X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/JournalMultiPeriods.git/blobdiff_plain/e922fb6744c31e70fef0af0686179ce3d60feae5..fc5104595f29a7b08dcc76c4e62cf7c76a9235f1:/article.tex?ds=inline diff --git a/article.tex b/article.tex index 520140e..192acf5 100644 --- a/article.tex +++ b/article.tex @@ -84,14 +84,11 @@ %e-mail: ali.idness@edu.univ-fcomte.fr, \\ %$\lbrace$karine.deschinkel, michel.salomon, raphael.couturier$\rbrace$@univ-fcomte.fr.} - -\author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$, \\ -Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$ \\ - $^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, \\ - University Bourgogne Franche-Comt\'e, Belfort, France}} \\ - $^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}} -} - +\author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$, \\ Michel + Salomon$^{a}$, and Rapha\"el Couturier $^{a}$ \\ $^{a}${\em{FEMTO-ST + Institute, UMR 6174 CNRS, \\ University Bourgogne Franche-Comt\'e, + Belfort, France}} \\ $^{b}${\em{Department of Computer Science, University + of Babylon, Babylon, Iraq}} } \begin{abstract} %One of the fundamental challenges in Wireless Sensor Networks (WSNs) @@ -99,31 +96,33 @@ Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$ \\ %continuously and effectively when monitoring a certain area (or %region) of interest. Coverage and lifetime are two paramount problems in Wireless Sensor Networks -(WSNs). In this paper, a method called Multiround Distributed Lifetime Coverage +(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. \textcolor{green}{The decision process is carried out by a leader node, which -solves an optimization problem to produce the best representative sets to be used -during the rounds of the sensing phase. The optimization problem formulated as an integer program is solved to optimality through a branch-and-Bound method for small instances. For larger instances, the best feasible solution found by the solver after a given time limit threshold is considered. } +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, with one set for each round of +a period, to remain active during the sensing phase and thus ensure coverage so +as to maximize the WSN lifetime. \textcolor{blue}{The decision process is + carried out by a leader node, which solves an optimization problem to produce + the best representative sets to be used during the rounds of the sensing + phase. The optimization problem formulated as an integer program is solved to + optimality through a Branch-and-Bound method for small instances. For larger + instances, the best feasible solution found by the solver after a given time + limit threshold is considered.} %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. %\textcolor{red}{The integer program is solved by either GLPK solver or Genetic Algorithm (GA)}. -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. - +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. \end{abstract} \begin{keyword} Wireless Sensor Networks, Area Coverage, Network Lifetime, Optimization, Scheduling, Distributed Computation. - \end{keyword} \end{frontmatter} @@ -167,10 +166,10 @@ the network lifetime by using an optimized multiround scheduling. The remainder of the paper is organized as follows. The next section % Section~\ref{rw} -reviews the related works in the field. Section~\ref{pd} is devoted to the +reviews the related works in the field. Section~\ref{pd} is devoted to the description of MuDiLCO protocol. Section~\ref{exp} shows the simulation results obtained using the discrete event simulator OMNeT++ \cite{varga}. They fully -demonstrate the usefulness of the proposed approach. Finally, we give +demonstrate the usefulness of the proposed approach. Finally, we give concluding remarks and some suggestions for future works in Section~\ref{sec:conclusion}. @@ -204,43 +203,47 @@ many cover sets) can be added to the above list. The major approach is to divide/organize the sensors into a suitable number of cover sets where each set completely covers an interest region and to activate these cover sets successively. The centralized algorithms always provide nearly -or close to optimal solution since the algorithm has global view of the whole +or close to optimal solution since the algorithm has global view of the whole network. Note that centralized algorithms have the advantage of requiring very low processing power from the