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7 \chapter{Multiround Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}
11 \section{Introduction}
14 \indent The fast developments of low-cost sensor devices and wireless
15 communications have allowed the emergence of WSNs. A WSN includes a large number
16 of small, limited-power sensors that can sense, process, and transmit data over
17 a wireless communication. They communicate with each other by using multi-hop
18 wireless communications and cooperate together to monitor the area of interest,
19 so that each measured data can be reported to a monitoring center called sink
20 for further analysis~\cite{ref222}. There are several fields of application
21 covering a wide spectrum for a WSN, including health, home, environmental,
22 military, and industrial applications~\cite{ref19}.
24 On the one hand sensor nodes run on batteries with limited capacities, and it is
25 often costly or simply impossible to replace and/or recharge batteries,
26 especially in remote and hostile environments. Obviously, to achieve a long life
27 of the network it is important to conserve battery power. Therefore, lifetime
28 optimization is one of the most critical issues in wireless sensor networks. On
29 the other hand we must guarantee coverage over the area of interest. To fulfill
30 these two objectives, the main idea is to take advantage of overlapping sensing
31 regions to turn-off redundant sensor nodes and thus save energy. In this paper,
32 we concentrate on the area coverage problem, with the objective of maximizing
33 the network lifetime by using an optimized multiround scheduling.
35 We study the problem of designing an energy-efficient optimization algorithm that divides the sensor nodes in a WSN into multiple cover sets such that the area of interest is monitored as long as possible. Providing multiple cover sets can be used to improve the energy efficiency of WSNs. Therefore, in order to increase the longevity of the WSN and conserve the energy, it can be useful to provide multiple cover sets in one time after that schedule them for multiple rounds, so that the battery life of a sensor is not wasted due to the repeated execution of the coverage optimization algorithm, as well as the information exchange and leader election.
37 The MuDiLCO protocol (for Multiround Distributed Lifetime Coverage Optimization protocol) presented in this chapter is an extension of the approach introduced in chapter 4. Simulation results have shown that it was more interesting to divide the area into several subregions, given the computation complexity. Compared to our protocol in chapter 4, in this one we study the possibility of dividing the sensing phase into multiple rounds. In fact, in this chapter we make a multiround optimization while it was a single round optimization in our protocol in chapter 4.
40 The remainder of the chapter continues with section \ref{ch5:sec:02} where a detail of MuDiLCO Protocol is presented. The next section describes the Primary Points based Multiround Coverage Problem formulation which is used to schedule the activation of sensors in T cover sets. Section \ref{ch5:sec:04} shows the simulation
41 results. The chapter ends with a conclusion and some suggestions for further work.
47 \section{MuDiLCO Protocol Description}
49 \noindent In this section, we introduce the MuDiLCO protocol which is distributed on each subregion in the area of interest. It is based on two energy-efficient
50 mechanisms: subdividing the area of interest into several subregions (like cluster architecture) using divide and conquer method, where the sensor nodes cooperate within each subregion as independent group in order to achieve a network leader election; and sensor activity scheduling for maintaining the coverage and prolonging the network lifetime, which are applied periodically. MuDiLCO protocol uses the same assumptions and network model that presented in chapter 4, section \ref{ch4:sec:02:01} and it has been used the primary point coverage model which is described in the same chapter, section \ref{ch4:sec:02:02}.
53 \subsection{Background Idea and Algorithm}
55 The area of interest can be divided using the divide-and-conquer strategy into
56 smaller areas, called subregions, and then our MuDiLCO protocol will be
57 implemented in each subregion in a distributed way.
59 As can be seen in Figure~\ref{fig2}, our protocol works in periods fashion,
60 where each is divided into 4 phases: Information~Exchange, Leader~Election,
61 Decision, and Sensing. The information exchange among wireless sensor nodes is described in chapter 4, section \ref{ch4:sec:02:03:01}. The leader election in each subregion is explained in chapter 4, section \ref{ch4:sec:02:03:02}, but the difference in that the elected leader in each subregion is for each period. In decision phase, each WSNL will solve an integer program to select which cover sets will be
62 activated in the following sensing phase to cover the subregion to which it belongs. The integer program will produce $T$ cover sets, one for each round. The WSNL will send an Active-Sleep packet to each sensor in the subregion based on the algorithm's results, indicating if the sensor should be active or not in
63 each round of the sensing phase. Each sensing phase may be itself divided into $T$ rounds
64 and for each round a set of sensors (a cover set) is responsible for the sensing
65 task. Each sensor node in the subregion will
66 receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
67 sleep for each round of the sensing phase. Algorithm~\ref{alg:MuDiLCO}, which
68 will be executed by each node at the beginning of a period, explains how the
69 Active-Sleep packet is obtained. In this way, a multiround optimization process is performed during each
70 period after Information~Exchange and Leader~Election phases, in order to
71 produce $T$ cover sets that will take the mission of sensing for $T$ rounds.
