\chapter{Multiround Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}
\label{ch5}
-\section{Summary}
+
+\section{Introduction}
\label{ch5:sec:01}
-Coverage and lifetime are two paramount problems in Wireless Sensor Networks (WSNs). In this paper, a method called Multiround Distributed Lifetime Coverage
-Optimization protocol (MuDiLCO) is proposed to maintain the coverage and to improve the lifetime in wireless sensor networks. The area of interest is first
-divided into subregions and then the MuDiLCO protocol is distributed on the sensor nodes in each subregion. The proposed MuDiLCO protocol works in periods
-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
-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
-during the rounds of the sensing phase. Compared with some existing protocols, simulation results based on multiple criteria (energy consumption, coverage
-ratio, and so on) show that the proposed protocol can prolong efficiently the network lifetime and improve the coverage performance.
+
+%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}.
+
+%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.
+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 and 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.
+
+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.
+
+
+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
+results. The chapter ends with a conclusion and some suggestions for further work.
+
+
+
+
\section{MuDiLCO Protocol Description}
\label{ch5:sec:02}
\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
-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}.
+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 uses the primary point coverage model which is described in the same chapter, section \ref{ch4:sec:02:02}.
\subsection{Background Idea and Algorithm}
where each is divided into 4 phases: Information~Exchange, Leader~Election,
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
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
-each round of the sensing phase. Each sensing phase may be itself divided into $T$ rounds
+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. Each sensor node in the subregion will
receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
sleep for each round of the sensing phase. Algorithm~\ref{alg:MuDiLCO}, which
will be executed by each node at the beginning of a period, explains how the
-Active-Sleep packet is obtained. In this way a multiround optimization process is performed during each
+Active-Sleep packet is obtained. In this way, a multiround optimization process is performed during each
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.
\begin{figure}[ht!]
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 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.
+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.
-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.
+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.
\BlankLine
%\emph{Initialize the sensor node and determine it's position and subregion} \;
- \If{ $RE_j \geq E_{R}$ }{
+ \If{ $RE_j \geq E_{th}$ }{
\emph{$s_j.status$ = COMMUNICATION}\;
\emph{Send $INFO()$ packet to other nodes in the subregion}\;
\emph{Wait $INFO()$ packet from other nodes in the subregion}\;
-\subsection{Primary Points based Multiround Coverage Problem Formulation}
-%\label{ch5:sec:02:02}
+\section{Primary Points based Multiround Coverage Problem Formulation}
+\label{ch5:sec:03}
+
According to our algorithm~\ref{alg:MuDiLCO}, the integer program is based on the model
proposed by \cite{ref156} with some modifications, where the objective is
For a primary point $p$, let $\alpha_{j,p}$ denote the indicator function of
-whether the point $p$ is covered, that is:
+whether the point $p$ is covered, that is
\begin{equation}
\alpha_{j,p} = \left \{
\begin{array}{l l}
%\label{eq12}
\end{equation}
The number of active sensors that cover the primary point $p$ during
-round $t$ is equal to $\sum_{j \in J} \alpha_{j,p} * X_{t,j}$ where:
+round $t$ is equal to $\sum_{j \in J} \alpha_{j,p} * X_{t,j}$ where
\begin{equation}
X_{t,j} = \left \{
\begin{array}{l l}
\end{array} \right.
