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7 \chapter{Distributed Lifetime Coverage Optimization Protocol}
12 \section{Introduction}
14 %Energy efficiency is a crucial issue in wireless sensor networks since the sensory consumption, in order to maximize the network lifetime, represents the major difficulty when designing WSNs. As a consequence, one of the scientific research challenges in WSNs, which has been addressed by a large amount of literature during the last few years, is the design of energy efficient approaches for coverage and connectivity~\cite{ref94}.
15 Coverage reflects how well a sensor field is monitored. On the one hand, we want to monitor the area of interest in the most efficient way~\cite{ref95}. On the other hand, we want to use as little energy as possible. Sensor nodes are battery-powered with no means of recharging or replacing, usually due to environmental (hostile or
16 unpractical environments) or cost reasons. Therefore, it is desired that the WSNs are deployed with high densities so as to exploit the overlapping sensing regions of some sensor nodes to save energy by turning off some of them during the sensing phase to prolong the network lifetime.
18 In this chapter, we design a protocol that focuses on the area coverage problem with the objective of maximizing the network lifetime. Our proposition, the Distributed Lifetime Coverage Optimization (DiLCO) protocol, maintains the coverage and improves the lifetime in WSNs. The area of interest is first
19 divided into subregions using a divide-and-conquer algorithm and an activity scheduling for sensor nodes is then planned by the elected leader in each subregion. In fact, the nodes in a subregion can be seen as a cluster where each node sends sensing data to the cluster head or the sink node. Furthermore, the activities in a subregion/cluster can continue even if another cluster stops due to too many node failures. Our DiLCO protocol considers periods, where a period starts with a discovery phase to exchange information between sensors of the same subregion, in order to choose in a suitable manner a sensor node (the leader) to carry out the coverage strategy. In each subregion, the activation of the sensors for the sensing phase of the current period is obtained by solving an integer program. The resulting activation vector is broadcasted by each leader node to every node of its subregion.
21 The remainder of this chapter is organized as follows. The next section is devoted to the DiLCO protocol description. Section \ref{ch4:sec:03} gives the primary points based coverage problem formulation which is used to schedule the activation of sensors. Section \ref{ch4:sec:04} shows the simulation results obtained using the discrete event simulator OMNeT++ \cite{ref158}. They fully demonstrate the usefulness of the proposed approach. Finally, we give concluding remarks in section \ref{ch4:sec:05}.
25 \section{Description of the DiLCO Protocol}
28 \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 techniques: network leader election and sensor activity scheduling for coverage preservation and energy conservation, applied periodically to efficiently maximize the lifetime of the network.
30 \subsection{Assumptions and Network Model}
32 \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}. Two sensor nodes are supposed to be neighbors if the euclidean distance between them is at most equal to 2$R_s$, where $R_s$ is the sensing range.
35 \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 $R_s$, each space point 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 consider multi-hop communication.
36 %We assume that each sensor node can directly transmit its measurements toward a mobile sink node.
37 %For example, a sink can be an unmanned aerial vehicle (UAV) flying regularly over the sensor field to collect measurements from sensor nodes. The mobile sink node collects the measurements and transmits them to the base station.
39 During the execution of the DiLCO protocol, two kinds of packet will be used:
41 \begin{enumerate} [(i)]
42 \item \textbf{INFO packet:} sent by each sensor node to all the nodes inside a same subregion for information exchange.
43 \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.
46 There are five possible status for each sensor node in the network:
47 %and each sensor node will have five possible status in the network:
48 \begin{enumerate}[(i)]
49 \item \textbf{LISTENING:} sensor is waiting for a decision (to be active or not).
50 \item \textbf{COMPUTATION:} sensor applies the optimization process as leader.
51 \item \textbf{ACTIVE:} sensor is active.
52 \item \textbf{SLEEP:} sensor is turned off.
53 \item \textbf{COMMUNICATION:} sensor is transmitting or receiving packet.
56 \subsection{Primary Point Coverage Model}
58 \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 sensing range $R_s$, 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.
