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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 3, section \ref{ch3:sec:02:01} and it has been used the primary point coverage model which is described in the same chapter, section \ref{ch3:sec:02:02}.
26 \subsection{Background Idea}
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. Each sensing phase may be itself divided into $T$ rounds
35 and for each round a set of sensors (a cover set) is responsible for the sensing
36 task. In this way a multiround optimization process is performed during each
37 period after Information~Exchange and Leader~Election phases, in order to
38 produce $T$ cover sets that will take the mission of sensing for $T$ rounds.
40 \centering \includegraphics[width=160mm]{Figures/ch4/GeneralModel.jpg} % 70mm Modelgeneral.pdf
41 \caption{The MuDiLCO protocol scheme executed on each node}
46 This protocol minimizes the impact of unexpected node failure (not due to batteries
47 running out of energy), because it works in periods.
49 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.
51 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.
54 These phases can be described in more details as follow:
55 \subsection{Information Exchange Phase}
56 \label{ch4:sec:02:02:01}
57 The information exchange among the wireless sensor nodes is similar to that one which is described in chapter 3, sections \ref{ch3:sec:02:03:01}.
59 \subsection{Leader Election phase}
60 \label{ch4:sec:02:02:02}
61 The leader election in each subregion is similar to that one which is described in chapter 3, sections\ref{ch3:sec:02:03:02}, but the difference in that the elected leader in each subregion is for each period.
63 \subsection{Decision phase}
64 \label{ch4:sec:02:02:03}
65 Each WSNL will solve an integer program to select which cover sets will be
66 activated in the following sensing phase to cover the subregion to which it
67 belongs. The integer program will produce $T$ cover sets, one for each round.
68 The WSNL will send an Active-Sleep packet to each sensor in the subregion based
69 on the algorithm's results, indicating if the sensor should be active or not in
70 each round of the sensing phase. The integer program is based on the model
71 proposed by \cite{ref156} with some modifications, where the objective is
72 to find a maximum number of disjoint cover sets. To fulfill this goal, the
73 authors proposed an integer program which forces undercoverage and overcoverage
74 of targets to become minimal at the same time. They use binary variables
75 $x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our model, we
76 consider binary variables $X_{t,j}$ to determine the possibility of activating
77 sensor $j$ during round $t$ of a given sensing phase. We also consider primary
78 points as targets. The set of primary points is denoted by $P$ and the set of
79 sensors by $J$. Only sensors able to be alive during at least one round are
80 involved in the integer program.
83 For a primary point $p$, let $\alpha_{j,p}$ denote the indicator function of
84 whether the point $p$ is covered, that is:
86 \alpha_{j,p} = \left \{
88 1 & \mbox{if the primary point $p$ is covered} \\
89 & \mbox{by sensor node $j$}, \\
90 0 & \mbox{otherwise.}\\
94 The number of active sensors that cover the primary point $p$ during
95 round $t$ is equal to $\sum_{j \in J} \alpha_{j,p} * X_{t,j}$ where:
99 1& \mbox{if sensor $j$ is active during round $t$,} \\
100 0 & \mbox{otherwise.}\\
104 We define the Overcoverage variable $\Theta_{t,p}$ as:
106 \Theta_{t,p} = \left \{
108 0 & \mbox{if the primary point $p$}\\
109 & \mbox{is not covered during round $t$,}\\
110 \left( \sum_{j \in J} \alpha_{jp} * X_{tj} \right)- 1 & \mbox{otherwise.}\\
114 More precisely, $\Theta_{t,p}$ represents the number of active sensor nodes
115 minus one that cover the primary point $p$ during round $t$. The
116 Undercoverage variable $U_{t,p}$ of the primary point $p$ during round $t$ is
121 1 &\mbox{if the primary point $p$ is not covered during round $t$,} \\
122 0 & \mbox{otherwise.}\\
127 Our coverage optimization problem can then be formulated as follows:
129 \min \sum_{t=1}^{T} \sum_{p=1}^{P} \left(W_{\theta}* \Theta_{t,p} + W_{U} * U_{t,p} \right) \label{eq15}
134 \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
138 \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
143 X_{t,j} \in \lbrace0,1\rbrace, \hspace{10 mm} \forall j \in J, t = 1,\dots,T \label{eq17}
147 U_{t,p} \in \lbrace0,1\rbrace, \hspace{10 mm}\forall p \in P, t = 1,\dots,T \label{eq18}
151 \Theta_{t,p} \geq 0 \hspace{10 mm}\forall p \in P, t = 1,\dots,T \label{eq178}
157 \item $X_{t,j}$: indicates whether or not the sensor $j$ is actively sensing
158 during round $t$ (1 if yes and 0 if not);
159 \item $\Theta_{t,p}$ - {\it overcoverage}: the number of sensors minus one that
160 are covering the primary point $p$ during round $t$;
161 \item $U_{t,p}$ - {\it undercoverage}: indicates whether or not the primary
162 point $p$ is being covered during round $t$ (1 if not covered and 0 if
166 The first group of constraints indicates that some primary point $p$ should be
167 covered by at least one sensor and, if it is not always the case, overcoverage
168 and undercoverage variables help balancing the restriction equations by taking
169 positive values. The constraint given by equation~(\ref{eq144}) guarantees that
170 the sensor has enough energy ($RE_j$ corresponds to its remaining energy) to be
171 alive during the selected rounds knowing that $E_{R}$ is the amount of energy
172 required to be alive during one round.
