1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
5 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
7 \chapter{Multiround Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}
12 Coverage and lifetime are two paramount problems in Wireless Sensor Networks (WSNs). In this paper, a method called Multiround Distributed Lifetime Coverage
13 Optimization protocol (MuDiLCO) is proposed to maintain the coverage and to improve the lifetime in wireless sensor networks. The area of interest is first
14 divided into subregions and then the MuDiLCO protocol is distributed on the sensor nodes in each subregion. The proposed MuDiLCO protocol works in periods
15 during which sets of sensor nodes are scheduled to remain active for a number of rounds during the sensing phase, to ensure coverage so as to maximize the
16 lifetime of WSN. The decision process is carried out by a leader node, which solves an integer program to produce the best representative sets to be used
17 during the rounds of the sensing phase. Compared with some existing protocols, simulation results based on multiple criteria (energy consumption, coverage
18 ratio, and so on) show that the proposed protocol can prolong efficiently the network lifetime and improve the coverage performance.
20 \section{MuDiLCO Protocol Description}
22 \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
23 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}.
26 \subsection{Background Idea and Algorithm}
28 The area of interest can be divided using the divide-and-conquer strategy into
29 smaller areas, called subregions, and then our MuDiLCO protocol will be
30 implemented in each subregion in a distributed way.
32 As can be seen in Figure~\ref{fig2}, our protocol works in periods fashion,
33 where each is divided into 4 phases: Information~Exchange, Leader~Election,
34 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
35 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
36 each round of the sensing phase. Each sensing phase may be itself divided into $T$ rounds
37 and for each round a set of sensors (a cover set) is responsible for the sensing
38 task. Each sensor node in the subregion will
39 receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
40 sleep for each round of the sensing phase. Algorithm~\ref{alg:MuDiLCO}, which
41 will be executed by each node at the beginning of a period, explains how the
42 Active-Sleep packet is obtained. In this way a multiround optimization process is performed during each
43 period after Information~Exchange and Leader~Election phases, in order to
44 produce $T$ cover sets that will take the mission of sensing for $T$ rounds.
46 \centering \includegraphics[width=160mm]{Figures/ch5/GeneralModel.jpg} % 70mm Modelgeneral.pdf
47 \caption{The MuDiLCO protocol scheme executed on each node}
52 This protocol minimizes the impact of unexpected node failure (not due to batteries running out of energy), because it works in periods.
54 On the one hand, if a node failure is detected before making the decision, the node will not participate to 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.
56 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.
61 % \KwIn{all the parameters related to information exchange}
62 % \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
64 %\emph{Initialize the sensor node and determine it's position and subregion} \;
66 \If{ $RE_j \geq E_{R}$ }{
67 \emph{$s_j.status$ = COMMUNICATION}\;
68 \emph{Send $INFO()$ packet to other nodes in the subregion}\;
69 \emph{Wait $INFO()$ packet from other nodes in the subregion}\;
70 %\emph{UPDATE $RE_j$ for every sent or received INFO Packet}\;
71 %\emph{ Collect information and construct the list L for all nodes in the subregion}\;
73 %\If{ the received INFO Packet = No. of nodes in it's subregion -1 }{
74 \emph{LeaderID = Leader election}\;
75 \If{$ s_j.ID = LeaderID $}{
76 \emph{$s_j.status$ = COMPUTATION}\;
77 \emph{$\left\{\left(X_{1,k},\dots,X_{T,k}\right)\right\}_{k \in J}$ =
78 Execute Integer Program Algorithm($T,J$)}\;
79 \emph{$s_j.status$ = COMMUNICATION}\;
80 \emph{Send $ActiveSleep()$ to each node $k$ in subregion a packet \\
81 with vector of activity scheduling $(X_{1,k},\dots,X_{T,k})$}\;
82 \emph{Update $RE_j $}\;
85 \emph{$s_j.status$ = LISTENING}\;
86 \emph{Wait $ActiveSleep()$ packet from the Leader}\;
87 % \emph{After receiving Packet, Retrieve the schedule and the $T$ rounds}\;
88 \emph{Update $RE_j $}\;
92 \Else { Exclude $s_j$ from entering in the current sensing phase}
95 \caption{MuDiLCO($s_j$)}
103 \subsection{Primary Points based Multiround Coverage Problem Formulation}
104 %\label{ch5:sec:02:02}
106 According to our algorithm~\ref{alg:MuDiLCO}, the integer program is based on the model
107 proposed by \cite{ref156} with some modifications, where the objective is
108 to find a maximum number of disjoint cover sets. To fulfill this goal, the
109 authors proposed an integer program which forces undercoverage and overcoverage
110 of targets to become minimal at the same time. They use binary variables
111 $x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our model, we
112 consider binary variables $X_{t,j}$ to determine the possibility of activating
113 sensor $j$ during round $t$ of a given sensing phase. We also consider primary
114 points as targets. The set of primary points is denoted by $P$ and the set of
115 sensors by $J$. Only sensors able to be alive during at least one round are
116 involved in the integer program.