73 \centering \includegraphics[width=160mm]{Figures/ch5/GeneralModel.jpg} % 70mm Modelgeneral.pdf
74 \caption{The MuDiLCO protocol scheme executed on each node}
79 This protocol minimizes the impact of unexpected node failure (not due to batteries running out of energy), because it works in periods.
81 On the one hand, if a node failure is detected before making the decision, the node will not participate during this phase, and, on the other hand, if the node failure occurs after the decision, the sensing task of the network will be temporarily affected: only during the period of sensing until a new period starts.
83 The energy consumption and some other constraints can easily be taken into account since the sensors can update and then exchange their information (including their residual energy) at the beginning of each period. However, the pre-sensing phases (Information Exchange, Leader Election, and Decision) are energy consuming for some nodes, even when they do not join the network to monitor the area.
88 % \KwIn{all the parameters related to information exchange}
89 % \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
91 %\emph{Initialize the sensor node and determine it's position and subregion} \;
93 \If{ $RE_j \geq E_{R}$ }{
94 \emph{$s_j.status$ = COMMUNICATION}\;
95 \emph{Send $INFO()$ packet to other nodes in the subregion}\;
96 \emph{Wait $INFO()$ packet from other nodes in the subregion}\;
97 %\emph{UPDATE $RE_j$ for every sent or received INFO Packet}\;
98 %\emph{ Collect information and construct the list L for all nodes in the subregion}\;
100 %\If{ the received INFO Packet = No. of nodes in it's subregion -1 }{
101 \emph{LeaderID = Leader election}\;
102 \If{$ s_j.ID = LeaderID $}{
103 \emph{$s_j.status$ = COMPUTATION}\;
104 \emph{$\left\{\left(X_{1,k},\dots,X_{T,k}\right)\right\}_{k \in J}$ =
105 Execute Integer Program Algorithm($T,J$)}\;
106 \emph{$s_j.status$ = COMMUNICATION}\;
107 \emph{Send $ActiveSleep()$ to each node $k$ in subregion a packet \\
108 with vector of activity scheduling $(X_{1,k},\dots,X_{T,k})$}\;
109 \emph{Update $RE_j $}\;
112 \emph{$s_j.status$ = LISTENING}\;
113 \emph{Wait $ActiveSleep()$ packet from the Leader}\;
114 % \emph{After receiving Packet, Retrieve the schedule and the $T$ rounds}\;
115 \emph{Update $RE_j $}\;
119 \Else { Exclude $s_j$ from entering in the current sensing phase}
122 \caption{MuDiLCO($s_j$)}
130 \section{Primary Points based Multiround Coverage Problem Formulation}
134 According to our algorithm~\ref{alg:MuDiLCO}, the integer program is based on the model
135 proposed by \cite{ref156} with some modifications, where the objective is
136 to find a maximum number of disjoint cover sets. To fulfill this goal, the
137 authors proposed an integer program which forces undercoverage and overcoverage
138 of targets to become minimal at the same time. They use binary variables
139 $x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our model, we
140 consider binary variables $X_{t,j}$ to determine the possibility of activating
141 sensor $j$ during round $t$ of a given sensing phase. We also consider primary
142 points as targets. The set of primary points is denoted by $P$ and the set of
143 sensors by $J$. Only sensors able to be alive during at least one round are
144 involved in the integer program.