174 There are two main objectives. First, we limit the overcoverage of primary
175 points in order to activate a minimum number of sensors. Second we prevent the
176 absence of monitoring on some parts of the subregion by minimizing the
177 undercoverage. The weights $W_\theta$ and $W_U$ must be properly chosen so as
178 to guarantee that the maximum number of points are covered during each round.
179 %% MS W_theta is smaller than W_u => problem with the following sentence
180 In our simulations priority is given to the coverage by choosing $W_{U}$ very
181 large compared to $W_{\theta}$.
183 \subsection{Sensing phase}
184 \label{ch4:sec:02:02:04}
185 The sensing phase consists of $T$ rounds. Each sensor node in the subregion will
186 receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
187 sleep for each round of the sensing phase. Algorithm~\ref{alg:MuDiLCO}, which
188 will be executed by each node at the beginning of a period, explains how the
189 Active-Sleep packet is obtained.
191 \begin{algorithm}[h!]
192 % \KwIn{all the parameters related to information exchange}
193 % \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
195 %\emph{Initialize the sensor node and determine it's position and subregion} \;
197 \If{ $RE_j \geq E_{R}$ }{
198 \emph{$s_j.status$ = COMMUNICATION}\;
199 \emph{Send $INFO()$ packet to other nodes in the subregion}\;
200 \emph{Wait $INFO()$ packet from other nodes in the subregion}\;
201 %\emph{UPDATE $RE_j$ for every sent or received INFO Packet}\;
202 %\emph{ Collect information and construct the list L for all nodes in the subregion}\;
204 %\If{ the received INFO Packet = No. of nodes in it's subregion -1 }{
205 \emph{LeaderID = Leader election}\;
206 \If{$ s_j.ID = LeaderID $}{
207 \emph{$s_j.status$ = COMPUTATION}\;
208 \emph{$\left\{\left(X_{1,k},\dots,X_{T,k}\right)\right\}_{k \in J}$ =
209 Execute Integer Program Algorithm($T,J$)}\;
210 \emph{$s_j.status$ = COMMUNICATION}\;
211 \emph{Send $ActiveSleep()$ to each node $k$ in subregion a packet \\
212 with vector of activity scheduling $(X_{1,k},\dots,X_{T,k})$}\;
213 \emph{Update $RE_j $}\;
216 \emph{$s_j.status$ = LISTENING}\;
217 \emph{Wait $ActiveSleep()$ packet from the Leader}\;
218 % \emph{After receiving Packet, Retrieve the schedule and the $T$ rounds}\;
219 \emph{Update $RE_j $}\;
223 \Else { Exclude $s_j$ from entering in the current sensing phase}
226 \caption{MuDiLCO($s_j$)}
234 \section{Experimental Study and Analysis}
237 \subsection{Simulation Setup}
238 \label{ch4:sec:03:01}
239 We conducted a series of simulations to evaluate the efficiency and the
240 relevance of our approach, using the discrete event simulator OMNeT++
241 \cite{ref158}. The simulation parameters are summarized in
242 Table~\ref{table3}. Each experiment for a network is run over 25~different
243 random topologies and the results presented hereafter are the average of these
245 %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.
246 We performed simulations for five different densities varying from 50 to
247 250~nodes deployed over a $50 \times 25~m^2 $ sensing field. More
248 precisely, the deployment is controlled at a coarse scale in order to ensure
249 that the deployed nodes can cover the sensing field with the given sensing
252 %%RC these parameters are realistic?