sensor nodes, which usually have limited -processing capabilities. The main drawback of this kind of approach is its +processing capabilities. The main drawback of this kind of approach is its higher cost in communications, since the node that will make the decision needs -information from all the sensor nodes. \textcolor{green} {Exact or heuristics approaches are designed to provide cover sets. - %(Moreover, centralized approaches usually +information from all the sensor nodes. \textcolor{blue} {Exact or heuristics + approaches are designed to provide cover sets. +%(Moreover, centralized approaches usually %suffer from the scalability problem, making them less competitive as the network %size increases.) -Contrary to exact methods, heuristic methods can handle very large and centralized problems. They are proposed to reduce computational overhead such as energy consumption, delay and generally increase in -the network lifetime. } +Contrary to exact methods, heuristic ones can handle very large and centralized +problems. They are proposed to reduce computational overhead such as energy +consumption, delay, and generally allow to increase the network lifetime.} The first algorithms proposed in the literature consider that the cover sets are disjoint: a sensor node appears in exactly one of the generated cover -sets~\cite{abrams2004set,cardei2005improving,Slijepcevic01powerefficient}. In -the case of non-disjoint algorithms \cite{pujari2011high}, sensors may -participate in more than one cover set. In some cases, this may prolong the +sets~\cite{abrams2004set,cardei2005improving,Slijepcevic01powerefficient}. In +the case of non-disjoint algorithms \cite{pujari2011high}, sensors may +participate in more than one cover set. In some cases, this may prolong the lifetime of the network in comparison to the disjoint cover set algorithms, but -designing algorithms for non-disjoint cover sets generally induces a higher +designing algorithms for non-disjoint cover sets generally induces a higher order of complexity. Moreover, in case of a sensor's failure, non-disjoint -scheduling policies are less resilient and reliable because a sensor may be +scheduling policies are less resilient and reliable because a sensor may be involved in more than one cover sets. %For instance, the proposed work in ~\cite{cardei2005energy, berman04} -In~\cite{yang2014maximum}, the authors have considered a linear programming +In~\cite{yang2014maximum}, the authors have considered a linear programming approach to select the minimum number of working sensor nodes, in order to -preserve a maximum coverage and to extend lifetime of the network. Cheng et +preserve a maximum coverage and to extend lifetime of the network. Cheng et al.~\cite{cheng2014energy} have defined a heuristic algorithm called Cover Sets Balance (CSB), which chooses a set of active nodes using the tuple (data coverage range, residual energy). Then, they have introduced a new Correlated -Node Set Computing (CNSC) algorithm to find the correlated node set for a given -node. After that, they proposed a High Residual Energy First (HREF) node -selection algorithm to minimize the number of active nodes so as to prolong the -network lifetime. Various centralized methods based on column generation -approaches have also been -proposed~\cite{gentili2013,castano2013column,rossi2012exact,deschinkel2012column}. -\textcolor{green}{In~\cite{gentili2013}, authors highlight the trade-off between the network lifetime and the coverage percentage. They show that network lifetime can be hugely improved by decreasing the coverage ratio. } +Node Set Computing (CNSC) algorithm to find the correlated node set for a given +node. After that, they proposed a High Residual Energy First (HREF) node +selection algorithm to minimize the number of active nodes so as to prolong the +network lifetime. Various centralized methods based on column generation +approaches have also been +proposed~\cite{gentili2013,castano2013column,rossi2012exact,deschinkel2012column}. +\textcolor{blue}{In~\cite{gentili2013}, authors highlight the trade-off between + the network lifetime and the coverage percentage. They show that network + lifetime can be hugely improved by decreasing the coverage ratio.