147 For a primary point $p$, let $\alpha_{j,p}$ denote the indicator function of
148 whether the point $p$ is covered, that is
150 \alpha_{j,p} = \left \{
152 1 & \mbox{if the primary point $p$ is covered} \\
153 & \mbox{by sensor node $j$}, \\
154 0 & \mbox{otherwise.}\\
158 The number of active sensors that cover the primary point $p$ during
159 round $t$ is equal to $\sum_{j \in J} \alpha_{j,p} * X_{t,j}$ where
163 1& \mbox{if sensor $j$ is active during round $t$,} \\
164 0 & \mbox{otherwise.}\\
168 We define the Overcoverage variable $\Theta_{t,p}$ as
170 \Theta_{t,p} = \left \{
172 0 & \mbox{if the primary point $p$}\\
173 & \mbox{is not covered during round $t$,}\\
174 \left( \sum_{j \in J} \alpha_{jp} * X_{tj} \right)- 1 & \mbox{otherwise.}\\
178 More precisely, $\Theta_{t,p}$ represents the number of active sensor nodes
179 minus one that cover the primary point $p$ during round $t$. The
180 Undercoverage variable $U_{t,p}$ of the primary point $p$ during round $t$ is
185 1 &\mbox{if the primary point $p$ is not covered during round $t$,} \\
186 0 & \mbox{otherwise.}\\
191 Our coverage optimization problem can then be formulated as follows
193 \min \sum_{t=1}^{T} \sum_{p=1}^{P} \left(W_{\theta}* \Theta_{t,p} + W_{U} * U_{t,p} \right) \label{eq15}
198 \sum_{j=1}^{|J|} \alpha_{j,p} * X_{t,j} = \Theta_{t,p} - U_{t,p} + 1 \label{eq16} \hspace{6 mm} \forall p \in P, t = 1,\dots,T
202 \sum_{t=1}^{T} X_{t,j} \leq \lfloor {RE_{j}/E_{R}} \rfloor \hspace{6 mm} \forall j \in J, t = 1,\dots,T
207 X_{t,j} \in \lbrace0,1\rbrace, \hspace{10 mm} \forall j \in J, t = 1,\dots,T \label{eq17}
211 U_{t,p} \in \lbrace0,1\rbrace, \hspace{10 mm}\forall p \in P, t = 1,\dots,T \label{eq18}
215 \Theta_{t,p} \geq 0 \hspace{10 mm}\forall p \in P, t = 1,\dots,T \label{eq178}
221 \item $X_{t,j}$: indicates whether or not the sensor $j$ is actively sensing
222 during round $t$ (1 if yes and 0 if not);
223 \item $\Theta_{t,p}$ - {\it overcoverage}: the number of sensors minus one that
224 are covering the primary point $p$ during round $t$;
225 \item $U_{t,p}$ - {\it undercoverage}: indicates whether or not the primary
226 point $p$ is being covered during round $t$ (1 if not covered and 0 if
230 The first group of constraints indicates that some primary point $p$ should be
231 covered by at least one sensor and, if it is not always the case, overcoverage
232 and undercoverage variables help balancing the restriction equations by taking
233 positive values. The constraint given by equation~(\ref{eq144}) guarantees that
234 the sensor has enough energy ($RE_j$ corresponds to its remaining energy) to be
235 alive during the selected rounds knowing that $E_{R}$ is the amount of energy
236 required to be alive during one round.
238 There are two main objectives. First, we limit the overcoverage of primary
239 points in order to activate a minimum number of sensors. Second we prevent the
240 absence of monitoring on some parts of the subregion by minimizing the
241 undercoverage. The weights $W_\theta$ and $W_U$ must be properly chosen so as
242 to guarantee that the maximum number of points are covered during each round.
243 %% MS W_theta is smaller than W_u => problem with the following sentence
244 In our simulations, priority is given to the coverage by choosing $W_{U}$ very
245 large compared to $W_{\theta}$.
251 \section{Experimental Study and Analysis}
254 \subsection{Simulation Setup}
255 \label{ch5:sec:04:01}
256 We conducted a series of simulations to evaluate the efficiency and the
257 relevance of our approach, using the discrete event simulator OMNeT++
258 \cite{ref158}. The simulation parameters are summarized in Table~\ref{table3}. Each experiment for a network is run over 25~different random topologies and the results presented hereafter are the average of these 25 runs.
259 %Based on the results of our proposed work in~\cite{idrees2014coverage}, we found as the region of interest are divided into larger subregions as the network lifetime increased. In this simulation, the network are divided into 16 subregions.
260 We performed simulations for five different densities varying from 50 to
261 250~nodes deployed over a $50 \times 25~m^2 $ sensing field. More
262 precisely, the deployment is controlled at a coarse scale in order to ensure
263 that the deployed nodes can cover the sensing field with the given sensing
266 %%RC these parameters are realistic?
267 %% maybe we can increase the field and sensing range. 5mfor Rs it seems very small... what do the other good papers consider ?