%\label{eq11}
\end{equation}
-We define the Overcoverage variable $\Theta_{t,p}$ as:
+We define the Overcoverage variable $\Theta_{t,p}$ as
\begin{equation}
\Theta_{t,p} = \left \{
\begin{array}{l l}
More precisely, $\Theta_{t,p}$ represents the number of active sensor nodes
minus one that cover the primary point $p$ during round $t$. The
Undercoverage variable $U_{t,p}$ of the primary point $p$ during round $t$ is
-defined by:
+defined by
\begin{equation}
U_{t,p} = \left \{
\begin{array}{l l}
\label{eq14}
\end{equation}
-Our coverage optimization problem can then be formulated as follows:
+Our coverage optimization problem can then be formulated as follows
\begin{equation}
\min \sum_{t=1}^{T} \sum_{p=1}^{P} \left(W_{\theta}* \Theta_{t,p} + W_{U} * U_{t,p} \right) \label{eq15}
\end{equation}
\end{equation}
\begin{equation}
- \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
+ \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
\label{eq144}
\end{equation}
and undercoverage variables help balancing the restriction equations by taking
positive values. 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 $E_{R}$ is the amount of energy
+alive during the selected rounds knowing that $E_{th}$ is the amount of energy
required to be alive during one round.
There are two main objectives. First, we limit the overcoverage of primary
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.
%% MS W_theta is smaller than W_u => problem with the following sentence
-In our simulations priority is given to the coverage by choosing $W_{U}$ very
+In our simulations, priority is given to the coverage by choosing $W_{U}$ very
large compared to $W_{\theta}$.
\section{Experimental Study and Analysis}
-\label{ch5:sec:03}
+\label{ch5:sec:04}
\subsection{Simulation Setup}
-\label{ch5:sec:03:01}
-We conducted a series of simulations to evaluate the efficiency and the
+\label{ch5:sec:04:01}
+We conducted a series of simulations to evaluate the efficiency and the
relevance of our approach, using the discrete event simulator OMNeT++
-\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.
-%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.
+\cite{ref158}. The simulation parameters are summarized in chapter 4, 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.
We performed simulations for five different densities varying from 50 to
250~nodes deployed over a $50 \times 25~m^2 $ sensing field. More
precisely, the deployment is controlled at a coarse scale in order to ensure
that the deployed nodes can cover the sensing field with the given sensing
range.
-%%RC these parameters are realistic?
-%% maybe we can increase the field and sensing range. 5mfor Rs it seems very small... what do the other good papers consider ?
-
-\begin{table}[ht]
-\caption{Relevant parameters for network initializing.}
-% title of Table
-\centering
-% used for centering table
-\begin{tabular}{c|c}
-% centered columns (4 columns)
- \hline
-%inserts double horizontal lines
-Parameter & Value \\ [0.5ex]
-
-%Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
-% inserts table
-%heading
-\hline
-% inserts single horizontal line
-Sensing field size & $(50 \times 25)~m^2 $ \\
-% inserting body of the table
-%\hline
-Network size & 50, 100, 150, 200 and 250~nodes \\
-%\hline
-Initial energy & 500-700~joules \\
-%\hline
-Sensing time for one round & 60 Minutes \\
-$E_{R}$ & 36 Joules\\
-$R_s$ & 5~m \\
-%\hline
-$W_{\Theta}$ & 1 \\
-% [1ex] adds vertical space
-%\hline
-$W_{U}$ & $|P|^2$
-%inserts single line
-\end{tabular}
-\label{table3}
-% is used to refer this table in the text
-\end{table}
-
-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 full distributed coverage algorithm. The second method, called
-GAF~\cite{GAF}, consists in dividing the region into fixed squares.
-During the decision phase, in each square, one sensor is then chosen to remain
-active during the sensing phase time.
-
-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, we have set the number of subregions to 16 rather than 32.
-
-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}.
-
-%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.
+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. DESK \cite{DESK} and GAF~\cite{GAF}.
+%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,
+we set the number of subregions to 16 rather than 32 as explained in chapter 4, section ref{ch4:sec:04:05}. We use the modeling language and the optimization solver which are mentioned in chapter 4, section \ref{ch4:sec:04:02}. In addition, the energy consumption model is presented in chapter 4, section \ref{ch4:sec:04:03}.