59 We can calculate the positions of the selected primary
60 points in the circle disk of the sensing range of a wireless sensor
61 node (see Figure~\ref{fig1}) as follows:\\
62 Assuming that the point center of a wireless sensor node is located at $(p_x,p_y)$, we can define up to 25 primary points $X_1$ to $X_{25}$.\\
63 %$(p_x,p_y)$ = point center of wireless sensor node\\
65 $X_2=( p_x + R_s * (1), p_y + R_s * (0) )$\\
66 $X_3=( p_x + R_s * (-1), p_y + R_s * (0)) $\\
67 $X_4=( p_x + R_s * (0), p_y + R_s * (1) )$\\
68 $X_5=( p_x + R_s * (0), p_y + R_s * (-1 )) $\\
69 $X_6= ( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (0)) $\\
70 $X_7=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (0))$\\
71 $X_8=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
72 $X_9=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
73 $X_{10}=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
74 $X_{11}=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
75 $X_{12}=( p_x + R_s * (0), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
76 $X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
77 $X_{14}=( p_x + R_s * (\frac{\sqrt{3}}{2}), p_y + R_s * (\frac{1}{2})) $\\
78 $X_{15}=( p_x + R_s * (\frac{-\sqrt{3}}{2}), p_y + R_s * (\frac{1}{2})) $\\
79 $X_{16}=( p_x + R_s * (\frac{\sqrt{3}}{2}), p_y + R_s * (\frac{- 1}{2})) $\\
80 $X_{17}=( p_x + R_s * (\frac{-\sqrt{3}}{2}), p_y + R_s * (\frac{- 1}{2})) $\\
81 $X_{18}=( p_x + R_s * (\frac{\sqrt{3}}{2}), p_y + R_s * (0) $\\
82 $X_{19}=( p_x + R_s * (\frac{-\sqrt{3}}{2}), p_y + R_s * (0) $\\
83 $X_{20}=( p_x + R_s * (0), p_y + R_s * (\frac{1}{2})) $\\
84 $X_{21}=( p_x + R_s * (0), p_y + R_s * (-\frac{1}{2})) $\\
85 $X_{22}=( p_x + R_s * (\frac{1}{2}), p_y + R_s * (\frac{\sqrt{3}}{2})) $\\
86 $X_{23}=( p_x + R_s * (\frac{- 1}{2}), p_y + R_s * (\frac{\sqrt{3}}{2})) $\\
87 $X_{24}=( p_x + R_s * (\frac{- 1}{2}), p_y + R_s * (\frac{-\sqrt{3}}{2})) $\\
88 $X_{25}=( p_x + R_s * (\frac{1}{2}), p_y + R_s * (\frac{-\sqrt{3}}{2})) $.
96 \includegraphics[scale=0.33]{Figures/ch4/fig21.pdf}\\~ ~ ~ ~ ~ ~ ~ ~(a)
97 \includegraphics[scale=0.33]{Figures/ch4/principles13.pdf}\\~ ~ ~ ~ ~ ~(c)
99 \includegraphics[scale=0.33]{Figures/ch4/fig25.pdf}\\~ ~ ~ ~ ~ ~(e)
100 \includegraphics[scale=0.33]{Figures/ch4/fig22.pdf}\\~ ~ ~ ~ ~ ~ ~ ~ ~(b)
102 \includegraphics[scale=0.33]{Figures/ch4/fig24.pdf}\\~ ~ ~ ~ ~ ~ ~(d)
103 \includegraphics[scale=0.33]{Figures/ch4/fig26.pdf}\\~ ~ ~ ~ ~ ~ ~(f)
105 \caption{Wireless Sensor Node represented by (a) 5, (b) 9, (c) 13, (d) 17, (e) 21 and (f) 25 primary points respectively}
112 \subsection{Main Idea}
113 \label{ch4:sec:02:03}
114 \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.
118 \includegraphics[scale=0.90]{Figures/ch4/OneSensingRound.jpg} % 70mm
119 \caption{DiLCO protocol}
123 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
124 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
125 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.
128 Below, we describe each phase in more details.
130 \subsubsection{Information Exchange Phase}
131 \label{ch4:sec:02:03:01}
132 Each sensor node $j$ sends, through multi-hop communication, its position, remaining energy $RE_j$, and the number of neighbors $NBR_j$ to all sensor nodes in its subregion by using an INFO packet (containing information on position coordinates, current remaining energy, sensor node ID, number of its one-hop live neighbors) and then waits for packets sent by other nodes. After that, each node will have information about
133 all the sensor nodes in the subregion. In our model, the remaining energy corresponds to the time that a sensor can live in the active mode.
135 \subsubsection{Leader Election Phase}
136 \label{ch4:sec:02:03:02}
137 This step includes choosing a wireless sensor node called leader, which will be responsible for executing the coverage algorithm. Each subregion in the area of interest will select its own leader independently for each period. All the sensor nodes cooperate to select the leader. 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 ID. Observations on previous simulations suggest using the number of one-hop neighbors as the primary criterion to reduce energy consumption due to the communications.
140 \subsubsection{Decision phase}
141 \label{ch4:sec:02:03:03}
142 The leader 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. It will send an ActiveSleep packet to each sensor in the subregion based on the algorithm's results.
144 %($RE_j$) corresponds to its remaining energy) to be alive during the selected periods knowing that $E_{th}$ is the amount of energy required to be alive during one period.
146 \subsubsection{Sensing phase}
147 \label{ch4:sec:02:03:04}
148 Active sensors in the period will execute their sensing task to preserve maximal coverage in the region of interest. We will assume that the cost of keeping a node awake (or asleep) for sensing task is the same for all wireless sensor nodes in the network. Each sensor will receive an ActiveSleep packet from the leader informing it to stay awake or to go to sleep for a time equal to the round of sensing until starting a new period.
