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7 \chapter{Multiround Distributed Lifetime Coverage Optimization Protocol}
11 \section{Introduction}
14 %The fast developments of low-cost sensor devices and wireless communications have allowed the emergence of WSNs. A WSN includes a large number of small, limited-power sensors that can sense, process, and transmit data over a wireless communication. They communicate with each other by using multi-hop wireless communications and cooperate together to monitor the area of interest, so that each measured data can be reported to a monitoring center called sink for further analysis~\cite{ref222}. There are several fields of application covering a wide spectrum for a WSN, including health, home, environmental, military, and industrial applications~\cite{ref19}.
16 %On the one hand sensor nodes run on batteries with limited capacities, and it is often costly or simply impossible to replace and/or recharge batteries, especially in remote and hostile environments. Obviously, to achieve a long life of the network it is important to conserve battery power. Therefore, lifetime optimization is one of the most critical issues in wireless sensor networks. On the other hand we must guarantee coverage over the area of interest. To fulfill these two objectives, the main idea is to take advantage of overlapping sensing regions to turn-off redundant sensor nodes and thus save energy. In this paper, we concentrate on the area coverage problem, with the objective of maximizing the network lifetime by using an optimized multiround scheduling.
17 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 step and schedule them for multiple rounds, so that the battery life of a sensor is not wasted due to the repeated execution of the presensing phases of MuDiLCO protocol.
19 The MuDiLCO protocol (for Multiround Distributed Lifetime Coverage Optimization protocol) presented in this chapter is an extension of the approach introduced in chapter 4.
20 %Simulation results have shown that it was more interesting to divide the area into several subregions, given the computation complexity.
21 Compared to DiLCO 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.
24 The remainder of this chapter continues with section \ref{ch5:sec:02} where a detailed description of MuDiLCO Protocol is given. The next section describes the primary points based multiround coverage problem formulation which is used to schedule the activation of sensors in multiple cover sets. Section \ref{ch5:sec:04} shows the simulation
25 results. The chapter ends with a conclusion and some suggestions for further works.
31 \section{Description of the MuDiLCO Protocol }
33 %\noindent In this section, we introduce the MuDiLCO protocol which is distributed on each subregion in the area of interest. It
34 Like DiLCO, the MuDiLCO protocol is based on two energy-efficient
35 mechanisms: subdividing the area of interest into several subregions (like a cluster architecture) using the divide and conquer method, where the sensor nodes cooperate within each subregion as independent group in order to achieve a network leader election. Sensor activity scheduling is used to maintain the coverage and to prolong the network lifetime, it is applied periodically. MuDiLCO uses the same assumptions, primary point coverage and network models, than DiLCO, given in section \ref{ch4:sec:02:01} and \ref{ch4:sec:02:02}, respectively.
38 %\subsection{Background Idea and Algorithm}
39 %\label{ch5:sec:02:02}
40 %The area of interest can be divided using the divide-and-conquer strategy into smaller areas, called subregions, and then our MuDiLCO protocol will be implemented in each subregion in a distributed way.
42 As can be seen in Figure~\ref{fig2}, our protocol works in periods fashion, where each is divided into 4 phases: Information~Exchange, Leader~Election, Decision, and Sensing.