} \subsection{Distributed approaches} %{\bf Distributed approaches} @@ -297,16 +300,19 @@ Indeed, each sensor maintains its own timer and its wake-up time is randomized \cite{Ye03} or regulated \cite{cardei2005maximum} over time. The MuDiLCO protocol (for Multiround Distributed Lifetime Coverage Optimization -protocol) presented in this paper is an extension of the approach introduced +protocol) presented in this paper is an extension of the approach introduced in~\cite{idrees2014coverage}. In~\cite{idrees2014coverage}, the protocol is -deployed over only two subregions. Simulation results have shown that it was +deployed over only two subregions. Simulation results have shown that it was more interesting to divide the area into several subregions, given the computation complexity. Compared to our previous paper, in this one we study the possibility of dividing the sensing phase into multiple rounds and we also add -an improved model of energy consumption to assess the efficiency of our +an improved model of energy consumption to assess the efficiency of our approach. In fact, in this paper we make a multiround optimization, while it was -a single round optimization in our previous work. \textcolor{green}{The idea is to take advantage of the pre-sensing phase - to plan the sensor's activity for several rounds instead of one, thus saving energy. In addition, when the optimization problem becomes more complex, its resolution is stopped after a given time threshold}. +a single round optimization in our previous work. \textcolor{blue}{The idea is + to take advantage of the pre-sensing phase to plan the sensor's activity for + several rounds instead of one, thus saving energy. In addition, when the + optimization problem becomes more complex, its resolution is stopped after a + given time threshold}. \iffalse @@ -540,12 +546,16 @@ active nodes. %Instead of working with a continuous coverage area, we make it discrete by considering for each sensor a set of points called primary points. Consequently, we assume that the sensing disk defined by a sensor is covered if all of its primary points are covered. The choice of number and locations of primary points is the subject of another study not presented here. +\indent Instead of working with the coverage area, we consider for each sensor a +set of points called primary points~\cite{idrees2014coverage}. We assume that +the sensing disk defined by a sensor is covered if all the primary points of +this sensor are covered. By knowing the position of wireless sensor node +(centered at the the position $\left(p_x,p_y\right)$) and it's sensing range +$R_s$, we define up to 25 primary points $X_1$ to $X_{25}$ as decribed on +Figure~\ref{fig1}. The optimal number of primary points is investigated in +subsection~\ref{ch4:sec:04:06}. -\indent Instead of working with the coverage area, we consider for each sensor a set of points called primary points~\cite{idrees2014coverage}. We also assume that the sensing disk defined by a sensor is covered if all the primary points of this sensor are covered. By knowing the position (point center: ($p_x,p_y$)) of a wireless sensor node and it's sensing range $R_s$, we calculate the primary points directly based on the proposed model. We use these primary points (that can be increased or decreased if necessary) as references to ensure that the monitored region of interest is covered by the selected set of sensors, instead of using all the points in the area. -We can calculate the positions of the selected primary -points in the circle disk of the sensing range of a wireless sensor -node (see Figure~\ref{fig1}) as follows:\\ -Assuming that the point center of a wireless sensor node is located at $(p_x,p_y)$, we can define up to 25 primary points $X_1$ to $X_{25}$.\\ +The coordinates of the primary points are defined as follows:\\ %$(p_x,p_y)$ = point center of wireless sensor node\\ $X_1=(p_x,p_y)$ \\ $X_2=( p_x + R_s * (1), p_y + R_s * (0) )$\\ @@ -564,8 +574,8 @@ $X_{14}=( p_x + R_s * (\frac{\sqrt{3}}{2}), p_y + R_s * (\frac{1}{2})) $\\ $X_{15}=( p_x + R_s * (\frac{-\sqrt{3}}{2}), p_y + R_s * (\frac{1}{2})) $\\ $X_{16}=( p_x + R_s * (\frac{\sqrt{3}}{2}), p_y + R_s * (\frac{- 1}{2})) $\\ $X_{17}=( p_x + R_s * (\frac{-\sqrt{3}}{2}), p_y + R_s * (\frac{- 1}{2})) $\\ -$X_{18}=( p_x + R_s * (\frac{\sqrt{3}}{2}), p_y + R_s * (0) $\\ -$X_{19}=( p_x + R_s * (\frac{-\sqrt{3}}{2}), p_y + R_s * (0) $\\ +$X_{18}=( p_x + R_s * (\frac{\sqrt{3}}{2}), p_y + R_s * (0)) $\\ +$X_{19}=( p_x + R_s * (\frac{-\sqrt{3}}{2}), p_y + R_s * (0)) $\\ $X_{20}=( p_x + R_s * (0), p_y + R_s * (\frac{1}{2})) $\\ $X_{21}=( p_x + R_s * (0), p_y + R_s * (-\frac{1}{2})) $\\ $X_{22}=( p_x + R_s * (\frac{1}{2}), p_y + R_s * (\frac{\sqrt{3}}{2})) $\\ @@ -574,28 +584,29 @@ $X_{24}=( p_x + R_s * (\frac{- 1}{2}), p_y + R_s * (\frac{-\sqrt{3}}{2})) $\\ $X_{25}=( p_x + R_s * (\frac{1}{2}), p_y + R_s * (\frac{-\sqrt{3}}{2})) $. - -\begin{figure} %[h!] -\centering - \begin{multicols}{2} -\centering -\includegraphics[scale=0.28]{fig21.pdf}\\~ (a) -\includegraphics[scale=0.28]{principles13.pdf}\\~(c) -\hfill \hfill -\includegraphics[scale=0.28]{fig25.pdf}\\~(e) -\includegraphics[scale=0.28]{fig22.pdf}\\~(b) -\hfill \hfill -\includegraphics[scale=0.28]{fig24.pdf}\\~(d) -\includegraphics[scale=0.28]{fig26.pdf}\\~(f) -\end{multicols} -\caption{Wireless Sensor Node represented by (a) 5, (b) 9, (c) 13, (d) 17, (e) 21 and (f) 25 primary points respectively} -\label{fig1} -\end{figure} +%\begin{figure} %[h!] +%\centering +% \begin{multicols}{2} +%\centering +%\includegraphics[scale=0.28]{fig21.pdf}\\~ (a) +%\includegraphics[scale=0.28]{principles13.pdf}\\~(c) +%\hfill \hfill +%\includegraphics[scale=0.28]{fig25.pdf}\\~(e) +%\includegraphics[scale=0.28]{fig22.pdf}\\~(b) +%\hfill \hfill +%\includegraphics[scale=0.28]{fig24.pdf}\\~(d) +%\includegraphics[scale=0.28]{fig26.pdf}\\~(f) +%\end{multicols} +%\caption{Wireless Sensor Node represented by (a) 5, (b) 9, (c) 13, (d) 17, (e) 21 and (f) 25 primary points respectively} +%\label{fig1} +%\end{figure} - - - - +\begin{figure}[h] + \centering + \includegraphics[scale=0.375]{fig26.pdf} + \label{fig1} + \caption{Wireless sensor node represented by up to 25~primary points} +\end{figure} %By knowing the position (point center: ($p_x,p_y$)) of a wireless %sensor node and its $R_s$, we calculate the primary points directly @@ -612,14 +623,22 @@ $X_{25}=( p_x + R_s * (\frac{1}{2}), p_y + R_s * (\frac{-\sqrt{3}}{2})) $. \subsection{Background idea} %%RC : we need to clarify the difference between round and period. Currently it seems to be the same (for me at least). -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. +%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. + +\textcolor{blue}{The WSN area of interest is, in a first step, divided into regular homogeneous +subregions using a divide-and-conquer algorithm. In a second step our protocol +will be executed in a distributed way in each subregion simultaneously to +schedule nodes' activities for one sensing period. Sensor nodes are assumed to +be deployed almost uniformly over the region. The regular subdivision is made +such that the number of hops between any pairs of sensors inside a subregion is +less than or equal to 3.} 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. Each sensing phase may be itself divided into $T$ rounds -\textcolor{green} {of equal duration} and for each round a set of sensors (a cover set) is responsible for the sensing +\textcolor{blue} {of equal duration} and for each round a set of sensors (a cover set) is responsible for the sensing task. 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. @@ -642,7 +661,7 @@ running out of energy), because it works in periods. 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. \textcolor{green}{The duration of the rounds are predefined parameters. Round duration should be long enough to hide the system control overhead and short enough to minimize the negative effects in case of node failure.} +period starts. \textcolor{blue}{The duration of the rounds are predefined parameters. Round duration should be long enough to hide the system control overhead and short enough to minimize the negative effects in case of node failure.} %%RC so if there are at least one failure per period, the coverage is bad... %%MS if we want to be reliable against many node failures we need to have an @@ -712,7 +731,7 @@ consumption due to the communications. \subsection{Decision phase} -Each WSNL will \textcolor{green}{ solve an integer program to select which cover sets will be +Each WSNL will \textcolor{blue}{ 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. $T$ cover sets will be produced, 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. } @@ -801,7 +820,7 @@ Subject to \end{equation} \begin{equation} - \sum_{t=1}^{T} X_{t,j} \leq \floor*{RE_{j}/E_{R}} \hspace{6 mm} \forall j \in J, t = 1,\dots,T + \sum_{t=1}^{T} X_{t,j} \leq \floor*{RE_{j}/E_{R}} \hspace{10 mm}\forall j \in J\hspace{6 mm} \label{eq144} \end{equation} @@ -849,6 +868,8 @@ 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 large compared to $W_{\theta}$. + +\textcolor{blue}{The size of the problem depends on the number of variables and constraints. The number of variables is linked to the number of alive sensors $A \subset J$, the number of rounds $T$, and the number of primary points $P$. Thus the integer program contains $A*T$ variables of type $X_{t,j}$, $P*T$ overcoverage variables and $P*T$ undercoverage variables. The number of constraints is equal to $P*T$ (for constraints (\ref{eq16})) $+$ $A$ (for constraints (\ref{eq144})).