150 \begin{algorithm}[h!]
153 %\emph{Initialize the sensor node and determine it's position and subregion} \;
155 \If{ $RE_j \geq E_{th}$ }{
156 \emph{$s_j.status$ = COMMUNICATION}\;
157 \emph{Send $INFO()$ packet to other nodes in the subregion}\;
158 \emph{Wait $INFO()$ packet from other nodes in the subregion}\;
159 %\emph{UPDATE $RE_j$ for every sent or received INFO Packet}\;
160 %\emph{ Collect information and construct the list L for all nodes in the subregion}\;
162 %\If{ the received INFO Packet = No. of nodes in it's subregion -1 }{
163 \emph{LeaderID = Leader election}\;
164 \If{$ s_j.ID = LeaderID $}{
165 \emph{$s_j.status$ = COMPUTATION}\;
166 \emph{$\left\{\left(X_{1},\dots,X_{k},\dots,X_{J}\right)\right\}$ =
167 Execute Integer Program Algorithm($J$)}\;
168 \emph{$s_j.status$ = COMMUNICATION}\;
169 \emph{Send $ActiveSleep()$ to each node $k$ in subregion} \;
170 \emph{Update $RE_j $}\;
173 \emph{$s_j.status$ = LISTENING}\;
174 \emph{Wait $ActiveSleep()$ packet from the Leader}\;
176 \emph{Update $RE_j $}\;
180 \Else { Exclude $s_j$ from entering in the current sensing phase}
183 \caption{DiLCO($s_j$)}
188 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 (i.e., the remaining energy $RE_j$ $\geq$ $E_{th}$ (the amount of energy required to be alive during one period)). 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, 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 criteria described in section \ref{ch4:sec:02:03:02}.
189 %the following criteria with decreasing importance: larger number of neighbors, larger remaining energy, and then in case of equality, larger index.
190 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 ActiveSleep 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 ActiveSleep packet to know its state for the coming sensing phase.
192 %Primary Points based
193 \section{Coverage Problem Formulation}
195 \indent Our model is based on the model proposed by \cite{ref156} where the
196 objective is to find a maximum number of disjoint cover sets. To accomplish
197 this goal, the authors proposed an integer program which forces undercoverage
198 and overcoverage of targets to become minimal at the same time. They use binary
199 variables $x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our
200 model, we consider that the binary variable $X_{j}$ determines the activation of
201 sensor $j$ in the sensing phase. We also consider primary points as targets.
202 The set of primary points is denoted by $P$ and the set of sensors by $J$.
204 \noindent Let $\alpha_{jp}$ denote the indicator function of whether the primary
205 point $p$ is covered, that is:
207 \alpha_{jp} = \left \{
209 1 & \mbox{if the primary point $p$ is covered} \\
210 & \mbox{by sensor node $j$}, \\
211 0 & \mbox{otherwise.}\\
215 The number of active sensors that cover the primary point $p$ can then be
216 computed by $\sum_{j \in J} \alpha_{jp} * X_{j}$ where:
220 1& \mbox{if sensor $j$ is active,} \\
221 0 & \mbox{otherwise.}\\
225 We define the Overcoverage variable $\Theta_{p}$ as:
227 \Theta_{p} = \left \{
229 0 & \mbox{if the primary point}\\
230 & \mbox{$p$ is not covered,}\\
231 \left( \sum_{j \in J} \alpha_{jp} * X_{j} \right)- 1 & \mbox{otherwise.}\\
235 \noindent More precisely, $\Theta_{p}$ represents the number of active sensor
236 nodes minus one that cover the primary point~$p$. The Undercoverage variable
237 $U_{p}$ of the primary point $p$ is defined by:
241 1 &\mbox{if the primary point $p$ is not covered,} \\
242 0 & \mbox{otherwise.}\\
247 \noindent Our coverage optimization problem can then be formulated as follows:
248 \begin{equation} \label{eq:ip2r}
251 \min \sum_{p \in P} (w_{\theta} \Theta_{p} + w_{U} U_{p})&\\
252 \textrm{subject to :}&\\
253 \sum_{j \in J} \alpha_{jp} X_{j} - \Theta_{p}+ U_{p} =1, &\forall p \in P\\
255 %\sum_{t \in T} X_{j,t} \leq \frac{RE_j}{e_t} &\forall j \in J \\
257 \Theta_{p}\in \mathbb{N}, &\forall p \in P\\
258 U_{p} \in \{0,1\}, &\forall p \in P \\
259 X_{j} \in \{0,1\}, &\forall j \in J
265 \item $X_{j}$ : indicates whether or not the sensor $j$ is actively sensing (1
266 if yes and 0 if not);
267 \item $\Theta_{p}$ : {\it overcoverage}, the number of sensors minus one that
268 are covering the primary point $p$;
269 \item $U_{p}$ : {\it undercoverage}, indicates whether or not the primary point
270 $p$ is being covered (1 if not covered and 0 if covered).