43 %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},
45 \centering \includegraphics[width=160mm]{Figures/ch5/GeneralModel.jpg} % 70mm Modelgeneral.pdf
46 \caption{MuDiLCO protocol.}
52 % \KwIn{all the parameters related to information exchange}
53 % \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
55 %\emph{Initialize the sensor node and determine it's position and subregion} \;
57 \If{ $RE_j \geq E_{th}$ }{
58 \emph{$s_j.status$ = COMMUNICATION}\;
59 \emph{Send $INFO()$ packet to other nodes in the subregion}\;
60 \emph{Wait $INFO()$ packet from other nodes in the subregion}\;
61 %\emph{UPDATE $RE_j$ for every sent or received INFO Packet}\;
62 %\emph{ Collect information and construct the list L for all nodes in the subregion}\;
64 %\If{ the received INFO Packet = No. of nodes in it's subregion -1 }{
65 \emph{LeaderID = Leader election}\;
66 \If{$ s_j.ID = LeaderID $}{
67 \emph{$s_j.status$ = COMPUTATION}\;
68 \emph{$\left\{\left(X_{1,k},\dots,X_{T,k}\right)\right\}_{k \in J}$ =
69 Execute Integer Program Algorithm($T,J$)}\;
70 \emph{$s_j.status$ = COMMUNICATION}\;
71 \emph{Send $ActiveSleep()$ to each node $k$ in subregion: a packet \\
72 with vector of activity scheduling $(X_{1,k},\dots,X_{T,k})$}\;
73 \emph{Update $RE_j $}\;
76 \emph{$s_j.status$ = LISTENING}\;
77 \emph{Wait $ActiveSleep()$ packet from the Leader}\;
78 % \emph{After receiving Packet, Retrieve the schedule and the $T$ rounds}\;
79 \emph{Update $RE_j $}\;
83 \Else { Exclude $s_j$ from entering in the current sensing phase}
86 \caption{MuDiLCO($s_j$)}
91 The difference with MuDiLCO in that the elected leader in each subregion is for each period. In the decision phase, each leader will solve an integer program to select which cover sets will be 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 leader will send an ActiveSleep packet to each sensor in the subregion based on the algorithm's results, indicating if the sensor should be active or not in
92 each round of the sensing phase. Each sensing phase is itself divided into $T$ rounds and for each round a set of sensors (a cover set) is responsible for the sensing task.
93 %Each sensor node in the subregion will receive an ActiveSleep packet from leader, informing it to stay awake or to go to sleep for each round of the sensing phase.
94 Algorithm~\ref{alg:MuDiLCO}, which will be executed by each node at the beginning of a period, explains how the ActiveSleep packet is obtained. In this way, a multiround optimization process is performed during each
95 period after Information~Exchange and Leader~Election phases, in order to produce $T$ cover sets that will take the mission of sensing for $T$ rounds.
98 %This protocol minimizes the impact of unexpected node failure (not due to batteries running out of energy), because it works in periods. On the one hand, if a node failure is detected before making the decision, the node will not participate during this phase. 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.
100 %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.
107 \section{Primary Points based Multiround Coverage Problem Formulation}
111 %According to Algorithm~\ref{alg:MuDiLCO}, the integer program is based on the model proposed by \cite{ref156} with some modifications, where the objective of our model is to find a maximum number of non-disjoint cover sets.
112 %To fulfill this goal, the authors proposed an integer program which forces undercoverage and overcoverage of targets to become minimal at the same time. They use binary variables $x_{jl}$ to indicate if sensor $j$ belongs to cover set $l$. In our model,
113 %We consider binary variables $X_{t,j}$ to determine the possibility of activating sensor $j$ during round $t$ of a given sensing phase. We also consider primary points as targets. The set of primary points is denoted by $P$ and the set of sensors by $J$. Only sensors able to be alive during at least one round are involved in the integer program.
