X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/JournalMultiPeriods.git/blobdiff_plain/e922fb6744c31e70fef0af0686179ce3d60feae5..01aef364b44f686503abfe937ebe9face8ef1f4c:/article.tex diff --git a/article.tex b/article.tex index 520140e..9625e1e 100644 --- a/article.tex +++ b/article.tex @@ -1131,10 +1131,35 @@ $W_{U}$ & $|P|^2$ \\ \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}. +and MuDiLCO-7, corresponding respectively to $T=1,3,5,7$ ($T$ the number of rounds in one sensing period). +The second protocol based based GLPK optimization solver with time limit is declined into four versions: TL-MuDiLCO-1, TL-MuDiLCO-3, TL-MuDiLCO-5, and TL-MuDiLCO-7. Table \ref{tl} shows time limit values for TL-MuDiLCO protocol versions. After extensive experiments, we chose the values that explained in Table \ref{tl} because they gave the best results. In these experiments, we started with the average execution time of the corresponding MuDiLCO version and network size divided by 3 as a time limit. After that, we increase these values until reaching the best results. In Table \ref{tl}, "NO" refers to apply the GLPK solver without time limit because we did not find improvement on the results of MuDiLCO protocol with the time limit. }. + +\begin{table}[ht] +\caption{Time limit values for TL-MuDiLCO protocol versions } +\centering +\begin{tabular}{|c|c|c|c|c|} + \hline + WSN size & TL-MuDiLCO-1 & TL-MuDiLCO-3 & TL-MuDiLCO-5 & TL-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 & 0.0094 & 0.020 & 0.06 \\ + \hline + 250 & NO & 0.013 & 0.03 & 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 @@ -1345,69 +1370,6 @@ 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} @@ -1455,7 +1417,7 @@ 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 +1443,7 @@ 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 +1467,7 @@ 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 +1483,9 @@ 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) $Lifetime_{50}$} @@ -1555,7 +1517,7 @@ 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 +1556,9 @@ 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) $Lifetime_{50}$}