273 The first group of constraints indicates that some primary point $p$ should be
274 covered by at least one sensor and, if it is not always the case, overcoverage
275 and undercoverage variables help balancing the restriction equations by taking
276 positive values. Two objectives can be noticed in our model. First, we limit the
277 overcoverage of primary points to activate as few sensors as possible. Second,
278 to avoid a lack of area monitoring in a subregion we minimize the
279 undercoverage. Both weights $w_\theta$ and $w_U$ must be carefully chosen in
280 order to guarantee that the maximum number of points are covered during each
281 period. In our simulations, priority is given to the coverage by choosing $W_{U}$ very
282 large compared to $W_{\theta}$.
284 \section{Simulation Results and Analysis}
287 \subsection{Simulation Framework}
288 \label{ch4:sec:04:01}
290 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.
293 \caption{Relevant parameters for network initializing.}
296 % used for centering table
298 % centered columns (4 columns)
300 %inserts double horizontal lines
301 Parameter & Value \\ [0.5ex]
305 % inserts single horizontal line
306 Sensing Field & $(50 \times 25)~m^2 $ \\
307 % inserting body of the table
309 Nodes Number & 50, 100, 150, 200 and 250~nodes \\
311 Initial Energy & 500-700~joules \\
313 Sensing Period & 60 Minutes \\
314 $E_{th}$ & 36 Joules\\
319 % [1ex] adds vertical space
325 % is used to refer this table in the text
328 Simulations with five different node densities going from 50 to 250~nodes were
329 performed considering each time 25~randomly generated networks, to obtain
330 experimental results which are relevant. The nodes are deployed on a field of
331 interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
335 \subsection{Modeling Language and Optimization Solver}
336 \label{ch4:sec:04:02}
337 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.
338 %Obviously, It is infeasible to use GLPK on a real sensor nodes, we use it in the simulation only for simplicity. GLPK is used to compute the optimal schedule.
340 \subsection{Energy Consumption Model}
341 \label{ch4:sec:04:03}
343 \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 dynamic sensing range is removed because we consider a fixed sensing range.
345 \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}.
348 \caption{Energy Consumption Model}
351 % used for centering table
352 \begin{tabular}{|c|c|c|c|c|}
353 % centered columns (4 columns)
355 %inserts double horizontal lines
356 Sensor status & MCU & Radio & Sensing & Power (mW) \\ [0.5ex]
358 % inserts single horizontal line
359 LISTENING & on & on & on & 20.05 \\
360 % inserting body of the table
362 ACTIVE & on & off & on & 9.72 \\
364 SLEEP & off & off & off & 0.02 \\
366 COMPUTATION & on & on & on & 26.83 \\
368 %\multicolumn{4}{|c|}{Energy needed to send/receive a 1-bit} & 0.2575\\
373 % is used to refer this table in the text
376 \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 received its status from leader), it can turn its radio off to save battery. DiLCO uses two types of packets
377 for communication. The size of the INFO packet and ActiveSleep packet
378 are 112 bits and 16 bits respectively. 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 $0.2575~mW$.
380 %We have used an energy consumption model, which is presented in chapter 1, section \ref{ch1:sec9:subsec2}.
382 The initial energy of each node is randomly set in the interval $[500;700]$. A sensor node will not participate in the next period if its remaining energy is less than $E_{th}=36~\mbox{Joules}$, the minimum energy needed for the node to stay alive during one period. This value has been computed by multiplying the energy consumed in the active state (9.72 mW) by the time in second 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 alive during at most 20 periods.
385 \subsection{Performance Metrics}
386 \label{ch4:sec:04:04}
387 In the simulations, we introduce the following performance metrics to evaluate
388 the efficiency of our approach:
390 \begin{enumerate}[i)]
392 \item {{\bf Network Lifetime}:} we define the network lifetime as the time until
393 the coverage ratio drops below a predefined threshold. We denote by
394 $Lifetime_{95}$ (respectively $Lifetime_{50}$) the amount of time during which
395 the network can satisfy an area coverage greater than $95\%$ (respectively
396 $50\%$). We assume that the sensor network can fulfill its task until all its
397 nodes have been drained of their energy or it becomes disconnected. Network
398 connectivity is crucial because an active sensor node without connectivity
399 towards a base station cannot transmit any information regarding an observed
400 event in the area that it monitors.
402 \item {{\bf Coverage Ratio (CR)}:} it measures how well the WSN is able to
403 observe the area of interest. In our case, we discretized the sensor field
404 as a regular grid, which yields the following equation to compute the
408 \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100,
410 where $n$ is the number of covered grid points by active sensors of every
411 subregions during the current sensing phase and $N$ is the total number of grid
412 points in the sensing field. In our simulations, we have a layout of $N = 51
413 \times 26 = 1326$ grid points.