119 For a primary point $p$, let $\alpha_{j,p}$ denote the indicator function of
120 whether the point $p$ is covered, that is:
122 \alpha_{j,p} = \left \{
124 1 & \mbox{if the primary point $p$ is covered} \\
125 & \mbox{by sensor node $j$}, \\
126 0 & \mbox{otherwise.}\\
130 The number of active sensors that cover the primary point $p$ during
131 round $t$ is equal to $\sum_{j \in J} \alpha_{j,p} * X_{t,j}$ where:
135 1& \mbox{if sensor $j$ is active during round $t$,} \\
136 0 & \mbox{otherwise.}\\
140 We define the Overcoverage variable $\Theta_{t,p}$ as:
142 \Theta_{t,p} = \left \{
144 0 & \mbox{if the primary point $p$}\\
145 & \mbox{is not covered during round $t$,}\\
146 \left( \sum_{j \in J} \alpha_{jp} * X_{tj} \right)- 1 & \mbox{otherwise.}\\
150 More precisely, $\Theta_{t,p}$ represents the number of active sensor nodes
151 minus one that cover the primary point $p$ during round $t$. The
152 Undercoverage variable $U_{t,p}$ of the primary point $p$ during round $t$ is
157 1 &\mbox{if the primary point $p$ is not covered during round $t$,} \\
158 0 & \mbox{otherwise.}\\
163 Our coverage optimization problem can then be formulated as follows:
165 \min \sum_{t=1}^{T} \sum_{p=1}^{P} \left(W_{\theta}* \Theta_{t,p} + W_{U} * U_{t,p} \right) \label{eq15}
170 \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
174 \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
179 X_{t,j} \in \lbrace0,1\rbrace, \hspace{10 mm} \forall j \in J, t = 1,\dots,T \label{eq17}
183 U_{t,p} \in \lbrace0,1\rbrace, \hspace{10 mm}\forall p \in P, t = 1,\dots,T \label{eq18}
187 \Theta_{t,p} \geq 0 \hspace{10 mm}\forall p \in P, t = 1,\dots,T \label{eq178}
193 \item $X_{t,j}$: indicates whether or not the sensor $j$ is actively sensing
194 during round $t$ (1 if yes and 0 if not);
195 \item $\Theta_{t,p}$ - {\it overcoverage}: the number of sensors minus one that
196 are covering the primary point $p$ during round $t$;
197 \item $U_{t,p}$ - {\it undercoverage}: indicates whether or not the primary
198 point $p$ is being covered during round $t$ (1 if not covered and 0 if
202 The first group of constraints indicates that some primary point $p$ should be
203 covered by at least one sensor and, if it is not always the case, overcoverage
204 and undercoverage variables help balancing the restriction equations by taking
205 positive values. The constraint given by equation~(\ref{eq144}) guarantees that
206 the sensor has enough energy ($RE_j$ corresponds to its remaining energy) to be
207 alive during the selected rounds knowing that $E_{R}$ is the amount of energy
208 required to be alive during one round.
210 There are two main objectives. First, we limit the overcoverage of primary
211 points in order to activate a minimum number of sensors. Second we prevent the
212 absence of monitoring on some parts of the subregion by minimizing the
213 undercoverage. The weights $W_\theta$ and $W_U$ must be properly chosen so as
214 to guarantee that the maximum number of points are covered during each round.
215 %% MS W_theta is smaller than W_u => problem with the following sentence
216 In our simulations priority is given to the coverage by choosing $W_{U}$ very
217 large compared to $W_{\theta}$.
223 \section{Experimental Study and Analysis}
226 \subsection{Simulation Setup}
227 \label{ch5:sec:03:01}
228 We conducted a series of simulations to evaluate the efficiency and the
229 relevance of our approach, using the discrete event simulator OMNeT++
230 \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
232 %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.
