year={1991}
}
-@BOOK{AMPL,
- AUTHOR = "Robert Fourer and David M. Gay and Brian W. Kernighan",
- TITLE = "AMPL: A Modeling Language for Mathematical Programming",
- PUBLISHER = "Cengage Learning",
- YEAR = "November 12, 2002",
- edition = "2nd",
-
-}
-
-@ARTICLE{glpk,
-author = {Andrew Makhorin},
-title = {The GLPK (GNU Linear Programming Kit)},
-journal = {Available: https://www.gnu.org/software/glpk/},
-year = {2012}
+@article{gentili2013,
+year={2013},
+journal={Optimization Letters},
+volume={7},
+number={1},
+title={α-Coverage to extend network lifetime on wireless sensor networks},
+publisher={Springer-Verlag},
+author={Gentili, Monica and Raiconi, Andrea},
+pages={157-172},
}
\ No newline at end of file
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}
