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high coverage ratio.
+\subsection{Modeling Language and Optimization Solver}
+\label{ch3:sec:04:02}
+The modeling language for Mathematical Programming (AMPL)~\cite{AMPL} is employed to generate the integer program instance in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method.
\subsection{Energy Consumption Model}
-\label{ch3:sec:04:02}
+\label{ch3:sec:04:03}
-\indent In this dissertation, we have used an energy consumption model proposed by~\cite{ref111} and based on \cite{ref112} with slight modifications. The energy consumption for sending/receiving the packets is added, whereas the part related to the sensing range is removed because we consider a fixed sensing range.
+\indent In this dissertation, we used an energy consumption model proposed by~\cite{ref111} and based on \cite{ref112} with slight modifications. The energy consumption for sending/receiving the packets is added, whereas the part related to the sensing range is removed because we consider a fixed sensing range.
\indent For our energy consumption model, we refer to the sensor node Medusa~II which uses an Atmels AVR ATmega103L microcontroller~\cite{ref112}. The typical architecture of a sensor is composed of four subsystems: the MCU subsystem which is capable of computation, communication subsystem (radio) which is responsible for transmitting/receiving messages, the sensing subsystem that collects data, and the power supply which powers the complete sensor node \cite{ref112}. Each of the first three subsystems can be turned on or off depending on the current status of the sensor. Energy consumption (expressed in milliWatt per second) for the different status of the sensor is summarized in Table~\ref{table1}.
\subsection{Performance Metrics}
-\label{ch3:sec:04:03}
+\label{ch3:sec:04:04}
In the simulations, we introduce the following performance metrics to evaluate
the efficiency of our approach:
\subsection{Performance Analysis for Different Subregions}
-\label{ch3:sec:04:04}
+\label{ch3:sec:04:05}
In this subsection, we are studied the performance of our DiLCO protocol for a different number of subregions (Leaders).
The DiLCO-1 protocol is a centralized approach on all the area of the interest, while DiLCO-2, DiLCO-4, DiLCO-8, DiLCO-16 and DiLCO-32 are distributed on two, four, eight, sixteen, and thirty-two subregions respectively. We did not take the DiLCO-1 protocol in our simulation results because it need high execution time to give the decision leading to consume all it's energy before producing the solution for optimization problem.
\subsection{Performance Analysis for Primary Point Models}
-\label{ch3:sec:04:03}
+\label{ch3:sec:04:06}
In this section, we are studied the performance of DiLCO~16 approach for a different primary point models. The objective of this comparison is to select the suitable primary point model to be used by DiLCO protocol.
\subsection{Performance Comparison with other Approaches}
-\label{ch3:sec:04:04}
+\label{ch3:sec:04:07}
Based on the results, which are conducted from previous two subsections, \ref{ch3:sec:04:02} and \ref{ch3:sec:04:03}, we have found that DiLCO-16 protocol and DiLCO-32 protocol with Model~2 are the best candidates to be compared with other two approaches. The first approach, called DESK that proposed by ~\cite{DESK}, which is a full distributed coverage algorithm. The second approach, called GAF~\cite{GAF}, consists in dividing the region into fixed squares. During the decision phase, in each square, one sensor is chosen to remain on during the sensing phase time.
\subsubsection{Coverage Ratio}