115 We extend the mathematical formulation given in section \ref{ch4:sec:03} to take into account multiple rounds.
117 For a primary point $p$, let $\alpha_{j,p}$ denote the indicator function of
118 whether the point $p$ is covered, that is
120 \alpha_{j,p} = \left \{
122 1 & \mbox{if the primary point $p$ is covered} \\
123 & \mbox{by sensor node $j$}, \\
124 0 & \mbox{otherwise.}\\
128 The number of active sensors that cover the primary point $p$ during
129 round $t$ is equal to $\sum_{j \in J} \alpha_{j,p} * X_{t,j}$ where
133 1& \mbox{if sensor $j$ is active during round $t$,} \\
134 0 & \mbox{otherwise.}\\
138 We define the Overcoverage variable $\Theta_{t,p}$ as
140 \Theta_{t,p} = \left \{
142 0 & \mbox{if the primary point $p$}\\
143 & \mbox{is not covered during round $t$,}\\
144 \left( \sum_{j \in J} \alpha_{jp} * X_{tj} \right)- 1 & \mbox{otherwise.}\\
148 More precisely, $\Theta_{t,p}$ represents the number of active sensor nodes
149 minus one that cover the primary point $p$ during round $t$. The
150 Undercoverage variable $U_{t,p}$ of the primary point $p$ during round $t$ is
155 1 &\mbox{if the primary point $p$ is not covered during round $t$,} \\
156 0 & \mbox{otherwise.}\\
161 Our coverage optimization problem can then be formulated as follows
163 \min \sum_{t=1}^{T} \sum_{p=1}^{P} \left(W_{\theta}* \Theta_{t,p} + W_{U} * U_{t,p} \right) \label{eq15}
168 \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
172 \sum_{t=1}^{T} X_{t,j} \leq \lfloor {RE_{j}/E_{th}} \rfloor \hspace{6 mm} \forall j \in J, t = 1,\dots,T
177 X_{t,j} \in \lbrace0,1\rbrace, \hspace{10 mm} \forall j \in J, t = 1,\dots,T \label{eq17}
181 U_{t,p} \in \lbrace0,1\rbrace, \hspace{10 mm}\forall p \in P, t = 1,\dots,T \label{eq18}
185 \Theta_{t,p} \geq 0 \hspace{10 mm}\forall p \in P, t = 1,\dots,T \label{eq178}
191 \item $X_{t,j}$: indicates whether or not the sensor $j$ is actively sensing
192 during round $t$ (1 if yes and 0 if not);
193 \item $\Theta_{t,p}$ - {\it overcoverage}: the number of sensors minus one that
194 are covering the primary point $p$ during round $t$;
195 \item $U_{t,p}$ - {\it undercoverage}: indicates whether or not the primary
196 point $p$ is being covered during round $t$ (1 if not covered and 0 if
200 %The first group of constraints indicates that some primary point $p$ should be covered by at least one sensor and, if it is not always the case, overcoverage and undercoverage variables help balancing the restriction equations by taking positive values.
201 The constraint given by equation~(\ref{eq144}) guarantees that the sensor has enough energy ($RE_j$ corresponds to its remaining energy) to be alive during the selected rounds knowing that $E_{th}$ is the amount of energy required to be alive during one round.
203 %There are two main objectives. First, we limit the overcoverage of primary points in order to activate a minimum number of sensors. Second we prevent the absence of monitoring on some parts of the subregion by minimizing the undercoverage. The weights $W_\theta$ and $W_U$ must be properly chosen so as to guarantee that the maximum number of points are covered during each round. In our simulations, priority is given to the coverage by choosing $W_{U}$ very large compared to $W_{\theta}$.
209 \section{Experimental Study and Analysis}
212 \subsection{Simulation Setup}
213 \label{ch5:sec:04:01}
214 We conducted a series of simulations to evaluate the efficiency and the
215 relevance of our approach, using the discrete event simulator OMNeT++
216 \cite{ref158}. We performed the optimization in the same manner than in chapter 4, considering the same energy model. The simulation parameters are summarized in Table~\ref{tablech4}. Each experiment for a network is run over 25~different random topologies and the results presented hereafter are the average of these 25 runs.
217 We performed simulations for five different densities varying from 50 to
218 250~nodes deployed over a $50 \times 25~m^2 $ sensing field. More
219 precisely, the deployment is controlled at a coarse scale in order to ensure
220 that the deployed nodes can cover the sensing field with the given sensing
223 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 three other methods. DESK \cite{DESK}, GAF~\cite{GAF}, and DiLCO~\cite{Idrees2}, where MuDiLCO-1 is the same of DiLCO.
224 %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 sizes. They show that as the number of subregions increases, so does the network lifetime. Moreover, it makes the MuDiLCO protocol more robust against random network disconnection due to node failures. However, too many subdivisions reduce the advantage of the optimization. In fact, there is a balance between the benefit from the optimization and the execution time needed to solve it. Therefore,
225 We set the number of subregions to 16 rather than 32 as explained in section \ref{ch4:sec:04:05}.
226 We use the modeling language and the optimization solver which are mentioned in section \ref{ch4:sec:04:02}.
227 %In addition, the energy consumption model is presented in chapter 4, section \ref{ch4:sec:04:03}.