} %The Active-Sleep packet includes the schedule vector with the number of rounds that should be applied by the receiving sensor node during the sensing phase. @@ -1129,12 +1150,37 @@ $W_{U}$ & $|P|^2$ \\ \label{table3} % is used to refer this table in the text \end{table} - -\textcolor{red}{Our first protocol based GLPK optimization solver 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). } -%The second protocol based GA is declined into four versions: GA-MuDiLCO-1, GA-MuDiLCO-3, GA-MuDiLCO-5, -%and GA-MuDiLCO-7 for the same reason of the first protocol. After extensive experiments, we chose the dedicated values for the parameters $P_c$, $P_m$, and $S_{pop}$ because they gave the best results}. + +\textcolor{blue}{The MuDilLCO 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). Since the time resolution may be prohibitif when the size of the problem increases, a time limit treshold has been fixed to solve large instances. In these cases, the solver returns the best solution found, which is not necessary the optimal solution. + Table \ref{tl} shows time limit values. These time limit treshold have been set empirically. The basic idea consists in considering the average execution time to solve the integer programs to optimality, then by dividing this average time by three to set the threshold value. After that, this treshold value is increased if necessary such that the solver is able to deliver a feasible solution within the time limit. In fact, selecting the optimal values for the time limits will be investigated in future. In Table \ref{tl}, "NO" indicates that the problem has been solved to optimality without time limit. }. + +\begin{table}[ht] +\caption{Time limit values for MuDiLCO protocol versions } +\centering +\begin{tabular}{|c|c|c|c|c|} + \hline + WSN size & MuDiLCO-1 & MuDiLCO-3 & MuDiLCO-5 & MuDiLCO-7 \\ [0.5ex] +\hline + 50 & NO & NO & NO & NO \\ + \hline +100 & NO & NO & NO & NO \\ +\hline +150 & NO & NO & NO & 0.03 \\ +\hline +200 & NO & NO & NO & 0.06 \\ + \hline + 250 & NO & NO & NO & 0.08 \\ + \hline +\end{tabular} + +\label{tl} + +\end{table} + + + + In the following, we will make comparisons with two other methods. The first method, called DESK and proposed by \cite{ChinhVu}, is a full distributed coverage algorithm. The second method, called @@ -1321,7 +1367,7 @@ indicate the energy consumed by the whole network in round $t$. \end{enumerate} -\subsection{Performance Analysis for Different Number of Primary Points} +\subsection{Performance analysis for different number of primary points} \label{ch4:sec:04:06} In this section, we study the performance of MuDiLCO-1 approach for different numbers of primary points. The objective of this comparison is to select the suitable primary point model to be used by a MuDiLCO protocol. In this comparison, MuDiLCO-1 protocol is used with five models, which are called Model-5 (it uses 5 primary points), Model-9, Model-13, Model-17, and Model-21. @@ -1330,7 +1376,7 @@ In this section, we study the performance of MuDiLCO-1 approach for different nu %\begin{enumerate}[i)] %\item {{\bf Coverage Ratio}} -\subsubsection{Coverage Ratio} +\subsubsection{Coverage ratio} Figure~\ref{Figures/ch4/R2/CR} shows the average coverage ratio for 150 deployed nodes. \parskip 0pt @@ -1345,72 +1391,9 @@ As can be seen in Figure~\ref{Figures/ch4/R2/CR}, at the beginning the models wh Moreover, when the number of periods increases, coverage ratio produced by all models decrease, but Model-5 is the one with the slowest decrease due to a smaller time computation of decision process for a smaller number of primary points. As shown in Figure ~\ref{Figures/ch4/R2/CR}, coverage ratio decreases when the number of periods increases due to dead nodes. Model-5 is slightly more