415 \item {{\bf Energy Consumption}:} energy consumption (EC) can be seen as the
416 total amount of energy consumed by the sensors during $Lifetime_{95}$
417 or $Lifetime_{50}$, divided by the number of periods. Formally, the computation
418 of EC can be expressed as follows:
421 \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m
422 + E^{a}_m+E^{s}_m \right)}{M},
425 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
426 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
427 (active and sleeping nodes).
429 \item{{\bf Number of Active Sensors Ratio (ASR)}:} it is important to have as few active nodes as possible in each period,
430 in order to minimize the communication overhead and maximize the
431 network lifetime. The Active Sensors Ratio is defined as follows:
434 \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$A_r$}}{\mbox{$J$}} \times 100,
436 where $A_r$ is the number of active sensors in the subregion $r$ during current period, $J$ is the total number of sensors in the network, and $R$ is the total number of subregions in the network.
438 \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 $\left( \frac{35330}{2} \times \frac{1}{6} \right)$.
440 \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 period it occurs.% ( in chapter 4, period consists of one round).
446 \subsection{Performance Analysis for Different Number of Subregions}
447 \label{ch4:sec:04:05}
449 In this subsection, we study the performance of our DiLCO protocol for different numbers of subregions.
450 The DiLCO-1 protocol is a centralized approach for the whole 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 do not take into account 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. DiLCO protocol uses 13 primary points.
452 \begin{enumerate}[i)]
453 \item {{\bf Coverage Ratio}}
454 %\subsubsection{Coverage Ratio}
455 %\label{ch4:sec:04:02:01}
457 Figure~\ref{Figures/ch4/R1/CR} shows the average coverage ratio for 150 deployed nodes.
461 \includegraphics[scale=0.8] {Figures/ch4/R1/CR.pdf}
462 \caption{Coverage ratio for 150 deployed nodes}
463 \label{Figures/ch4/R1/CR}
465 It can be seen that DiLCO protocol (with 4, 8, 16 and 32 subregions) gives nearly similar coverage ratios during the first thirty periods.
466 DiLCO-2 protocol gives a coverage ratio very close to the other protocols for the first 10 periods, and then the coverage decreases until the death of the network in the period $18^{th}$. In case of only 2 subregions, the energy consumption is high and the network is rapidly disconnected.
467 As can be seen in 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 periods. Coverage ratio decreases when the number of periods 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 periods. 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.
469 \item {{\bf Active Sensors Ratio}}
470 %\subsubsection{Active Sensors Ratio}
472 Figure~\ref{Figures/ch4/R1/ASR} shows the average active nodes ratio for 150 deployed nodes.
475 \includegraphics[scale=0.8]{Figures/ch4/R1/ASR.pdf}
476 \caption{Active sensors ratio for 150 deployed nodes }
477 \label{Figures/ch4/R1/ASR}
480 The results presented in the figure show that increasing the number of subregions lead to the increase of the number of active nodes. The DiLCO-16 and DiLCO-32 protocols have a larger number of active nodes, but they both preserve the coverage for a larger number of periods. 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 continue the optimization process, and this extends the lifetime of the network.
482 \item {{\bf Stopped simulation runs}}
483 %\subsubsection{The percentage of stopped simulation runs}
485 Figure~\ref{Figures/ch4/R1/SR} illustrates the percentage of stopped simulation runs per period for 150 deployed nodes. DiLCO-2 is the approach which stops first because it applies the optimization on only two subregions and the high energy consumption accelerate the network disconnection. Thus, as explained previously, in case of DiLCO-16 and DiLCO-32 which have many subregions, the optimization effectively continues as long as a subnetwork in a subregion is still connected. This longer partial coverage optimization participates in extending the network lifetime.
488 \includegraphics[scale=0.8]{Figures/ch4/R1/SR.pdf}
489 \caption{Percentage of stopped simulation runs for 150 deployed nodes }
490 \label{Figures/ch4/R1/SR}
495 \item {{\bf Energy Consumption}}
496 %\subsubsection{The Energy Consumption}
498 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/EC}(a) and~\ref{Figures/ch4/R1/EC}(b) illustrate the energy consumption for different network sizes for $Lifetime_{95}$ and $Lifetime_{50}$. The results show that DiLCO-16 and DiLCO-32 are the most competitive from the energy consumption point of view. The other approaches have a high energy consumption due to the energy consumed during the different modes of the sensor node.
502 %\begin{multicols}{1}
504 \includegraphics[scale=0.8]{Figures/ch4/R1/EC95.pdf}\\~ ~ ~ ~ ~(a) \\
506 \includegraphics[scale=0.8]{Figures/ch4/R1/EC50.pdf}\\~ ~ ~ ~ ~(b)
509 \caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
510 \label{Figures/ch4/R1/EC}
513 As shown in Figures~\ref{Figures/ch4/R1/EC}(a) and~\ref{Figures/ch4/R1/EC}(b), 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 computation time to solve the optimization problem, as well as the higher energy consumed during the communication. In fact, the distribution of the computation over many subregions greatly reduces the number of communications, the time of listening and computation.