230 \label{ch5:sec:04:02}
231 To evaluate our approach we consider the following performance metrics
233 \begin{enumerate}[i)]
235 \item {{\bf Coverage Ratio (CR)}:} The coverage ratio can be calculated by:
238 \mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100,
240 where $n^t$ is the number of covered grid points by the active sensors of all
241 subregions during round $t$ in the current sensing phase.
242 % and $N$ is the total number of grid points in the sensing field of the network. In our simulations $N = 51 \times 26 = 1326$ grid points.
244 \item{{\bf Number of Active Sensors Ratio (ASR)}:} The Active Sensors
245 Ratio for round t is defined as follows:
247 \scriptsize \mbox{$ASR^t$}(\%) = \frac{\sum\limits_{r=1}^R
248 \mbox{$A_r^t$}}{\mbox{$|J|$}} \times 100,
250 where $A_r^t$ is the number of active sensors in the subregion $r$ during round
251 $t$ in the current sensing phase.
252 %, $|J|$ is the total number of sensors in the network, and $R$ is the total number of subregions in the network.
254 \item {{\bf Energy Consumption (EC)}:} EC can be computed as follows:
258 \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left[ \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T} \left( E^{a}_t+E^{s}_t \right) \right]}{\sum\limits_{m=1}^{M} T},
261 The energy factors of above equation are described in section \ref{ch4:sec:04:04}. $E^a_t$ and $E^s_t$
262 indicate the energy consumed by the whole network in round $t$ of the sensing phase.
264 %where $M$ is the number of periods and $T$ the number of rounds in a period~$m$, both during $Lifetime_{95}$ or $Lifetime_{50}$. The total energy consumed by the sensors (EC) comes through taking into consideration four main energy factors.
265 %The first one , denoted $E^{\scriptsize \mbox{com}}_m$, represents the energy consumption spent by all the nodes for wireless communications during period $m$. $E^{\scriptsize \mbox{list}}_m$, the next factor, corresponds to the energy consumed by the sensors in LISTENING status before receiving the decision to go active or sleep in period $m$. $E^{\scriptsize \mbox{comp}}_m$ refers to the energy needed by all the leader nodes to solve the integer program during a period. Finally, $E^a_t$ and $E^s_t$ indicate the energy consumed by the whole network in round $t$.
269 \item {{\bf Execution Time}:}
270 \item {{\bf Stopped simulation runs}:} \makebox(0,0){\put(0,2.2\normalbaselineskip){%
271 $\left.\rule{0pt}{2.3\normalbaselineskip}\right\}$ Described in section \ref{ch4:sec:04:04}.}}
272 \item {{\bf Network Lifetime}:}
278 \subsection{Results Analysis and Comparison }
279 \label{ch5:sec:04:03}
282 \begin{enumerate}[i)]
284 \item {{\bf Coverage Ratio}}
285 %\subsection{Coverage ratio}
286 %\label{ch5:sec:03:02:01}
288 Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes. We
289 can notice that for the first thirty rounds both DESK and GAF provide a coverage
290 which is a little bit better than the one of MuDiLCO.
292 This is due to the fact that, in comparison with MuDiLCO which uses optimization
293 to put in sleep status redundant sensors, more sensor nodes remain active with
294 DESK and GAF. As a consequence, when the number of rounds increases, a larger
295 number of node failures can be observed in DESK and GAF, resulting in a faster
296 decrease of the coverage ratio. Furthermore, our protocol allows to maintain a
297 coverage ratio greater than 50\% for far more rounds. Overall, the proposed
298 sensor activity scheduling based on optimization in MuDiLCO maintains higher
299 coverage ratios of the area of interest for a larger number of rounds. It also
300 means that MuDiLCO saves more energy, with fewer dead nodes, at most for several
301 rounds, and thus should extend the network lifetime.
305 \includegraphics[scale=0.8] {Figures/ch5/R1/CR.pdf}
306 \caption{Average coverage ratio for 150 deployed nodes}
311 \item {{\bf Active sensors ratio}}
312 %\subsection{Active sensors ratio}
313 %\label{ch5:sec:03:02:02}
315 %It is crucial to have as few active nodes as possible in each round, in order to minimize the communication overhead and maximize the network lifetime.