efficient than other models, because it offers a good coverage ratio for a larger number of periods in comparison with other models. -%\item {{\bf Active Sensors Ratio}} -\subsubsection{Active Sensors Ratio} - -Figure~\ref{Figures/ch4/R2/ASR} shows the average active nodes ratio for 150 deployed nodes. -\begin{figure}[h!] -\centering -\includegraphics[scale=0.5]{R2/ASR.pdf} -\caption{Active sensors ratio for 150 deployed nodes } -\label{Figures/ch4/R2/ASR} -\end{figure} -The results presented in Figure~\ref{Figures/ch4/R2/ASR} show the superiority of the proposed Model-5, in comparison with the other models. The model with fewer number of primary points uses fewer active nodes than the other models. -According to the results presented in Figure~\ref{Figures/ch4/R2/CR}, we observe that Model-5 continues for a larger number of periods with a better coverage ratio compared with other models. The advantage of Model-5 is to use fewer number of active nodes for each period compared with Model-9, Model-13, Model-17, and Model-21. This led to continuing for a larger number of periods and thus extending the network lifetime. - - -%\item {{\bf Stopped simulation runs}} -\subsubsection{Stopped simulation runs} - -Figure~\ref{Figures/ch4/R2/SR} illustrates the percentage of stopped simulation runs per period for 150 deployed nodes. - -\begin{figure}[h!] -\centering -\includegraphics[scale=0.5]{R2/SR.pdf} -\caption{Percentage of stopped simulation runs for 150 deployed nodes } -\label{Figures/ch4/R2/SR} -\end{figure} - -When the number of primary points is increased, the percentage of the stopped simulation runs per period is increased. The reason behind the increase is the increasing number of dead sensors when the primary points increase. Model-5 is better than other models because it conserves more energy by turning on less sensors during the sensing phase and in the same time it preserves a good coverage for a larger number of periods in comparison with other models. Model~5 seems to be more suitable to be used in wireless sensor networks. \\ - - -%\item {{\bf Energy Consumption}} -\subsubsection{Energy Consumption} - -In this experiment, we study the effect of increasing the primary points to represent the area of the sensor on the energy consumed by the wireless sensor network for different network densities. Figures~\ref{Figures/ch4/R2/EC}(a) and~\ref{Figures/ch4/R2/EC}(b) illustrate the energy consumption for different network sizes for $Lifetime_{95}$ and $Lifetime_{50}$. - -\begin{figure}[h!] -\centering - %\begin{multicols}{1} -\centering -\includegraphics[scale=0.5]{R2/EC95.pdf}\\~ ~ ~ ~ ~(a) \\ -%\vfill -\includegraphics[scale=0.5]{R2/EC50.pdf}\\~ ~ ~ ~ ~(b) - -%\end{multicols} -\caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$} -\label{Figures/ch4/R2/EC} -\end{figure} - -We see from the results presented in both figures that the energy consumed by the network for each period increases when the number of primary points increases. Indeed, the decision for the optimization process requires more time, which leads to consuming more energy during the listening mode. The results show that Model-5 is the most competitive from the energy consumption point of view and the coverage ratio point of view. The other models have a high energy consumption due to the increase in the primary points. In fact, Model-5 is a good candidate to be used by wireless sensor network because it preserves a good coverage ratio with a suitable energy consumption in comparison with other models. - -%\item {{\bf Execution Time}} -\subsubsection{Execution Time} - -In this experiment, we study the impact of the increase in primary points on the execution time of DiLCO protocol. Figure~\ref{Figures/ch4/R2/T} gives the average execution times in seconds for the decision phase (solving of the optimization problem) during one period. The original execution time is computed as described in section \ref{et}. - -\begin{figure}[h!] -\centering -\includegraphics[scale=0.5]{R2/T.pdf} -\caption{Execution Time (in seconds)} -\label{Figures/ch4/R2/T} -\end{figure} - -They are given for the different primary point models and various numbers of sensors. We can see from Figure~\ref{Figures/ch4/R2/T}, that Model-5 has lower execution time in comparison with other models because it uses the smaller number of primary points to represent the area of the sensor. Conversely, the other primary