-We chose as energy consumption model the one described in chapter 1, section \ref{ch1:sec9:subsec2}. Each node has an initial energy level, in Joules, which is randomly drawn in $[500-700]$. If its energy provision reaches a value below the threshold $E_{th}=36$~Joules, the minimum energy needed for a node to stay active during
-one period, it will no longer take part in the coverage task. This value corresponds to the energy needed by the sensing phase, obtained by multiplying the energy consumed in active state (9.72 mW) by the time in seconds for one period (3,600 seconds), and adding the energy for the pre-sensing phases.
-According to the interval of initial energy, a sensor may be active during at most 20 periods.
+
+\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:04:03}
+
+\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}.
+
+\begin{table}[ht]
+\caption{The Energy Consumption Model}
+% title of Table
+\centering
+% used for centering table
+\begin{tabular}{|c|c|c|c|c|}
+% centered columns (4 columns)
+ \hline
+%inserts double horizontal lines
+Sensor status & MCU & Radio & Sensing & Power (mW) \\ [0.5ex]
+\hline
+% inserts single horizontal line
+LISTENING & on & on & on & 20.05 \\
+% inserting body of the table
+\hline
+ACTIVE & on & off & on & 9.72 \\
+\hline
+SLEEP & off & off & off & 0.02 \\
+\hline
+COMPUTATION & on & on & on & 26.83 \\
+%\hline
+%\multicolumn{4}{|c|}{Energy needed to send/receive a 1-bit} & 0.2575\\
+ \hline
+\end{tabular}
+
+\label{table1}
+% is used to refer this table in the text
+\end{table}
+
+\indent For the sake of simplicity we ignore the energy needed to turn on the radio, to start up the sensor node, to move from one status to another, etc. Thus, when a sensor becomes active (i.e., it has already chosen its status), it can turn its radio off to save battery. The value of energy spent to send a 1-bit-content message is obtained by using the equation in ~\cite{ref112} to calculate the energy cost for transmitting messages and we propose the same value for receiving the packets. The energy needed to send or receive a 1-bit packet is equal to $0.2575~mW$.
+
+
+%We have used an energy consumption model, which is presented in chapter 1, section \ref{ch1:sec9:subsec2}.
+
+The initial energy of each node is randomly set in the interval $[500;700]$. A sensor node will not participate in the next round if its remaining energy is less than $E_{th}=36~\mbox{Joules}$, the minimum energy needed for the node to stay alive during one round. This value has been computed by multiplying the energy consumed in active state (9.72 mW) by the time in second for one round (3600 seconds), and adding the energy for the pre-sensing phases. According to the interval of initial energy, a sensor may be alive during at most 20 rounds.