316 Figure~\ref{fig4} presents the active sensor ratio for 150 deployed
317 nodes all along the network lifetime. It appears that up to round thirteen, DESK
318 and GAF have respectively 37.6\% and 44.8\% of nodes in active mode, whereas
319 MuDiLCO clearly outperforms them with only 23.7\% of active nodes. After the
320 thirty-sixth round, MuDiLCO exhibits larger numbers of active nodes, which agrees
321 with the dual observation of higher level of coverage made previously.
322 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.
326 \includegraphics[scale=0.8]{Figures/ch5/R1/ASR.pdf}
327 \caption{Active sensors ratio for 150 deployed nodes}
331 \item {{\bf Stopped simulation runs}}
332 %\subsection{Stopped simulation runs}
333 %\label{ch5:sec:03:02:03}
335 Figure~\ref{fig6} reports the cumulative percentage of stopped simulations runs per round for 150 deployed nodes. This figure gives the breakpoint for each method.
336 DESK stops first, after approximately 45~rounds, because it consumes the more energy by turning on a large number of redundant nodes during the sensing phase. GAF stops secondly for the same reason than DESK. MuDiLCO overcomes DESK and GAF because the optimization process distributed on several subregions leads to coverage preservation and so extends the network lifetime. Let us
337 emphasize that the simulation continues as long as a network in a subregion is still connected. \\
342 \includegraphics[scale=0.8]{Figures/ch5/R1/SR.pdf}
343 \caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes }
348 \item {{\bf Energy consumption}} \label{subsec:EC}
349 %\subsection{Energy consumption}
350 %\label{ch5:sec:03:02:04}
352 We measure the energy consumed by the sensors during the communication,
353 listening, computation, active, and sleep status for different network densities
354 and compare it with the two other methods. Figures~\ref{fig7}(a)
355 and~\ref{fig7}(b) illustrate the energy consumption, considering different
356 network sizes, for $Lifetime_{95}$ and $Lifetime_{50}$.
361 %\begin{multicols}{1}
363 \includegraphics[scale=0.8]{Figures/ch5/R1/EC95.pdf}\\~ ~ ~ ~ ~(a) \\
365 \includegraphics[scale=0.8]{Figures/ch5/R1/EC50.pdf}\\~ ~ ~ ~ ~(b)
368 \caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
373 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
374 the number of sensors involved in the integer program, the larger the time computation to solve the optimization problem. 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.
378 \item {{\bf Execution time}}
379 %\subsection{Execution time}
380 %\label{ch5:sec:03:02:05}
382 We observe the impact of the network size and of the number of rounds on the
383 computation time. Figure~\ref{fig77} gives the average execution times in
384 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}.
386 %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.
390 \includegraphics[scale=0.8]{Figures/ch5/R1/T.pdf}
391 \caption{Execution Time (in seconds)}
395 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,
396 we need to choose a relevant number of subregions in order to avoid a complicated and cumbersome optimization.
398 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. %\\ \\ \\ \\ \\ \\ \\
400 \item {{\bf Network lifetime}}
401 %\subsection{Network lifetime}
402 %\label{ch5:sec:03:02:06}
403 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
404 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.
408 % \begin{multicols}{0}
410 \includegraphics[scale=0.8]{Figures/ch5/R1/LT95.pdf}\\~ ~ ~ ~ ~(a) \\
412 \includegraphics[scale=0.8]{Figures/ch5/R1/LT50.pdf}\\~ ~ ~ ~ ~(b)
415 \caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
420 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.
421 This point was already noticed in \ref{subsec:EC} devoted to the
422 energy consumption, since network lifetime and energy consumption are directly linked.
429 %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.
430 In this chapter, we have presented a protocol, called MuDiLCO (Multiround Distributed Lifetime Coverage Optimization) that combines two efficient techniques: network leader election and sensor activity scheduling. 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.
432 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. Compared with DiLCO, it is clear that MuDiLCO improves the network lifetime especially for the dense network, but it is less robust than DiLCO under sensor nodes failures. Therefore, choosing the number of rounds $T$ depends on the type of application the WSN is deployed for.
