. The original execution time is computed as described in section \ref{ch4:sec:04:02}.
639 \includegraphics[scale=0.8]{Figures/ch4/R2/T.pdf}
640 \caption{Execution Time(s) vs The Number of Sensors }
641 \label{Figures/ch4/R2/T}
644 They are given for the different primary point models and various numbers of sensors. We can see from Figure~\ref{Figures/ch4/R2/T}, that Model~1 has lower execution time in comparison with other Models because it used smaller number of primary points to represent the area of the sensor. Conversely, the other primary point models have been presented a higher execution times.
645 Moreover, Model~2 has more suitable times and coverage ratio that lead to continue for a larger number of rounds extending the network lifetime. We think that a good primary point model, this one that balances between the coverage ratio and the number of rounds during the lifetime of the network.
647 \item {{\bf The Network Lifetime}}
648 %\subsubsection{The Network Lifetime}
649 Finally, we will study the effect of increasing the primary points on the lifetime of the network. In Figure~\ref{Figures/ch4/R2/LT95} and in Figure~\ref{Figures/ch4/R2/LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes.
653 \includegraphics[scale=0.8]{Figures/ch4/R2/LT95.pdf}
654 \caption{Network Lifetime for $Lifetime95$}
655 \label{Figures/ch4/R2/LT95}
661 \includegraphics[scale=0.8]{Figures/ch4/R2/LT50.pdf}
662 \caption{Network Lifetime for $Lifetime50$}
663 \label{Figures/ch4/R2/LT50}
667 As highlighted by figures~\ref{Figures/ch4/R2/LT95} and \ref{Figures/ch4/R2/LT50}, the network lifetime obviously increases when the size of the network increases, with Model~1 that leads to the larger lifetime improvement.
668 Comparison shows that the Model~1, which uses less number of primary points, is the best one because it is less energy consumption during the network lifetime. It is also the worst one from the point of view of coverage ratio. Our proposed Model~2 efficiently prolongs the network lifetime with a good coverage ratio in comparison with other models.
672 \subsection{Performance Comparison with other Approaches}
673 \label{ch4:sec:04:07}
674 Based on the results, which are conducted from previous two subsections, \ref{ch4:sec:04:02} and \ref{ch4:sec:04:03}, we have found that DiLCO-16 protocol and DiLCO-32 protocol with Model~2 are the best candidates to be compared with other two approaches. The first approach is called DESK~\cite{DESK}, which is a fully distributed coverage algorithm. The second approach is called GAF~\cite{GAF}, consists in dividing the region into fixed squares. During the decision phase, in each square, one sensor is chosen to remain on during the sensing phase time.
676 \begin{enumerate}[i)]
678 \item {{\bf Coverage Ratio}}
679 %\subsubsection{Coverage Ratio}
680 In this experiment, the average coverage ratio for 150 deployed nodes has been demonstrated figure~\ref{Figures/ch4/R3/CR}.
685 \includegraphics[scale=0.8] {Figures/ch4/R3/CR.pdf}
686 \caption{Coverage ratio for 150 deployed nodes}
687 \label{Figures/ch4/R3/CR}
690 It has been shown that DESK and GAF provide a little better coverage ratio with 99.99\% and 99.91\% against 99.1\% and 99.2\% produced by DiLCO-16 and DiLCO-32 for the lowest number of rounds. This is due to the fact that DiLCO protocol versions put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more nodes are active in the case of DESK and GAF.
692 Moreover, when the number of rounds increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO-16 protocol and DiLCO-32 protocol maintain almost a good coverage. This is because they optimized the coverage and the lifetime in wireless sensor network by selecting the best representative sensor nodes to take the responsibility of coverage during the sensing phase, and this will lead to continuing for a larger number of rounds and prolonging the network lifetime. Furthermore, although some nodes are dead, sensor activity scheduling of our protocol chooses other nodes to ensure the coverage of the area of interest.
694 \item {{\bf Active Sensors Ratio}}
695 %\subsubsection{Active Sensors Ratio}
696 It is important to have as few active nodes as possible in each round, in order to minimize the energy consumption and maximize the network lifetime. Figure~\ref{Figures/ch4/R3/ASR} shows the average active nodes ratio for 150 deployed nodes.
700 \includegraphics[scale=0.8]{Figures/ch4/R3/ASR.pdf}
701 \caption{Active sensors ratio for 150 deployed nodes }
702 \label{Figures/ch4/R3/ASR}
705 The results presented in figure~\ref{Figures/ch4/R3/ASR} show the superiority of the proposed DiLCO-16 protocol and DiLCO-32 protocol, in comparison with the other approaches. We have observed that DESK and GAF have 37.5 \% and 44.5 \% active nodes and DiLCO-16 protocol and DiLCO-32 protocol compete perfectly with only 17.4 \%, 24.8 \% and 26.8 \% active nodes for the first 14 rounds. Then as the number of rounds increases DiLCO-16 protocol and DiLCO-32 protocol have larger number of active nodes in comparison with DESK and GAF, especially from round $35^{th}$ because they give a better coverage ratio than other approaches. We see that DESK and GAF have less number of active nodes beginning at the rounds $35^{th}$ and $32^{th}$ because there are many nodes are died due to the high energy consumption by the redundant nodes during the sensing phase.