515 \item {{\bf Execution Time}}
516 %\subsubsection{Execution Time}
518 In this experiment, the execution time of the 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 period. 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:04:04}. \\ \\ \\ \\
524 \includegraphics[scale=0.8]{Figures/ch4/R1/T.pdf}
525 \caption{Execution Time (in seconds)}
526 \label{Figures/ch4/R1/T}
529 We can see from Figure~\ref{Figures/ch4/R1/T} that DiLCO-32 has very low execution times in comparison with other DiLCO versions because it is distributed on larger number of small subregions. Conversely, DiLCO-2 requires to solve an optimization problem considering half the nodes in each subregion and thus presents high execution times. Overall, to be able to deal with very large networks, a distributed method is clearly required.
531 \item {{\bf Network Lifetime}}
532 %\subsubsection{The Network Lifetime}
534 In Figures~\ref{Figures/ch4/R1/LT}(a) and \ref{Figures/ch4/R1/LT}(b), network lifetime, $Lifetime_{95}$ and $Lifetime_{50}$ respectively, are illustrated for different network sizes.
540 \includegraphics[scale=0.8]{Figures/ch4/R1/LT95.pdf}\\~ ~ ~ ~ ~(a) \\
542 \includegraphics[scale=0.8]{Figures/ch4/R1/LT50.pdf}\\~ ~ ~ ~ ~(b)
544 \caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
545 \label{Figures/ch4/R1/LT}
548 For DiLCO-2 protocol, execution times quickly become unsuitable for a sensor network, and the energy consumed during the communication, seems to be huge because it is distributed over only two subregions. As highlighted by Figures~\ref{Figures/ch4/R1/LT}(a) and \ref{Figures/ch4/R1/LT}(b), the network lifetime obviously increases when the size of the network increases. The network lifetime also increases with the number of subregions, but only up to a given number. Thus we can see that DiLCO-16 leads to the larger lifetime improvement and not DiLCO-32. In fact, DilCO-32 protocol puts in active mode a larger number of sensor nodes especially near the borders of the subdivisions. It means that distributing the protocol in each node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is a relevant way to maximize the lifetime of a network.
553 \subsection{Performance Analysis for Different Number of Primary Points}
554 \label{ch4:sec:04:06}
556 In this section, we study the performance of DiLCO~16 approach for different numbers of primary points. The objective of this comparison is to select the suitable primary point model to be used by a DiLCO protocol. In this comparison, DiLCO-16 protocol is used with five models, which are called Model-5 (it uses 5 primary points), Model-9, Model-13, Model-17, and Model-21.
559 \begin{enumerate}[i)]
561 \item {{\bf Coverage Ratio}}
562 %\subsubsection{Coverage Ratio}
564 Figure~\ref{Figures/ch4/R2/CR} shows the average coverage ratio for 150 deployed nodes.
568 \includegraphics[scale=0.8] {Figures/ch4/R2/CR.pdf}
569 \caption{Coverage ratio for 150 deployed nodes}
570 \label{Figures/ch4/R2/CR}
572 As can be seen in Figure~\ref{Figures/ch4/R2/CR}, at the beginning the models which use a larger number of primary points provide slightly better coverage ratios, but latter they are the worst.
573 %Moreover, when the number of periods increases, coverage ratio produced by Model-9, Model-13, Model-17, and Model-21 decreases in comparison with Model-5 due to a larger time computation for the decision process for larger number of primary points.
574 Moreover, when the number of periods increases, coverage ratio produced by all models decrease, but Model-5 is the one with the slowest decrease due to a smaller time computation of decision process for a smaller number of primary points.
575 As shown in Figure ~\ref{Figures/ch4/R2/CR}, coverage ratio decreases when the number of periods increases due to dead nodes. Model-5 is slightly more efficient than other models, because it offers a good coverage ratio for a larger number of periods in comparison with other models.
577 \item {{\bf Active Sensors Ratio}}
578 %\subsubsection{Active Sensors Ratio}
580 Figure~\ref{Figures/ch4/R2/ASR} shows the average active nodes ratio for 150 deployed nodes.
583 \includegraphics[scale=0.8]{Figures/ch4/R2/ASR.pdf}
584 \caption{Active sensors ratio for 150 deployed nodes }
585 \label{Figures/ch4/R2/ASR}
588 The results presented in Figure~\ref{Figures/ch4/R2/ASR} show the superiority of the proposed Model-5, in comparison with the other models. The model with fewer number of primary points uses fewer active nodes than the other models.
