\subsection{Primary Point Coverage Model}
\label{ch4:sec:02:02}
\indent Instead of working with the coverage area, we consider for each sensor a set of points called primary points. 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 $R_s$, 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.
-
-\indent We can calculate the positions of the selected primary
+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:\\
$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!]
+
+
+\begin{figure} %[h!]
\centering
- \begin{multicols}{3}
+ \begin{multicols}{2}
\centering
-\includegraphics[scale=0.20]{Figures/ch4/fig21.pdf}\\~ ~ ~ ~ ~(a)
-\includegraphics[scale=0.20]{Figures/ch4/fig22.pdf}\\~ ~ ~ ~ ~(b)
-\includegraphics[scale=0.20]{Figures/ch4/principles13.pdf}\\~ ~ ~ ~ ~(c)
-\hfill
-\includegraphics[scale=0.20]{Figures/ch4/fig24.pdf}\\~ ~ ~(d)
-\includegraphics[scale=0.20]{Figures/ch4/fig25.pdf}\\~ ~ ~(e)
-\includegraphics[scale=0.20]{Figures/ch4/fig26.pdf}\\~ ~ ~(f)
+\includegraphics[scale=0.33]{Figures/ch4/fig21.pdf}\\~ ~ ~ ~ ~ ~ ~ ~(a)
+\includegraphics[scale=0.33]{Figures/ch4/principles13.pdf}\\~ ~ ~ ~ ~ ~(c)
+\hfill \hfill
+\includegraphics[scale=0.33]{Figures/ch4/fig25.pdf}\\~ ~ ~ ~ ~ ~(e)
+\includegraphics[scale=0.33]{Figures/ch4/fig22.pdf}\\~ ~ ~ ~ ~ ~ ~ ~ ~(b)
+\hfill \hfill
+\includegraphics[scale=0.33]{Figures/ch4/fig24.pdf}\\~ ~ ~ ~ ~ ~ ~(d)
+\includegraphics[scale=0.33]{Figures/ch4/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}
-
+
+
\subsection{Main Idea}
\contentsline {section}{\numberline {3.3}Optimization Solvers}{68}{section.3.3}
\contentsline {section}{\numberline {3.4}Conclusion}{71}{section.3.4}
\contentsline {part}{II\hspace {1em}Contributions}{73}{part.2}
-\contentsline {chapter}{\numberline {4}Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}{75}{chapter.4}
+\contentsline {chapter}{\numberline {4}Distributed Lifetime Coverage Optimization Protocol in WSNs}{75}{chapter.4}
\contentsline {section}{\numberline {4.1}Introduction}{75}{section.4.1}
\contentsline {section}{\numberline {4.2}Description of the DiLCO Protocol}{76}{section.4.2}
\contentsline {subsection}{\numberline {4.2.1}Assumptions and Network Model}{76}{subsection.4.2.1}
\contentsline {subsection}{\numberline {4.2.2}Primary Point Coverage Model}{77}{subsection.4.2.2}
-\contentsline {subsection}{\numberline {4.2.3}Main Idea}{78}{subsection.4.2.3}
+\contentsline {subsection}{\numberline {4.2.3}Main Idea}{79}{subsection.4.2.3}
\contentsline {subsubsection}{\numberline {4.2.3.1}Information Exchange Phase}{79}{subsubsection.4.2.3.1}
\contentsline {subsubsection}{\numberline {4.2.3.2}Leader Election Phase}{79}{subsubsection.4.2.3.2}
-\contentsline {subsubsection}{\numberline {4.2.3.3}Decision phase}{79}{subsubsection.4.2.3.3}
-\contentsline {subsubsection}{\numberline {4.2.3.4}Sensing phase}{79}{subsubsection.4.2.3.4}
+\contentsline {subsubsection}{\numberline {4.2.3.3}Decision phase}{80}{subsubsection.4.2.3.3}
+\contentsline {subsubsection}{\numberline {4.2.3.4}Sensing phase}{80}{subsubsection.4.2.3.4}
\contentsline {section}{\numberline {4.3}Primary Points based Coverage Problem Formulation}{80}{section.4.3}
\contentsline {section}{\numberline {4.4}Simulation Results and Analysis}{82}{section.4.4}
\contentsline {subsection}{\numberline {4.4.1}Simulation Framework}{82}{subsection.4.4.1}
-\contentsline {subsection}{\numberline {4.4.2}Modeling Language and Optimization Solver}{82}{subsection.4.4.2}
-\contentsline {subsection}{\numberline {4.4.3}Energy Consumption Model}{82}{subsection.4.4.3}
-\contentsline {subsection}{\numberline {4.4.4}Performance Metrics}{83}{subsection.4.4.4}
-\contentsline {subsection}{\numberline {4.4.5}Performance Analysis for Different Subregions}{84}{subsection.4.4.5}
+\contentsline {subsection}{\numberline {4.4.2}Modeling Language and Optimization Solver}{83}{subsection.4.4.2}
+\contentsline {subsection}{\numberline {4.4.3}Energy Consumption Model}{83}{subsection.4.4.3}
+\contentsline {subsection}{\numberline {4.4.4}Performance Metrics}{84}{subsection.4.4.4}
+\contentsline {subsection}{\numberline {4.4.5}Performance Analysis for Different Subregions}{85}{subsection.4.4.5}
\contentsline {subsection}{\numberline {4.4.6}Performance Analysis for Primary Point Models}{90}{subsection.4.4.6}
\contentsline {subsection}{\numberline {4.4.7}Performance Comparison with other Approaches}{95}{subsection.4.4.7}
-\contentsline {section}{\numberline {4.5}Conclusion}{101}{section.4.5}
+\contentsline {section}{\numberline {4.5}Conclusion}{102}{section.4.5}
\contentsline {chapter}{\numberline {5}Multiround Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}{103}{chapter.5}
\contentsline {section}{\numberline {5.1}Introduction}{103}{section.5.1}
\contentsline {section}{\numberline {5.2}MuDiLCO Protocol Description}{104}{section.5.2}