233 We performed simulations for five different densities varying from 50 to
234 250~nodes deployed over a $50 \times 25~m^2 $ sensing field. More
235 precisely, the deployment is controlled at a coarse scale in order to ensure
236 that the deployed nodes can cover the sensing field with the given sensing
239 %%RC these parameters are realistic?
240 %% maybe we can increase the field and sensing range. 5mfor Rs it seems very small... what do the other good papers consider ?
243 \caption{Relevant parameters for network initializing.}
246 % used for centering table
248 % centered columns (4 columns)
250 %inserts double horizontal lines
251 Parameter & Value \\ [0.5ex]
253 %Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
257 % inserts single horizontal line
258 Sensing field size & $(50 \times 25)~m^2 $ \\
259 % inserting body of the table
261 Network size & 50, 100, 150, 200 and 250~nodes \\
263 Initial energy & 500-700~joules \\
265 Sensing time for one round & 60 Minutes \\
266 $E_{R}$ & 36 Joules\\
270 % [1ex] adds vertical space
276 % is used to refer this table in the text
279 Our protocol is declined into four versions: MuDiLCO-1, MuDiLCO-3, MuDiLCO-5,
280 and MuDiLCO-7, corresponding respectively to $T=1,3,5,7$ ($T$ the number of
281 rounds in one sensing period). In the following, we will make comparisons with
282 two other methods. The first method, called DESK and proposed by \cite{DESK},
283 is a full distributed coverage algorithm. The second method, called
284 GAF~\cite{GAF}, consists in dividing the region into fixed squares.
285 During the decision phase, in each square, one sensor is then chosen to remain
286 active during the sensing phase time.
288 Some preliminary experiments were performed in chapter 4 to study the choice of the number of
289 subregions which subdivides the sensing field, considering different network
290 sizes. They show that as the number of subregions increases, so does the network
291 lifetime. Moreover, it makes the MuDiLCO protocol more robust against random
292 network disconnection due to node failures. However, too many subdivisions
293 reduce the advantage of the optimization. In fact, there is a balance between
294 the benefit from the optimization and the execution time needed to solve
295 it. Therefore, we have set the number of subregions to 16 rather than 32.
297 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}.
299 %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.
302 \label{ch5:sec:03:02}
303 To evaluate our approach we consider the following performance metrics:
307 \item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much of the area
308 of a sensor field is covered. In our case, the sensing field is represented as
309 a connected grid of points and we use each grid point as a sample point to
310 compute the coverage. The coverage ratio can be calculated by:
313 \mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100,
315 where $n^t$ is the number of covered grid points by the active sensors of all
316 subregions during round $t$ in the current sensing phase and $N$ is the total number
317 of grid points in the sensing field of the network. In our simulations $N = 51
318 \times 26 = 1326$ grid points.
320 \item{{\bf Number of Active Sensors Ratio (ASR)}:} it is important to have as
321 few active nodes as possible in each round, in order to minimize the
322 communication overhead and maximize the network lifetime. The Active Sensors
323 Ratio is defined as follows:
325 \scriptsize \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R
326 \mbox{$A_r^t$}}{\mbox{$|J|$}} \times 100,
328 where $A_r^t$ is the number of active sensors in the subregion $r$ during round
329 $t$ in the current sensing phase, $|J|$ is the total number of sensors in the
330 network, and $R$ is the total number of subregions in the network.
332 \item {{\bf Network Lifetime}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
334 \item {{\bf Energy Consumption (EC)}:} the average energy consumption can be
335 seen as the total energy consumed by the sensors during the $Lifetime_{95}$ or
336 $Lifetime_{50}$ divided by the number of rounds. EC can be computed as
339 % New version with global loops on period
342 \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},
346 where $M_L$ is the number of periods and $T_m$ the number of rounds in a
347 period~$m$, both during $Lifetime_{95}$ or $Lifetime_{50}$. The total energy
348 consumed by the sensors (EC) comes through taking into consideration four main
349 energy factors. The first one , denoted $E^{\scriptsize \mbox{com}}_m$,
350 represents the energy consumption spent by all the nodes for wireless
351 communications during period $m$. $E^{\scriptsize \mbox{list}}_m$, the next
352 factor, corresponds to the energy consumed by the sensors in LISTENING status
353 before receiving the decision to go active or sleep in period $m$.