\subsection{Metrics}
-\label{ch5:sec:03:02}
+\label{ch5:sec:04:02}
To evaluate our approach we consider the following performance metrics:
-\begin{enumerate}[i]
+\begin{enumerate}[i)]
-\item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much of the area
- of a sensor field is covered. In our case, the sensing field is represented as
- a connected grid of points and we use each grid point as a sample point to
- compute the coverage. The coverage ratio can be calculated by:
+\item {{\bf Coverage Ratio (CR)}:} The coverage ratio can be calculated by:
\begin{equation*}
\scriptsize
\mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100,
of grid points in the sensing field of the network. In our simulations $N = 51
\times 26 = 1326$ grid points.
-\item{{\bf Number of Active Sensors Ratio (ASR)}:} it is important to have as
- few active nodes as possible in each round, in order to minimize the
- communication overhead and maximize the network lifetime. The Active Sensors
- Ratio is defined as follows:
+\item{{\bf Number of Active Sensors Ratio (ASR)}:} The Active Sensors
+ Ratio for round t is defined as follows:
\begin{equation*}
-\scriptsize \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R
+\scriptsize \mbox{$ASR^t$}(\%) = \frac{\sum\limits_{r=1}^R
\mbox{$A_r^t$}}{\mbox{$|J|$}} \times 100,
\end{equation*}
where $A_r^t$ is the number of active sensors in the subregion $r$ during round
$t$ in the current sensing phase, $|J|$ is the total number of sensors in the
network, and $R$ is the total number of subregions in the network.
-\item {{\bf Network Lifetime}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
+\item {{\bf Network Lifetime}:} Described in chapter 4, section \ref{ch4:sec:04:04}.
\item {{\bf Energy Consumption (EC)}:} the average energy consumption can be
seen as the total energy consumed by the sensors during the $Lifetime_{95}$ or
% New version with global loops on period
\begin{equation*}
\scriptsize
- \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},
+ \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},
\end{equation*}
-where $M_L$ is the number of periods and $T_m$ the number of rounds in a
+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. The first one , denoted $E^{\scriptsize \mbox{com}}_m$,
indicate the energy consumed by the whole network in round $t$.
-\item {{\bf Execution Time}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
+\item {{\bf Execution Time}:} Described in chapter 4, section \ref{ch4:sec:04:04}.
-\item {{\bf Stopped simulation runs}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
+\item {{\bf Stopped simulation runs}:} Described in chapter 4, section \ref{ch4:sec:04:04}.
\end{enumerate}
\subsection{Results Analysis and Comparison }
-\label{ch5:sec:03:02}
+\label{ch5:sec:04:02}
-\begin{enumerate}[(i)]
+\begin{enumerate}[i)]
\item {{\bf Coverage Ratio}}
%\subsection{Coverage ratio}
which is a little bit better than the one of MuDiLCO.
This is due to the fact that, in comparison with MuDiLCO which uses optimization
-to put in SLEEP status redundant sensors, more sensor nodes remain active with
-DESK and GAF. As a consequence, when the number of rounds increases, a larger
+to put in sleep status redundant sensors, more sensor nodes remain active with
+DESK and GAF. As a consequence, when the number of rounds increases, a larger
number of node failures can be observed in DESK and GAF, resulting in a faster
decrease of the coverage ratio. Furthermore, our protocol allows to maintain a
coverage ratio greater than 50\% for far more rounds. Overall, the proposed
sensor activity scheduling based on optimization in MuDiLCO maintains higher
coverage ratios of the area of interest for a larger number of rounds. It also
-means that MuDiLCO saves more energy, with less dead nodes, at most for several
+means that MuDiLCO saves more energy, with fewer dead nodes, at most for several
rounds, and thus should extend the network lifetime.
-\begin{figure}[ht!]
+\begin{figure}[h!]