270 \caption{Relevant parameters for network initializing.}
273 % used for centering table
275 % centered columns (4 columns)
277 %inserts double horizontal lines
278 Parameter & Value \\ [0.5ex]
280 %Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
284 % inserts single horizontal line
285 Sensing field size & $(50 \times 25)~m^2 $ \\
286 % inserting body of the table
288 Network size & 50, 100, 150, 200 and 250~nodes \\
290 Initial energy & 500-700~joules \\
292 Sensing time for one round & 60 Minutes \\
293 $E_{R}$ & 36 Joules\\
297 % [1ex] adds vertical space
303 % is used to refer this table in the text
306 Our protocol is declined into four versions: MuDiLCO-1, MuDiLCO-3, MuDiLCO-5, and MuDiLCO-7, corresponding respectively to $T=1,3,5,7$ ($T$ the number of rounds in one sensing period). In the following, we will make comparisons with two other methods. The first method, called DESK and proposed by \cite{DESK}, is a fully distributed coverage algorithm. The second method is called
307 GAF~\cite{GAF}, consists in dividing the region into fixed squares.
308 During the decision phase, in each square, one sensor is then chosen to remain active during the sensing phase time.
310 Some preliminary experiments were performed in chapter 4 to study the choice of the number of subregions which subdivides the sensing field, considering different network
311 sizes. They show that as the number of subregions increases, so does the network
312 lifetime. Moreover, it makes the MuDiLCO protocol more robust against random
313 network disconnection due to node failures. However, too many subdivisions
314 reduce the advantage of the optimization. In fact, there is a balance between
315 the benefit from the optimization and the execution time needed to solve
316 it. Therefore, we have set the number of subregions to 16 rather than 32.
318 We used the modeling language and the optimization solver which are mentioned in chapter 4, section \ref{ch4:sec:04:02}. In addition, we employed an energy consumption model, which is presented in chapter 4, section \ref{ch4:sec:04:03}.
320 %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 $E_{R}=36~\mbox{Joules}$, the minimum energy needed for the node to stay alive during one round. This value has been computed by multiplying the energy consumed in active state (9.72 mW) by the time in second for one round (3600 seconds). According to the interval of initial energy, a sensor may be alive during at most 20 rounds.
323 \label{ch5:sec:04:02}
324 To evaluate our approach we consider the following performance metrics:
328 \item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much of the area
329 of a sensor field is covered. In our case, the sensing field is represented as
330 a connected grid of points and we use each grid point as a sample point to
331 compute the coverage. The coverage ratio can be calculated by:
334 \mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100,
336 where $n^t$ is the number of covered grid points by the active sensors of all
337 subregions during round $t$ in the current sensing phase and $N$ is the total number
338 of grid points in the sensing field of the network. In our simulations $N = 51
339 \times 26 = 1326$ grid points.
341 \item{{\bf Number of Active Sensors Ratio (ASR)}:} it is important to have as
342 few active nodes as possible in each round, in order to minimize the
343 communication overhead and maximize the network lifetime. The Active Sensors
344 Ratio is defined as follows:
346 \scriptsize \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R
347 \mbox{$A_r^t$}}{\mbox{$|J|$}} \times 100,
349 where $A_r^t$ is the number of active sensors in the subregion $r$ during round
350 $t$ in the current sensing phase, $|J|$ is the total number of sensors in the
351 network, and $R$ is the total number of subregions in the network.
353 \item {{\bf Network Lifetime}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
355 \item {{\bf Energy Consumption (EC)}:} the average energy consumption can be
356 seen as the total energy consumed by the sensors during the $Lifetime_{95}$ or
357 $Lifetime_{50}$ divided by the number of rounds. EC can be computed as
360 % New version with global loops on period
363 \mbox{EC} = \frac{\sum\limits_{m=1}^{M_L} \left[ \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T_m} \left( E^{a}_t+E^{s}_t \right) \right]}{\sum\limits_{m=1}^{M_L} T_m},
367 where $M_L$ is the number of periods and $T_m$ the number of rounds in a
368 period~$m$, both during $Lifetime_{95}$ or $Lifetime_{50}$. The total energy
369 consumed by the sensors (EC) comes through taking into consideration four main
370 energy factors. The first one , denoted $E^{\scriptsize \mbox{com}}_m$,
371 represents the energy consumption spent by all the nodes for wireless
372 communications during period $m$. $E^{\scriptsize \mbox{list}}_m$, the next
373 factor, corresponds to the energy consumed by the sensors in LISTENING status
374 before receiving the decision to go active or sleep in period $m$.
