\section{\uppercase{Simulation Results}}
\label{exp}
-In this section, we conducted a series of simulations, to evaluate the
+In this section, we conducted a series of simulations to evaluate the
efficiency and relevance of our approach, using the discrete event
simulator OMNeT++ \cite{varga}. We performed simulations for five
different densities varying from 50 to 250~nodes. Experimental results
the sensing period which will have a duration of 60 seconds. Thus, an
active node will consume 12~joules during sensing phase, while a
sleeping node will use 0.002 joules. Each sensor node will not
-participate in the next round if it's remaining energy is less than 12
+participate in the next round if its remaining energy is less than 12
joules. In all experiments the parameters are set as follows:
$R_s=5m$, $w_{\Theta}=1$, and $w_{U}=|P^2|$.
for the three approaches. It can be seen that the three approaches
give similar coverage ratios during the first rounds. From the
9th~round the coverage ratio decreases continuously with the simple
-heuristic, while the other two strategies provide superior coverage to
+heuristic, while the two other strategies provide superior coverage to
$90\%$ for five more rounds. Coverage ratio decreases when the number
of rounds increases due to dead nodes. Although some nodes are dead,
thanks to strategy~1 or~2, other nodes are preserved to ensure the
the second strategy, because the global optimization permit to turn
off more sensors. Indeed, when there are two subregions more nodes
remain awake near the border shared by them. Note that again as the
-number of rounds increase the two leader strategy becomes the most
+number of rounds increases the two leader strategy becomes the most
performing, since its takes longer to have the two subregion networks
simultaneously disconnected.
\subsection{The Network Lifetime}
We have defined the network lifetime as the time until all nodes have
-been drained of their energy or each sensor network monitoring a area
+been drained of their energy or each sensor network monitoring an area
becomes disconnected. In figure~\ref{fig6}, the network lifetime for
different network sizes and for the three approaches is illustrated.
increases when the size of the network increase, with our approaches
that lead to the larger lifetime improvement. By choosing for each
round the well suited nodes to cover the region of interest and by
-leaving sleep the other ones to be used later in next rounds, both
+letting the other ones sleep in order to be used later in next rounds, both
proposed strategies efficiently prolong the lifetime. Comparison shows
-that the larger the sensor number, the more our strategies outperform
-the heuristic. Strategy~2, which uses two leaders, is the best one
+that the larger the sensor number is, the more our strategies outperform
+the simple heuristic. Strategy~2, which uses two leaders, is the best one
because it is robust to network disconnection in one subregion. It
also means that distributing the algorithm in each node and
subdividing the sensing field into many subregions, which are managed