253 %% maybe we can increase the field and sensing range. 5mfor Rs it seems very small... what do the other good papers consider ?
256 \caption{Relevant parameters for network initializing.}
259 % used for centering table
261 % centered columns (4 columns)
263 %inserts double horizontal lines
264 Parameter & Value \\ [0.5ex]
266 %Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
270 % inserts single horizontal line
271 Sensing field size & $(50 \times 25)~m^2 $ \\
272 % inserting body of the table
274 Network size & 50, 100, 150, 200 and 250~nodes \\
276 Initial energy & 500-700~joules \\
278 Sensing time for one round & 60 Minutes \\
279 $E_{R}$ & 36 Joules\\
283 % [1ex] adds vertical space
289 % is used to refer this table in the text
292 Our protocol is declined into four versions: MuDiLCO-1, MuDiLCO-3, MuDiLCO-5,
293 and MuDiLCO-7, corresponding respectively to $T=1,3,5,7$ ($T$ the number of
294 rounds in one sensing period). In the following, we will make comparisons with
295 two other methods. The first method, called DESK and proposed by \cite{DESK},
296 is a full distributed coverage algorithm. The second method, called
297 GAF~\cite{GAF}, consists in dividing the region into fixed squares.
298 During the decision phase, in each square, one sensor is then chosen to remain
299 active during the sensing phase time.
301 Some preliminary experiments were performed in chapter 3 to study the choice of the number of
302 subregions which subdivides the sensing field, considering different network
303 sizes. They show that as the number of subregions increases, so does the network
304 lifetime. Moreover, it makes the MuDiLCO protocol more robust against random
305 network disconnection due to node failures. However, too many subdivisions
306 reduce the advantage of the optimization. In fact, there is a balance between
307 the benefit from the optimization and the execution time needed to solve
308 it. Therefore, we have set the number of subregions to 16 rather than 32.
310 We used the modeling language and the optimization solver which are mentioned in chapter 3, section \ref{ch3:sec:04:02}. In addition, we employed an energy consumption model, which is presented in chapter 3, section \ref{ch3:sec:04:03}.
312 %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.
315 \label{ch4:sec:03:02}
316 To evaluate our approach we consider the following performance metrics:
320 \item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much of the area
321 of a sensor field is covered. In our case, the sensing field is represented as
322 a connected grid of points and we use each grid point as a sample point to
323 compute the coverage. The coverage ratio can be calculated by:
326 \mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100,
328 where $n^t$ is the number of covered grid points by the active sensors of all
329 subregions during round $t$ in the current sensing phase and $N$ is the total number
330 of grid points in the sensing field of the network. In our simulations $N = 51
331 \times 26 = 1326$ grid points.
333 \item{{\bf Number of Active Sensors Ratio (ASR)}:} it is important to have as
334 few active nodes as possible in each round, in order to minimize the
335 communication overhead and maximize the network lifetime. The Active Sensors
336 Ratio is defined as follows:
338 \scriptsize \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R
339 \mbox{$A_r^t$}}{\mbox{$|J|$}} \times 100,
341 where $A_r^t$ is the number of active sensors in the subregion $r$ during round
342 $t$ in the current sensing phase, $|J|$ is the total number of sensors in the
343 network, and $R$ is the total number of subregions in the network.
345 \item {{\bf Network Lifetime}:} is described in chapter 3, section \ref{ch3:sec:04:04}.
347 \item {{\bf Energy Consumption (EC)}:} the average energy consumption can be
348 seen as the total energy consumed by the sensors during the $Lifetime_{95}$ or
349 $Lifetime_{50}$ divided by the number of rounds. EC can be computed as
352 % New version with global loops on period
355 \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},
359 where $M_L$ is the number of periods and $T_m$ the number of rounds in a
360 period~$m$, both during $Lifetime_{95}$ or $Lifetime_{50}$. The total energy
361 consumed by the sensors (EC) comes through taking into consideration four main
362 energy factors. The first one , denoted $E^{\scriptsize \mbox{com}}_m$,
363 represents the energy consumption spent by all the nodes for wireless
364 communications during period $m$. $E^{\scriptsize \mbox{list}}_m$, the next
365 factor, corresponds to the energy consumed by the sensors in LISTENING status
366 before receiving the decision to go active or sleep in period $m$.