\centering
- \includegraphics[scale=0.6] {Figures/ch5/R1/CR.pdf}
+ \includegraphics[scale=0.8] {Figures/ch5/R1/CR.pdf}
\caption{Average coverage ratio for 150 deployed nodes}
\label{fig3}
\end{figure}
minimize the communication overhead and maximize the network
lifetime. Figure~\ref{fig4} presents the active sensor ratio for 150 deployed
nodes all along the network lifetime. It appears that up to round thirteen, DESK
-and GAF have respectively 37.6\% and 44.8\% of nodes in ACTIVE status, whereas
+and GAF have respectively 37.6\% and 44.8\% of nodes in active mode, whereas
MuDiLCO clearly outperforms them with only 24.8\% of active nodes. After the
thirty-fifth round, MuDiLCO exhibits larger numbers of active nodes, which agrees
with the dual observation of higher level of coverage made previously.
-Obviously, in that case DESK and GAF have less active nodes, since they have
-activated many nodes at the beginning. Anyway, MuDiLCO activates the available
-nodes in a more efficient manner.
+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.
-\begin{figure}[ht!]
+\begin{figure}[h!]
\centering
-\includegraphics[scale=0.6]{Figures/ch5/R1/ASR.pdf}
+\includegraphics[scale=0.8]{Figures/ch5/R1/ASR.pdf}
\caption{Active sensors ratio for 150 deployed nodes}
\label{fig4}
\end{figure}
still connected.
-\begin{figure}[ht!]
+\begin{figure}[h!]
\centering
-\includegraphics[scale=0.6]{Figures/ch5/R1/SR.pdf}
+\includegraphics[scale=0.8]{Figures/ch5/R1/SR.pdf}
\caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes }
\label{fig6}
\end{figure}
\centering
%\begin{multicols}{1}
\centering
-\includegraphics[scale=0.6]{Figures/ch5/R1/EC95.pdf}\\~ ~ ~ ~ ~(a) \\
+\includegraphics[scale=0.8]{Figures/ch5/R1/EC95.pdf}\\~ ~ ~ ~ ~(a) \\
%\vfill
-\includegraphics[scale=0.6]{Figures/ch5/R1/EC50.pdf}\\~ ~ ~ ~ ~(b)
+\includegraphics[scale=0.8]{Figures/ch5/R1/EC50.pdf}\\~ ~ ~ ~ ~(b)
%\end{multicols}
\caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
\end{figure}
-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
-the number of sensors involved in the integer program are, 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 less
-sensors to consider in the integer program.
+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
+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.
%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.
-\begin{figure}[ht!]
+\begin{figure}[H]
\centering
-\includegraphics[scale=0.6]{Figures/ch5/R1/T.pdf}
+\includegraphics[scale=0.8]{Figures/ch5/R1/T.pdf}
\caption{Execution Time (in seconds)}
\label{fig77}
\end{figure}
-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,
-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.
+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,
+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. \\
%\subsection{Network lifetime}
%\label{ch5:sec:03:02:06}
-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
-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.
+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
+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.
This point was already noticed in \ref{subsec:EC} devoted to the
-energy consumption, since network lifetime and energy consumption are directly
-linked.
+energy consumption, since network lifetime and energy consumption are directly linked.
-\begin{figure}[h!]
+\begin{figure}[hi]
\centering
% \begin{multicols}{0}
\centering
-\includegraphics[scale=0.6]{Figures/ch5/R1/LT95.pdf}\\~ ~ ~ ~ ~(a) \\
+\includegraphics[scale=0.8]{Figures/ch5/R1/LT95.pdf}\\~ ~ ~ ~ ~(a) \\
%\hfill
-\includegraphics[scale=0.6]{Figures/ch5/R1/LT50.pdf}\\~ ~ ~ ~ ~(b)
+\includegraphics[scale=0.8]{Figures/ch5/R1/LT50.pdf}\\~ ~ ~ ~ ~(b)
%\end{multicols}
\caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
\section{Conclusion}
-\label{ch5:sec:04}
+\label{ch5:sec:05}
+
+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,
+called MuDiLCO (Multiround Distributed Lifetime Coverage Optimization) 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.
-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,
-called MuDiLCO (Multiround Distributed Lifetime Coverage Optimization) 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.
-
-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 in 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.
+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.