point models have presented higher execution times. -Moreover, Model-5 has more suitable execution times and coverage ratio that lead to continue for a larger number of period extending the network lifetime. We think that a good primary point model is one that balances between the coverage ratio and the number of periods during the lifetime of the network. %\item {{\bf Network Lifetime}} -\subsubsection{Network Lifetime} +\subsubsection{Network lifetime} Finally, we study the effect of increasing the primary points on the lifetime of the network. %In Figure~\ref{Figures/ch4/R2/LT95} and in Figure~\ref{Figures/ch4/R2/LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes. @@ -1427,11 +1410,10 @@ As highlighted by Figures~\ref{Figures/ch4/R2/LT}(a) and \ref{Figures/ch4/R2/LT} \label{Figures/ch4/R2/LT} \end{figure} -Comparison shows that Model-5, which uses less number of primary points, is the best one because it is less energy consuming during the network lifetime. It is also the better one from the point of view of coverage ratio. Our proposed Model-5 efficiently prolongs the network lifetime with a good coverage ratio in comparison with other models. Therefore, we have chosen Model-5 for all the experiments presented thereafter. +Comparison shows that Model-5, which uses less number of primary points, is the best one because it is less energy consuming during the network lifetime. It is also the better one from the point of view of coverage ratio. Our proposed Model-5 efficiently prolongs the network lifetime with a good coverage ratio in comparison with other models. Therefore, we have chosen the model with five primary points for all the experiments presented thereafter. %\end{enumerate} - \subsection{Results and analysis} \subsubsection{Coverage ratio} @@ -1455,7 +1437,7 @@ rounds, and thus should extend the network lifetime. \begin{figure}[ht!] \centering - \includegraphics[scale=0.5] {R/CR.pdf} + \includegraphics[scale=0.5] {F/CR.pdf} \caption{Average coverage ratio for 150 deployed nodes} \label{fig3} \end{figure} @@ -1481,7 +1463,7 @@ Obviously, in that case DESK and GAF have less active nodes, since they have a \begin{figure}[ht!] \centering -\includegraphics[scale=0.5]{R/ASR.pdf} +\includegraphics[scale=0.5]{F/ASR.pdf} \caption{Active sensors ratio for 150 deployed nodes} \label{fig4} \end{figure} @@ -1505,7 +1487,7 @@ Let us emphasize that the simulation continues as long as a network in a subre \begin{figure}[ht!] \centering -\includegraphics[scale=0.5]{R/SR.pdf} +\includegraphics[scale=0.5]{F/SR.pdf} \caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes } \label{fig6} \end{figure} @@ -1521,9 +1503,9 @@ network sizes, for $Lifetime_{95}$ and $Lifetime_{50}$. \begin{figure}[h!] \centering \begin{tabular}{cl} - \parbox{9.5cm}{\includegraphics[scale=0.5]{R/EC95.pdf}} & (a) \\ + \parbox{9.5cm}{\includegraphics[scale=0.5]{F/EC95.pdf}} & (a) \\ \verb+ + \\ - \parbox{9.5cm}{\includegraphics[scale=0.5]{R/EC50.pdf}} & (b) + \parbox{9.5cm}{\includegraphics[scale=0.5]{F/EC50.pdf}} & (b) \end{tabular} \caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$} @@ -1532,8 +1514,9 @@ network sizes, for $Lifetime_{95}$ and $Lifetime_{50}$. 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. +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. %\textcolor{red}{As shown in Figure~\ref{fig7}, GA-MuDiLCO consumes less energy than both DESK and GAF, but a little bit higher than MuDiLCO because it provides a near optimal solution by activating a larger number of nodes during the sensing phase. GA-MuDiLCO consumes less energy in comparison with MuDiLCO-7 version, especially for the dense networks. However, MuDiLCO protocol and GA-MuDiLCO protocol are 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.} @@ -1555,7 +1538,7 @@ for different network sizes. \begin{figure}[ht!] \centering -\includegraphics[scale=0.5]{R/T.pdf} +\includegraphics[scale=0.5]{F/T.pdf} \caption{Execution Time (in seconds)} \label{fig77} \end{figure} @@ -1594,9 +1577,9 @@ linked. \begin{figure}[t!] \centering \begin{tabular}{cl} - \parbox{9.5cm}{\includegraphics[scale=0.5]{R/LT95.pdf}} & (a) \\ + \parbox{9.5cm}{\includegraphics[scale=0.5]{F/LT95.pdf}} & (a) \\ \verb+ + \\ - \parbox{9.5cm}{\includegraphics[scale=0.5]{R/LT50.pdf}} & (b) + \parbox{9.5cm}{\includegraphics[scale=0.5]{F/LT50.pdf}} & (b) \end{tabular} \caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}