+\subsection{Metrics}
+\label{ch5:sec:04:02}
+To evaluate our approach we consider the following performance metrics:
+
+\begin{enumerate}[i]
+
+\item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much of the area
+ of a sensor field is covered. In our case, the sensing field is represented as
+ a connected grid of points and we use each grid point as a sample point to
+ compute the coverage. The coverage ratio can be calculated by:
+\begin{equation*}
+\scriptsize
+\mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100,
+\end{equation*}
+where $n^t$ is the number of covered grid points by the active sensors of all
+subregions during round $t$ in the current sensing phase and $N$ is the total number
+of grid points in the sensing field of the network. In our simulations $N = 51
+\times 26 = 1326$ grid points.
+
+\item{{\bf Number of Active Sensors Ratio (ASR)}:} it is important to have as
+ few active nodes as possible in each round, in order to minimize the
+ communication overhead and maximize the network lifetime. The Active Sensors
+ Ratio is defined as follows:
+\begin{equation*}
+\scriptsize \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R
+ \mbox{$A_r^t$}}{\mbox{$|J|$}} \times 100,
+\end{equation*}
+where $A_r^t$ is the number of active sensors in the subregion $r$ during round
+$t$ in the current sensing phase, $|J|$ is the total number of sensors in the
+network, and $R$ is the total number of subregions in the network.
+
+\item {{\bf Network Lifetime}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
+
+\item {{\bf Energy Consumption (EC)}:} the average energy consumption can be
+ seen as the total energy consumed by the sensors during the $Lifetime_{95}$ or
+ $Lifetime_{50}$ divided by the number of rounds. EC can be computed as
+ follows:
+
+ % New version with global loops on period
+ \begin{equation*}
+ \scriptsize
+ \mbox{EC} = \frac{\sum\limits_{m=1}^{M_L} \left[ \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T_m} \left( E^{a}_t+E^{s}_t \right) \right]}{\sum\limits_{m=1}^{M_L} T_m},
+ \end{equation*}
+
+
+where $M_L$ is the number of periods and $T_m$ the number of rounds in a
+period~$m$, both during $Lifetime_{95}$ or $Lifetime_{50}$. The total energy
+consumed by the sensors (EC) comes through taking into consideration four main
+energy factors. The first one , denoted $E^{\scriptsize \mbox{com}}_m$,
+represents the energy consumption spent by all the nodes for wireless
+communications during period $m$. $E^{\scriptsize \mbox{list}}_m$, the next
+factor, corresponds to the energy consumed by the sensors in LISTENING status
+before receiving the decision to go active or sleep in period $m$.
+$E^{\scriptsize \mbox{comp}}_m$ refers to the energy needed by all the leader
+nodes to solve the integer program during a period. Finally, $E^a_t$ and $E^s_t$
+indicate the energy consumed by the whole network in round $t$.
+
+
+\item {{\bf Execution Time}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
+
+\item {{\bf Stopped simulation runs}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