375 $E^{\scriptsize \mbox{comp}}_m$ refers to the energy needed by all the leader
376 nodes to solve the integer program during a period. Finally, $E^a_t$ and $E^s_t$
377 indicate the energy consumed by the whole network in round $t$.
380 \item {{\bf Execution Time}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
382 \item {{\bf Stopped simulation runs}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
388 \subsection{Results Analysis and Comparison }
389 \label{ch5:sec:04:02}
392 \begin{enumerate}[(i)]
394 \item {{\bf Coverage Ratio}}
395 %\subsection{Coverage ratio}
396 %\label{ch5:sec:03:02:01}
398 Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes. We
399 can notice that for the first thirty rounds both DESK and GAF provide a coverage
400 which is a little bit better than the one of MuDiLCO.
402 This is due to the fact that, in comparison with MuDiLCO which uses optimization
403 to put in SLEEP status redundant sensors, more sensor nodes remain active with
404 DESK and GAF. As a consequence, when the number of rounds increases, a larger
405 number of node failures can be observed in DESK and GAF, resulting in a faster
406 decrease of the coverage ratio. Furthermore, our protocol allows to maintain a
407 coverage ratio greater than 50\% for far more rounds. Overall, the proposed
408 sensor activity scheduling based on optimization in MuDiLCO maintains higher
409 coverage ratios of the area of interest for a larger number of rounds. It also
410 means that MuDiLCO saves more energy, with fewer dead nodes, at most for several
411 rounds, and thus should extend the network lifetime.
415 \includegraphics[scale=0.8] {Figures/ch5/R1/CR.pdf}
416 \caption{Average coverage ratio for 150 deployed nodes}
421 \item {{\bf Active sensors ratio}}
422 %\subsection{Active sensors ratio}
423 %\label{ch5:sec:03:02:02}
425 It is crucial to have as few active nodes as possible in each round, in order to
426 minimize the communication overhead and maximize the network
427 lifetime. Figure~\ref{fig4} presents the active sensor ratio for 150 deployed
428 nodes all along the network lifetime. It appears that up to round thirteen, DESK
429 and GAF have respectively 37.6\% and 44.8\% of nodes in ACTIVE status, whereas
430 MuDiLCO clearly outperforms them with only 24.8\% of active nodes. After the
431 thirty-fifth round, MuDiLCO exhibits larger numbers of active nodes, which agrees
432 with the dual observation of higher level of coverage made previously.
433 Obviously, in that case, DESK and GAF have fewer active nodes since they have activated many nodes in the beginning. Anyway, MuDiLCO activates the available nodes in a more efficient manner.
437 \includegraphics[scale=0.8]{Figures/ch5/R1/ASR.pdf}
438 \caption{Active sensors ratio for 150 deployed nodes}
442 \item {{\bf Stopped simulation runs}}
443 %\subsection{Stopped simulation runs}
444 %\label{ch5:sec:03:02:03}
446 Figure~\ref{fig6} reports the cumulative percentage of stopped simulations runs
447 per round for 150 deployed nodes. This figure gives the breakpoint for each method. DESK stops first, after approximately 45~rounds, because it consumes the
448 more energy by turning on a large number of redundant nodes during the sensing
449 phase. GAF stops secondly for the same reason than DESK. MuDiLCO overcomes
450 DESK and GAF because the optimization process distributed on several subregions
451 leads to coverage preservation and so extends the network lifetime. Let us
452 emphasize that the simulation continues as long as a network in a subregion is
458 \includegraphics[scale=0.8]{Figures/ch5/R1/SR.pdf}
459 \caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes }
465 \item {{\bf Energy consumption}} \label{subsec:EC}
466 %\subsection{Energy consumption}
467 %\label{ch5:sec:03:02:04}
469 We measure the energy consumed by the sensors during the communication,
470 listening, computation, active, and sleep status for different network densities
471 and compare it with the two other methods. Figures~\ref{fig7}(a)
472 and~\ref{fig7}(b) illustrate the energy consumption, considering different
473 network sizes, for $Lifetime_{95}$ and $Lifetime_{50}$.