589 According to the results presented in Figure~\ref{Figures/ch4/R2/CR}, we observe that Model-5 continues to a larger number of periods with a better coverage ratio compared with other models. The advantage of Model-5 is to use fewer number of active nodes for each period compared with Model-9, Model-13, Model-17, and Model-21. This led to continuing for a larger number of periods and thus extending the network lifetime.
592 \item {{\bf Stopped simulation runs}}
593 %\subsubsection{The percentage of stopped simulation runs}
595 Figure~\ref{Figures/ch4/R2/SR} illustrates the percentage of stopped simulation runs per period for 150 deployed nodes.
599 \includegraphics[scale=0.8]{Figures/ch4/R2/SR.pdf}
600 \caption{Percentage of stopped simulation runs for 150 deployed nodes }
601 \label{Figures/ch4/R2/SR}
604 When the number of primary points is increased, the percentage of the stopped simulation runs per period is increased. The reason behind the increase is the increasing number of dead sensors when the primary points increase. Model-5 is better than other models because it conserves more energy by turning on less sensors during the sensing phase and in the same time it preserves a good coverage for a larger number of periods in comparison with other models. Model~5 seems to be more suitable to be used in wireless sensor networks. \\
607 \item {{\bf Energy Consumption}}
608 %\subsubsection{The Energy Consumption}
610 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/EC}(a) and~\ref{Figures/ch4/R2/EC}(b) illustrate the energy consumption for different network sizes for $Lifetime_{95}$ and $Lifetime_{50}$.
614 %\begin{multicols}{1}
616 \includegraphics[scale=0.8]{Figures/ch4/R2/EC95.pdf}\\~ ~ ~ ~ ~(a) \\
618 \includegraphics[scale=0.8]{Figures/ch4/R2/EC50.pdf}\\~ ~ ~ ~ ~(b)
621 \caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
622 \label{Figures/ch4/R2/EC}
625 We see from the results presented in both figures that the energy consumed by the network for each period increases when the number of primary points increases. Indeed, the decision for the optimization process requires more time, which leads to consuming more energy during the listening mode. The results show that Model-5 is the most competitive from the energy consumption point of view and the coverage ratio point of view. The other models have a high energy consumption due to the increase in the primary points. In fact, Model-5 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.
627 \item {{\bf Execution Time}}
628 %\subsubsection{Execution Time}
630 In this experiment, we study 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 period. The original execution time is computed as described in section \ref{ch4:sec:04:04}.
634 \includegraphics[scale=0.8]{Figures/ch4/R2/T.pdf}
635 \caption{Execution Time (in seconds)}
636 \label{Figures/ch4/R2/T}
639 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-5 has lower execution time in comparison with other models because it used the smaller number of primary points to represent the area of the sensor. Conversely, the other primary point models have presented higher execution times.
640 Moreover, Model-5 has more suitable execution times and coverage ratio that lead to continue for a larger number of period extending the network lifetime. We think that a good primary point model is one that balances between the coverage ratio and the number of periods during the lifetime of the network.
642 \item {{\bf Network Lifetime}}
643 %\subsubsection{The Network Lifetime}
645 Finally, we study the effect of increasing the primary points on the lifetime of the network.
646 %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.
647 As highlighted by Figures~\ref{Figures/ch4/R2/LT}(a) and \ref{Figures/ch4/R2/LT}(b), the network lifetime obviously increases when the size of the network increases, with Model-5 that leads to the larger lifetime improvement. \\ \\
649 Comparison shows that Model-5, which uses less number of primary points, is the best one because it is less energy consuming during the network lifetime. It is also the better one from the point of view of coverage ratio. Our proposed Model-5 efficiently prolongs the network lifetime with a good coverage ratio in comparison with other models. Therefore, we have chosen Model-5 for all the experiments presented thereafter.
655 \includegraphics[scale=0.8]{Figures/ch4/R2/LT95.pdf}\\~ ~ ~ ~ ~(a) \\
657 \includegraphics[scale=0.8]{Figures/ch4/R2/LT50.pdf}\\~ ~ ~ ~ ~(b)
659 \caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
660 \label{Figures/ch4/R2/LT}
665 \subsection{Performance Comparison with other Approaches}
666 \label{ch4:sec:04:07}
668 Based on the results, conducted in the previous subsections, \ref{ch4:sec:04:02} and \ref{ch4:sec:04:03}, DiLCO-16 and DiLCO-32 protocols, both with Model-5, seem to be the best candidates to be compared with other approaches. The first approach is called DESK~\cite{DESK}, which is a fully distributed coverage algorithm. The second approach 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 active during the sensing phase time. \\ \\
670 \begin{enumerate}[i)]
671 \item {{\bf Coverage Ratio}}
672 %\subsubsection{Coverage Ratio}
674 The average coverage ratio for 150 deployed nodes is demonstrated in Figure~\ref{Figures/ch4/R3/CR}.
678 \includegraphics[scale=0.8] {Figures/ch4/R3/CR.eps}
679 \caption{Coverage ratio for 150 deployed nodes}
680 \label{Figures/ch4/R3/CR}
682 DESK and GAF provide a little better coverage ratio with 99.99\% and 99.91\% against 98.4\% and 98.9\% produced by DiLCO-16 and DiLCO-32 for the lowest number of periods. \\ \\ \\
684 This is due to the fact that DiLCO protocol versions put in sleep mode redundant sensors thanks to the optimization (which lightly decreases the coverage ratio), while there are more active nodes in the case of DESK and GAF.