354 $E^{\scriptsize \mbox{comp}}_m$ refers to the energy needed by all the leader
355 nodes to solve the integer program during a period. Finally, $E^a_t$ and $E^s_t$
356 indicate the energy consumed by the whole network in round $t$.
359 \item {{\bf Execution Time}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
361 \item {{\bf Stopped simulation runs}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
367 \subsection{Results Analysis and Comparison }
368 \label{ch5:sec:03:02}
371 \begin{enumerate}[(i)]
373 \item {{\bf Coverage Ratio}}
374 %\subsection{Coverage ratio}
375 %\label{ch5:sec:03:02:01}
377 Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes. We
378 can notice that for the first thirty rounds both DESK and GAF provide a coverage
379 which is a little bit better than the one of MuDiLCO.
381 This is due to the fact that, in comparison with MuDiLCO which uses optimization
382 to put in SLEEP status redundant sensors, more sensor nodes remain active with
383 DESK and GAF. As a consequence, when the number of rounds increases, a larger
384 number of node failures can be observed in DESK and GAF, resulting in a faster
385 decrease of the coverage ratio. Furthermore, our protocol allows to maintain a
386 coverage ratio greater than 50\% for far more rounds. Overall, the proposed
387 sensor activity scheduling based on optimization in MuDiLCO maintains higher
388 coverage ratios of the area of interest for a larger number of rounds. It also
389 means that MuDiLCO saves more energy, with less dead nodes, at most for several
390 rounds, and thus should extend the network lifetime.
394 \includegraphics[scale=0.6] {Figures/ch5/R1/CR.pdf}
395 \caption{Average coverage ratio for 150 deployed nodes}
400 \item {{\bf Active sensors ratio}}
401 %\subsection{Active sensors ratio}
402 %\label{ch5:sec:03:02:02}
404 It is crucial to have as few active nodes as possible in each round, in order to
405 minimize the communication overhead and maximize the network
406 lifetime. Figure~\ref{fig4} presents the active sensor ratio for 150 deployed
407 nodes all along the network lifetime. It appears that up to round thirteen, DESK
408 and GAF have respectively 37.6\% and 44.8\% of nodes in ACTIVE status, whereas
409 MuDiLCO clearly outperforms them with only 24.8\% of active nodes. After the
410 thirty-fifth round, MuDiLCO exhibits larger numbers of active nodes, which agrees
411 with the dual observation of higher level of coverage made previously.
412 Obviously, in that case DESK and GAF have less active nodes, since they have
413 activated many nodes at the beginning. Anyway, MuDiLCO activates the available
414 nodes in a more efficient manner.
418 \includegraphics[scale=0.6]{Figures/ch5/R1/ASR.pdf}
419 \caption{Active sensors ratio for 150 deployed nodes}
423 \item {{\bf Stopped simulation runs}}
424 %\subsection{Stopped simulation runs}
425 %\label{ch5:sec:03:02:03}
427 Figure~\ref{fig6} reports the cumulative percentage of stopped simulations runs
428 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
429 more energy by turning on a large number of redundant nodes during the sensing
430 phase. GAF stops secondly for the same reason than DESK. MuDiLCO overcomes
431 DESK and GAF because the optimization process distributed on several subregions
432 leads to coverage preservation and so extends the network lifetime. Let us
433 emphasize that the simulation continues as long as a network in a subregion is
439 \includegraphics[scale=0.6]{Figures/ch5/R1/SR.pdf}
440 \caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes }
446 \item {{\bf Energy consumption}} \label{subsec:EC}
447 %\subsection{Energy consumption}
448 %\label{ch5:sec:03:02:04}
450 We measure the energy consumed by the sensors during the communication,
451 listening, computation, active, and sleep status for different network densities
452 and compare it with the two other methods. Figures~\ref{fig7}(a)
453 and~\ref{fig7}(b) illustrate the energy consumption, considering different
454 network sizes, for $Lifetime_{95}$ and $Lifetime_{50}$.