367 $E^{\scriptsize \mbox{comp}}_m$ refers to the energy needed by all the leader
368 nodes to solve the integer program during a period. Finally, $E^a_t$ and $E^s_t$
369 indicate the energy consumed by the whole network in round $t$.
372 \item {{\bf Execution Time}:} is described in chapter 3, section \ref{ch3:sec:04:04}.
374 \item {{\bf Stopped simulation runs}:} is described in chapter 3, section \ref{ch3:sec:04:04}.
380 \subsection{Results analysis and Comparison }
381 \label{ch4:sec:03:02}
383 \subsection{Coverage ratio}
384 \label{ch4:sec:03:02:01}
385 Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes. We
386 can notice that for the first thirty rounds both DESK and GAF provide a coverage
387 which is a little bit better than the one of MuDiLCO.
389 This is due to the fact that, in comparison with MuDiLCO which uses optimization
390 to put in SLEEP status redundant sensors, more sensor nodes remain active with
391 DESK and GAF. As a consequence, when the number of rounds increases, a larger
392 number of node failures can be observed in DESK and GAF, resulting in a faster
393 decrease of the coverage ratio. Furthermore, our protocol allows to maintain a
394 coverage ratio greater than 50\% for far more rounds. Overall, the proposed
395 sensor activity scheduling based on optimization in MuDiLCO maintains higher
396 coverage ratios of the area of interest for a larger number of rounds. It also
397 means that MuDiLCO saves more energy, with less dead nodes, at most for several
398 rounds, and thus should extend the network lifetime.
402 \includegraphics[scale=0.5] {Figures/ch4/R1/CR.pdf}
403 \caption{Average coverage ratio for 150 deployed nodes}
407 \subsection{Active sensors ratio}
408 \label{ch4:sec:03:02:02}
409 It is crucial to have as few active nodes as possible in each round, in order to
410 minimize the communication overhead and maximize the network
411 lifetime. Figure~\ref{fig4} presents the active sensor ratio for 150 deployed
412 nodes all along the network lifetime. It appears that up to round thirteen, DESK
413 and GAF have respectively 37.6\% and 44.8\% of nodes in ACTIVE status, whereas
414 MuDiLCO clearly outperforms them with only 24.8\% of active nodes. After the
415 thirty-fifth round, MuDiLCO exhibits larger numbers of active nodes, which agrees
416 with the dual observation of higher level of coverage made previously.
417 Obviously, in that case DESK and GAF have less active nodes, since they have
418 activated many nodes at the beginning. Anyway, MuDiLCO activates the available
419 nodes in a more efficient manner.
423 \includegraphics[scale=0.5]{Figures/ch4/R1/ASR.pdf}
424 \caption{Active sensors ratio for 150 deployed nodes}
428 \subsection{Stopped simulation runs}
429 \label{ch4:sec:03:02:03}
430 Figure~\ref{fig6} reports the cumulative percentage of stopped simulations runs
431 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
432 more energy by turning on a large number of redundant nodes during the sensing
433 phase. GAF stops secondly for the same reason than DESK. MuDiLCO overcomes
434 DESK and GAF because the optimization process distributed on several subregions
435 leads to coverage preservation and so extends the network lifetime. Let us
436 emphasize that the simulation continues as long as a network in a subregion is
442 \includegraphics[scale=0.5]{Figures/ch4/R1/SR.pdf}
443 \caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes }
447 \subsection{Energy consumption} \label{subsec:EC}
448 \label{ch4:sec:03:02:04}
449 We measure the energy consumed by the sensors during the communication,
450 listening, computation, active, and sleep status for different network densities
451 and compare it with the two other methods. Figures~\ref{fig7}(a)
452 and~\ref{fig7}(b) illustrate the energy consumption, considering different
453 network sizes, for $Lifetime_{95}$ and $Lifetime_{50}$.
458 \parbox{9.5cm}{\includegraphics[scale=0.5]{Figures/ch4/R1/EC95.pdf}} & (a) \\
460 \parbox{9.5cm}{\includegraphics[scale=0.5]{Figures/ch4/R1/EC50.pdf}} & (b)
462 \caption{Energy consumption for (a) $Lifetime_{95}$ and
467 The results show that MuDiLCO is the most competitive from the energy
468 consumption point of view. The other approaches have a high energy consumption
469 due to activating a larger number of redundant nodes as well as the energy
470 consumed during the different status of the sensor node. Among the different
471 versions of our protocol, the MuDiLCO-7 one consumes more energy than the other
472 versions. This is easy to understand since the bigger the number of rounds and
473 the number of sensors involved in the integer program are, the larger the time
474 computation to solve the optimization problem is. To improve the performances of
475 MuDiLCO-7, we should increase the number of subregions in order to have less
476 sensors to consider in the integer program.