478 %\begin{multicols}{1}
480 \includegraphics[scale=0.8]{Figures/ch5/R1/EC95.pdf}\\~ ~ ~ ~ ~(a) \\
482 \includegraphics[scale=0.8]{Figures/ch5/R1/EC50.pdf}\\~ ~ ~ ~ ~(b)
485 \caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
490 The results show that MuDiLCO is 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 status of the sensor node. Among the different versions of our protocol, the MuDiLCO-7 one consumes more energy than the other versions. This is easy to understand since the bigger the number of rounds and
491 the number of sensors involved in the integer program is the larger the time computation to solve the optimization problem is. To improve the performances of MuDiLCO-7, we should increase the number of subregions in order to have fewer sensors to consider in the integer program.
495 \item {{\bf Execution time}}
496 %\subsection{Execution time}
497 %\label{ch5:sec:03:02:05}
499 We observe the impact of the network size and of the number of rounds on the
500 computation time. Figure~\ref{fig77} gives the average execution times in
501 seconds (needed to solve optimization problem) for different values of $T$. The original execution time is computed as described in chapter 4, section \ref{ch4:sec:04:02}.
503 %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 $\left( \frac{35330}{2} \times \frac{1}{6} \right)$ and reported on Figure~\ref{fig77} for different network sizes.
507 \includegraphics[scale=0.8]{Figures/ch5/R1/T.pdf}
508 \caption{Execution Time (in seconds)}
512 As expected, the execution time increases with the number of rounds $T$ taken into account to schedule the sensing phase. The times obtained for $T=1,3$ or $5$ seem bearable, but for $T=7$ they become quickly unsuitable for a sensor node, especially when the sensor network size increases. Again, we can notice that if we want to schedule the nodes activities for a large number of rounds,
513 we need to choose a relevant number of subregions in order to avoid a complicated and cumbersome optimization. On the one hand, a large value for $T$ permits to reduce the energy overhead due to the three pre-sensing phases, on the other hand a leader node may waste a considerable amount of energy to solve the optimization problem.
517 \item {{\bf Network lifetime}}
518 %\subsection{Network lifetime}
519 %\label{ch5:sec:03:02:06}
521 The next two figures, Figures~\ref{fig8}(a) and \ref{fig8}(b), illustrate the network lifetime for different network sizes, respectively for $Lifetime_{95}$ and $Lifetime_{50}$. Both figures show that the network lifetime increases together with the number of sensor nodes, whatever the protocol, thanks to the node density which results in more and more redundant nodes that can be deactivated and thus save energy. Compared to the other approaches, our MuDiLCO
522 protocol maximizes the lifetime of the network. In particular, the gain in lifetime for a coverage over 95\% is greater than 38\% when switching from GAF to MuDiLCO-3. The slight decrease that can be observed for MuDiLCO-7 in case of $Lifetime_{95}$ with large wireless sensor networks results from the difficulty of the optimization problem to be solved by the integer program.
523 This point was already noticed in \ref{subsec:EC} devoted to the
524 energy consumption, since network lifetime and energy consumption are directly linked.
529 % \begin{multicols}{0}
531 \includegraphics[scale=0.8]{Figures/ch5/R1/LT95.pdf}\\~ ~ ~ ~ ~(a) \\
533 \includegraphics[scale=0.8]{Figures/ch5/R1/LT50.pdf}\\~ ~ ~ ~ ~(b)
536 \caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
548 We have addressed the problem of the coverage and of the lifetime optimization in wireless sensor networks. This is a key issue as sensor nodes have limited resources in terms of memory, energy, and computational power. To cope with this problem, the field of sensing is divided into smaller subregions using the concept of divide-and-conquer method, and then we propose a protocol which optimizes coverage and lifetime performances in each subregion. Our protocol,
549 called MuDiLCO (Multiround Distributed Lifetime Coverage Optimization) combines two efficient techniques: network leader election and sensor activity scheduling.
551 The activity scheduling in each subregion works in periods, where each period consists of four phases: (i) Information Exchange, (ii) Leader Election, (iii) Decision Phase to plan the activity of the sensors over $T$ rounds, (iv) Sensing Phase itself divided into T rounds.
553 Simulations results show the relevance of the proposed protocol in terms of lifetime, coverage ratio, active sensors ratio, energy consumption, execution time. Indeed, when dealing with large wireless sensor networks, a distributed approach, like the one we propose, allows to reduce the difficulty of a single global optimization problem by partitioning it into many smaller problems, one per subregion, that can be solved more easily. Nevertheless, results also show that it is not possible to plan the activity of sensors over too many rounds because the resulting optimization problem leads to too high-resolution times and thus to an excessive energy consumption.