459 %\begin{multicols}{1}
461 \includegraphics[scale=0.6]{Figures/ch5/R1/EC95.pdf}\\~ ~ ~ ~ ~(a) \\
463 \includegraphics[scale=0.6]{Figures/ch5/R1/EC50.pdf}\\~ ~ ~ ~ ~(b)
466 \caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
471 The results show that MuDiLCO is the most competitive from the energy
472 consumption point of view. The other approaches have a high energy consumption
473 due to activating a larger number of redundant nodes as well as the energy
474 consumed during the different status of the sensor node. Among the different
475 versions of our protocol, the MuDiLCO-7 one consumes more energy than the other
476 versions. This is easy to understand since the bigger the number of rounds and
477 the number of sensors involved in the integer program are, the larger the time
478 computation to solve the optimization problem is. To improve the performances of
479 MuDiLCO-7, we should increase the number of subregions in order to have less
480 sensors to consider in the integer program.
484 \item {{\bf Execution time}}
485 %\subsection{Execution time}
486 %\label{ch5:sec:03:02:05}
488 We observe the impact of the network size and of the number of rounds on the
489 computation time. Figure~\ref{fig77} gives the average execution times in
490 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}.
492 %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.
496 \includegraphics[scale=0.6]{Figures/ch5/R1/T.pdf}
497 \caption{Execution Time (in seconds)}
501 As expected, the execution time increases with the number of rounds $T$ taken
502 into account to schedule the sensing phase. The times obtained for $T=1,3$
503 or $5$ seem bearable, but for $T=7$ they become quickly unsuitable for a sensor
504 node, especially when the sensor network size increases. Again, we can notice
505 that if we want to schedule the nodes activities for a large number of rounds,
506 we need to choose a relevant number of subregions in order to avoid a complicated
507 and cumbersome optimization. On the one hand, a large value for $T$ permits to
508 reduce the energy-overhead due to the three pre-sensing phases, on the other
509 hand a leader node may waste a considerable amount of energy to solve the
510 optimization problem.
514 \item {{\bf Network lifetime}}
515 %\subsection{Network lifetime}
516 %\label{ch5:sec:03:02:06}
518 The next two figures, Figures~\ref{fig8}(a) and \ref{fig8}(b), illustrate the
519 network lifetime for different network sizes, respectively for $Lifetime_{95}$
520 and $Lifetime_{50}$. Both figures show that the network lifetime increases
521 together with the number of sensor nodes, whatever the protocol, thanks to the
522 node density which results in more and more redundant nodes that can be
523 deactivated and thus save energy. Compared to the other approaches, our MuDiLCO
524 protocol maximizes the lifetime of the network. In particular the gain in
525 lifetime for a coverage over 95\% is greater than 38\% when switching from GAF
526 to MuDiLCO-3. The slight decrease that can be observed for MuDiLCO-7 in case
527 of $Lifetime_{95}$ with large wireless sensor networks results from the
528 difficulty of the optimization problem to be solved by the integer program.
529 This point was already noticed in \ref{subsec:EC} devoted to the
530 energy consumption, since network lifetime and energy consumption are directly
536 % \begin{multicols}{0}
538 \includegraphics[scale=0.6]{Figures/ch5/R1/LT95.pdf}\\~ ~ ~ ~ ~(a) \\
540 \includegraphics[scale=0.6]{Figures/ch5/R1/LT50.pdf}\\~ ~ ~ ~ ~(b)
543 \caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
555 We have addressed the problem of the coverage and of the lifetime optimization in
556 wireless sensor networks. This is a key issue as sensor nodes have limited
557 resources in terms of memory, energy, and computational power. To cope with this
558 problem, the field of sensing is divided into smaller subregions using the
559 concept of divide-and-conquer method, and then we propose a protocol which
560 optimizes coverage and lifetime performances in each subregion. Our protocol,
561 called MuDiLCO (Multiround Distributed Lifetime Coverage Optimization) combines
562 two efficient techniques: network leader election and sensor activity
565 The activity scheduling in each subregion works in periods, where each period
566 consists of four phases: (i) Information Exchange, (ii) Leader Election, (iii)
567 Decision Phase to plan the activity of the sensors over $T$ rounds, (iv) Sensing
568 Phase itself divided into T rounds.
570 Simulations results show the relevance of the proposed protocol in terms of
571 lifetime, coverage ratio, active sensors ratio, energy consumption, execution
572 time. Indeed, when dealing with large wireless sensor networks, a distributed
573 approach, like the one we propose, allows to reduce the difficulty of a single
574 global optimization problem by partitioning it in many smaller problems, one per
575 subregion, that can be solved more easily. Nevertheless, results also show that
576 it is not possible to plan the activity of sensors over too many rounds, because
577 the resulting optimization problem leads to too high resolution times and thus to
578 an excessive energy consumption.