479 \subsection{Execution time}
480 \label{ch4:sec:03:02:05}
481 We observe the impact of the network size and of the number of rounds on the
482 computation time. Figure~\ref{fig77} gives the average execution times in
483 seconds (needed to solve optimization problem) for different values of $T$. The original execution time is computed as described in chapter 3, section \ref{ch3:sec:04:02}.
485 %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.
489 \includegraphics[scale=0.5]{Figures/ch4/R1/T.pdf}
490 \caption{Execution Time (in seconds)}
494 As expected, the execution time increases with the number of rounds $T$ taken
495 into account to schedule the sensing phase. The times obtained for $T=1,3$
496 or $5$ seem bearable, but for $T=7$ they become quickly unsuitable for a sensor
497 node, especially when the sensor network size increases. Again, we can notice
498 that if we want to schedule the nodes activities for a large number of rounds,
499 we need to choose a relevant number of subregions in order to avoid a complicated
500 and cumbersome optimization. On the one hand, a large value for $T$ permits to
501 reduce the energy-overhead due to the three pre-sensing phases, on the other
502 hand a leader node may waste a considerable amount of energy to solve the
503 optimization problem.
505 \subsection{Network lifetime}
506 \label{ch4:sec:03:02:06}
507 The next two figures, Figures~\ref{fig8}(a) and \ref{fig8}(b), illustrate the
508 network lifetime for different network sizes, respectively for $Lifetime_{95}$
509 and $Lifetime_{50}$. Both figures show that the network lifetime increases
510 together with the number of sensor nodes, whatever the protocol, thanks to the
511 node density which results in more and more redundant nodes that can be
512 deactivated and thus save energy. Compared to the other approaches, our MuDiLCO
513 protocol maximizes the lifetime of the network. In particular the gain in
514 lifetime for a coverage over 95\% is greater than 38\% when switching from GAF
515 to MuDiLCO-3. The slight decrease that can be observed for MuDiLCO-7 in case
516 of $Lifetime_{95}$ with large wireless sensor networks results from the
517 difficulty of the optimization problem to be solved by the integer program.
518 This point was already noticed in subsection \ref{subsec:EC} devoted to the
519 energy consumption, since network lifetime and energy consumption are directly
525 \parbox{9.5cm}{\includegraphics[scale=0.5]{Figures/ch4/R1/LT95.pdf}} & (a) \\
527 \parbox{9.5cm}{\includegraphics[scale=0.5]{Figures/ch4/R1/LT50.pdf}} & (b)
529 \caption{Network lifetime for (a) $Lifetime_{95}$ and
538 We have addressed the problem of the coverage and of the lifetime optimization in
539 wireless sensor networks. This is a key issue as sensor nodes have limited
540 resources in terms of memory, energy, and computational power. To cope with this
541 problem, the field of sensing is divided into smaller subregions using the
542 concept of divide-and-conquer method, and then we propose a protocol which
543 optimizes coverage and lifetime performances in each subregion. Our protocol,
544 called MuDiLCO (Multiround Distributed Lifetime Coverage Optimization) combines
545 two efficient techniques: network leader election and sensor activity
548 The activity scheduling in each subregion works in periods, where each period
549 consists of four phases: (i) Information Exchange, (ii) Leader Election, (iii)
550 Decision Phase to plan the activity of the sensors over $T$ rounds, (iv) Sensing
551 Phase itself divided into T rounds.
553 Simulations results show the relevance of the proposed protocol in terms of
554 lifetime, coverage ratio, active sensors ratio, energy consumption, execution
555 time. Indeed, when dealing with large wireless sensor networks, a distributed
556 approach, like the one we propose, allows to reduce the difficulty of a single
557 global optimization problem by partitioning it in many smaller problems, one per
558 subregion, that can be solved more easily. Nevertheless, results also show that
559 it is not possible to plan the activity of sensors over too many rounds, because
560 the resulting optimization problem leads to too high resolution times and thus to
561 an excessive energy consumption.