686 Moreover, when the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases.
687 %This is due to dead nodes. However, DiLCO-16 protocol and DiLCO-32 protocol maintain almost a good coverage.
688 GAF exhibits in particular a fast decrease. Our protocols also provide decreasing coverage ratio, but far more better than those of DESK and GAF. DiLCO-16 and DiLCO-32 clearly outperform DESK and GAF for number of periods between 32 and 103.
689 This is because they optimize 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.
690 %, and this will lead to continuing for a larger number of periods 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.
692 \item {{\bf Active Sensors Ratio}}
693 %\subsubsection{Active Sensors Ratio}
695 It is important to have as few active nodes as possible in each period, 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.
699 \includegraphics[scale=0.8]{Figures/ch4/R3/ASR.eps}
700 \caption{Active sensors ratio for 150 deployed nodes }
701 \label{Figures/ch4/R3/ASR}
704 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. DESK and GAF have, respectively, 37.5 \% and 44.5 \% active nodes, whereas DiLCO-16 and DiLCO-32 protocols compete perfectly with only 23.7 \% and 25.8 \% active nodes for the first 14 periods. Then as the number of periods increases DiLCO-16 and DiLCO-32 protocols have larger number of active nodes in comparison with DESK and GAF, especially from period $35^{th}$ 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 periods $35^{th}$ and $32^{th}$ because there are many dead nodes due to the high energy consumption by the redundant nodes during the previous sensing phases. \\
707 \item {{\bf Stopped simulation runs}}
708 %\subsubsection{The percentage of stopped simulation runs}
709 %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 period.
711 Figure~\ref{Figures/ch4/R3/SR} illustrates the percentage of stopped simulation runs per period for 150 deployed nodes.
714 \includegraphics[scale=0.8]{Figures/ch4/R3/SR.eps}
715 \caption{Percentage of stopped simulation runs for 150 deployed nodes }
716 \label{Figures/ch4/R3/SR}
718 On the one hand, 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 they distribute the optimization on several subregions.
719 % 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.
722 \item {{\bf Energy Consumption}}
723 %\subsubsection{The Energy Consumption}
724 %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.
726 Figures~\ref{Figures/ch4/R3/EC}(a) and~\ref{Figures/ch4/R3/EC}(b) illustrate the energy consumption for different network sizes for $Lifetime_{95}$ and $Lifetime_{50}$.
730 %\begin{multicols}{1}
732 \includegraphics[scale=0.8]{Figures/ch4/R3/EC95.eps}\\~ ~ ~ ~ ~(a) \\
734 \includegraphics[scale=0.8]{Figures/ch4/R3/EC50.eps}\\~ ~ ~ ~ ~(b)
737 \caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
738 \label{Figures/ch4/R3/EC}
742 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.
743 %as well as the energy consumed during the different modes of sensor nodes.
744 In fact, the distribution of computation over the subregions greatly reduces the number of communications and the time of listening, thanks to the partitioning of the initial network into several independent subnetworks.
747 \item {{\bf Network Lifetime}}
748 %\subsubsection{The Network Lifetime}
749 %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.
751 %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.
755 % \begin{multicols}{0}
757 \includegraphics[scale=0.8]{Figures/ch4/R3/LT95.eps}\\~ ~ ~ ~ ~(a) \\
759 \includegraphics[scale=0.8]{Figures/ch4/R3/LT50.eps}\\~ ~ ~ ~ ~(b)
762 \caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
763 \label{Figures/ch4/R3/LT}
766 As highlighted by Figures~\ref{Figures/ch4/R3/LT}(a) and \ref{Figures/ch4/R3/LT}(b), the network lifetime obviously increases when the size of the network increases, with DiLCO-16 protocol and DiLCO-32 protocol which lead to maximize the lifetime of the network compared with other approaches.
767 By choosing the best suited nodes, for each period, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next periods, DiLCO-16 protocol and DiLCO-32 protocol efficiently prolong the network lifetime.
768 Comparison shows that DiLCO-16 protocol and DiLCO-32 protocol, which use distributed optimization over the subregions, are the best ones because they are robust to network disconnection during the network lifetime as well as they consume less energy in comparison with other approaches.
769 %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.
776 A crucial problem in WSN is to schedule the sensing activities of the different nodes in order to ensure both 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
777 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.