708 \item {{\bf The percentage of stopped simulation runs}}
709 %\subsubsection{The percentage of stopped simulation runs}
710 The results presented in this experiment, are to show the comparison of DiLCO-16 protocol and DiLCO-32 protocol with other two approaches from the point of view of stopped simulation runs per round.
711 Figure~\ref{Figures/ch4/R3/SR} illustrates the percentage of stopped simulation runs per round for 150 deployed nodes.
714 \includegraphics[scale=0.8]{Figures/ch4/R3/SR.pdf}
715 \caption{Percentage of stopped simulation runs for 150 deployed nodes }
716 \label{Figures/ch4/R3/SR}
718 It has been observed that DESK is the approach, which stops first because it consumes more energy for communication as well as it turns on a large number of redundant nodes during the sensing phase. On the other hand DiLCO-16 protocol and DiLCO-32 protocol have less stopped simulation runs in comparison with DESK and GAF because it distributed the optimization on several subregions in order to optimize the coverage and the lifetime of the network by activating a less number of nodes during the sensing phase leading to extending the network lifetime and coverage preservation. The optimization effectively continues as long as a network in a subregion is still connected.
721 \item {{\bf The Energy Consumption}}
722 %\subsubsection{The Energy Consumption}
723 In this experiment, we have studied the effect of the energy consumed by the wireless sensor network during the communication, computation, listening, active, and sleep modes for different network densities and compare it with other approaches. Figures~\ref{Figures/ch4/R3/EC95} and ~\ref{Figures/ch4/R3/EC50} illustrate the energy consumption for different network sizes for $Lifetime95$ and $Lifetime50$.
727 \includegraphics[scale=0.8]{Figures/ch4/R3/EC95.pdf}
728 \caption{Energy Consumption with $95\%-Lifetime$}
729 \label{Figures/ch4/R3/EC95}
734 \includegraphics[scale=0.8]{Figures/ch4/R3/EC50.pdf}
735 \caption{Energy Consumption with $Lifetime50$}
736 \label{Figures/ch4/R3/EC50}
739 The results show that DiLCO-16 protocol and DiLCO-32 protocol are the most competitive from the energy consumption point of view. The other approaches have a high energy consumption due to activating a larger number of redundant nodes, as well as the energy consumed during the different modes of sensor nodes. 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.
742 \item {{\bf The Network Lifetime}}
743 %\subsubsection{The Network Lifetime}
744 In this experiment, we have observed the superiority of DiLCO-16 protocol and DiLCO-32 protocol against other two approaches in prolonging the network lifetime. In figures~\ref{Figures/ch4/R3/LT95} and \ref{Figures/ch4/R3/LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes.
748 \includegraphics[scale=0.8]{Figures/ch4/R3/LT95.pdf}
749 \caption{Network Lifetime for $Lifetime95$}
750 \label{Figures/ch4/R3/LT95}
756 \includegraphics[scale=0.8]{Figures/ch4/R3/LT50.pdf}
757 \caption{Network Lifetime for $Lifetime50$}
758 \label{Figures/ch4/R3/LT50}
761 As highlighted by figures~\ref{Figures/ch4/R3/LT95} and \ref{Figures/ch4/R3/LT50}, the network lifetime obviously increases when the size of the network increases, with DiLCO-16 protocol and DiLCO-32 protocol that leads to maximize the lifetime of the network compared with other approaches.
762 By choosing the best suited nodes, for each round, 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 periods, DiLCO-16 protocol and DiLCO-32 protocol efficiently prolonged the network lifetime.
763 Comparison shows that DiLCO-16 protocol and DiLCO-32 protocol, which are used distributed optimization over the subregions, is the best one because it is robust to network disconnection during the network lifetime as well as it consumes less energy in comparison with other approaches. 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.
770 A crucial problem in WSN is to schedule the sensing activities of the different nodes in order to ensure both of coverage of the area of interest and longer network lifetime. The inherent limitations of sensor nodes, in energy provision, communication and computing capacities, require protocols that optimize the use of the available resources to fulfill the sensing task. To address this problem, this chapter proposes a two-step approach. Firstly, the field of sensing
771 is divided into smaller subregions using the concept of divide-and-conquer method. Secondly, a distributed protocol called Distributed Lifetime Coverage Optimization is applied in each subregion to optimize the coverage and lifetime performances. In a subregion, our protocol consists in electing a leader node, which will then perform a sensor activity scheduling. The challenges include how to select the most efficient leader in each subregion and the best representative set of active nodes to ensure a high level of coverage. To assess the performance of our approach, we compared it with two other approaches using many performance metrics like coverage ratio or network lifetime. We have also studied the impact of the number of subregions chosen to subdivide the area of interest, considering different network sizes. The experiments show that increasing the number of subregions improves the lifetime. The more subregions there are, the more robust the network is against random disconnection resulting from dead nodes. However, for a given sensing field and network size there is an optimal number of subregions. Therefore, in case of our simulation context a subdivision in $16$~subregions seems to be the most relevant.
