As can be seen in Figure~\ref{fig2}, our protocol works in periods fashion, where each is divided into 4 phases: Information~Exchange, Leader~Election, Decision, and Sensing.
%The information exchange among wireless sensor nodes is described in chapter 4, section \ref{ch4:sec:02:03:01}. The leader election in each subregion is explained in chapter 4, section \ref{ch4:sec:02:03:02},
-The difference with MuDiLCO in that the elected leader in each subregion is for each period. In the decision phase, each leader will solve an integer program to select which cover sets will be activated in the following sensing phase to cover the subregion to which it belongs. The integer program will produce $T$ cover sets, one for each round. The leader will send an ActiveSleep packet to each sensor in the subregion based on the algorithm's results, indicating if the sensor should be active or not in
-each round of the sensing phase. Each sensing phase is itself divided into $T$ rounds and for each round a set of sensors (a cover set) is responsible for the sensing task.
-%Each sensor node in the subregion will receive an ActiveSleep packet from leader, informing it to stay awake or to go to sleep for each round of the sensing phase.
-Algorithm~\ref{alg:MuDiLCO}, which will be executed by each node at the beginning of a period, explains how the ActiveSleep packet is obtained. In this way, a multiround optimization process is performed during each
-period after Information~Exchange and Leader~Election phases, in order to produce $T$ cover sets that will take the mission of sensing for $T$ rounds.
\begin{figure}[ht!]
\centering \includegraphics[width=160mm]{Figures/ch5/GeneralModel.jpg} % 70mm Modelgeneral.pdf
\caption{MuDiLCO protocol.}
\end{figure}
-%This protocol minimizes the impact of unexpected node failure (not due to batteries running out of energy), because it works in periods. On the one hand, if a node failure is detected before making the decision, the node will not participate during this phase. On the other hand, if the node failure occurs after the decision, the sensing task of the network will be temporarily affected: only during the period of sensing until a new period starts.
-
-%The energy consumption and some other constraints can easily be taken into account since the sensors can update and then exchange their information (including their residual energy) at the beginning of each period. However, the pre-sensing phases (Information Exchange, Leader Election, and Decision) are energy consuming for some nodes, even when they do not join the network to monitor the area.
-
-
-
\begin{algorithm}[h!]
% \KwIn{all the parameters related to information exchange}
% \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
\end{algorithm}
+The difference with MuDiLCO in that the elected leader in each subregion is for each period. In the decision phase, each leader will solve an integer program to select which cover sets will be activated in the following sensing phase to cover the subregion to which it belongs. The integer program will produce $T$ cover sets, one for each round. The leader will send an ActiveSleep packet to each sensor in the subregion based on the algorithm's results, indicating if the sensor should be active or not in
+each round of the sensing phase. Each sensing phase is itself divided into $T$ rounds and for each round a set of sensors (a cover set) is responsible for the sensing task.
+%Each sensor node in the subregion will receive an ActiveSleep packet from leader, informing it to stay awake or to go to sleep for each round of the sensing phase.
+Algorithm~\ref{alg:MuDiLCO}, which will be executed by each node at the beginning of a period, explains how the ActiveSleep packet is obtained. In this way, a multiround optimization process is performed during each
+period after Information~Exchange and Leader~Election phases, in order to produce $T$ cover sets that will take the mission of sensing for $T$ rounds.
+
+
+%This protocol minimizes the impact of unexpected node failure (not due to batteries running out of energy), because it works in periods. On the one hand, if a node failure is detected before making the decision, the node will not participate during this phase. On the other hand, if the node failure occurs after the decision, the sensing task of the network will be temporarily affected: only during the period of sensing until a new period starts.
+
+%The energy consumption and some other constraints can easily be taken into account since the sensors can update and then exchange their information (including their residual energy) at the beginning of each period. However, the pre-sensing phases (Information Exchange, Leader Election, and Decision) are energy consuming for some nodes, even when they do not join the network to monitor the area.
+
+
+
%\subsection{Stopped simulation runs}
%\label{ch5:sec:03:02:03}
-Figure~\ref{fig6} reports the cumulative percentage of stopped simulations runs per round for 150 deployed nodes. This figure gives the breakpoint for each method. \\ \\ \\ \\
+Figure~\ref{fig6} reports the cumulative percentage of stopped simulations runs per round for 150 deployed nodes. This figure gives the breakpoint for each method.
DESK stops first, after approximately 45~rounds, because it consumes the more energy by turning on a large number of redundant nodes during the sensing phase. GAF stops secondly for the same reason than DESK. MuDiLCO overcomes DESK and GAF because the optimization process distributed on several subregions leads to coverage preservation and so extends the network lifetime. Let us
emphasize that the simulation continues as long as a network in a subregion is still connected. \\
The results show that MuDiLCO is the most competitive from the energy consumption point of view. The other approaches have a high energy consumption due to activating a larger number of redundant nodes, as well as the energy consumed during the different status of the sensor node. Among the different versions of our protocol, the MuDiLCO-7 one consumes more energy than the other versions. This is easy to understand since the bigger the number of rounds and
the number of sensors involved in the integer program, the larger the time computation to solve the optimization problem. To improve the performances of MuDiLCO-7, we should increase the number of subregions in order to have fewer sensors to consider in the integer program.
-\\ \\ \\
+
\item {{\bf Execution time}}
\end{figure}
As expected, the execution time increases with the number of rounds $T$ taken into account to schedule the sensing phase. The times obtained for $T=1,3$ or $5$ seem bearable, but for $T=7$ they become quickly unsuitable for a sensor node, especially when the sensor network size increases. Again, we can notice that if we want to schedule the nodes activities for a large number of rounds,
-we need to choose a relevant number of subregions in order to avoid a complicated and cumbersome optimization. On the one hand, a large value for $T$ permits to reduce the energy overhead due to the three pre-sensing phases, on the other hand a leader node may waste a considerable amount of energy to solve the optimization problem. \\
+we need to choose a relevant number of subregions in order to avoid a complicated and cumbersome optimization.
+On the one hand, a large value for $T$ permits to reduce the energy overhead due to the three pre-sensing phases, on the other hand a leader node may waste a considerable amount of energy to solve the optimization problem. %\\ \\ \\ \\ \\ \\ \\
\item {{\bf Network lifetime}}
%\subsection{Network lifetime}
%\label{ch5:sec:03:02:06}
The next two figures, Figures~\ref{fig8}(a) and \ref{fig8}(b), illustrate the network lifetime for different network sizes, respectively for $Lifetime_{95}$ and $Lifetime_{50}$. Both figures show that the network lifetime increases together with the number of sensor nodes, whatever the protocol, thanks to the node density which results in more and more redundant nodes that can be deactivated and thus save energy. Compared to the other approaches, our MuDiLCO
-protocol maximizes the lifetime of the network. In particular, the gain in lifetime for a coverage over 95\% is greater than 38\% when switching from GAF to MuDiLCO-3. \\ \\ \\
+protocol maximizes the lifetime of the network. In particular, the gain in lifetime for a coverage over 95\% is greater than 38\% when switching from GAF to MuDiLCO-3.
\begin{figure}[h!]
\centering
\end{figure}
-\end{enumerate}
The slight decrease that can be observed for MuDiLCO-7 in case of $Lifetime_{95}$ with large wireless sensor networks results from the difficulty of the optimization problem to be solved by the integer program.
This point was already noticed in \ref{subsec:EC} devoted to the
energy consumption, since network lifetime and energy consumption are directly linked.
+\end{enumerate}
+
\section{Conclusion}
\label{ch5:sec:05}
