\iffalse

\section{\uppercase{Introduction}}
\label{sec:introduction}

\noindent In the last years, there  has been an increasing development in wireless
networking,  Micro-Electro-Mechanical  Systems  (MEMS), and  embedded  computing
technologies, which  have led to construct low-cost,  small-sized, and low-power
sensor nodes that can perform  detection, computation, and data communication of
surrounding environment. A  WSN includes a large number  of small, limited-power
sensors  that   can  sense,   process,  and  transmit   data  over   a  wireless
communication.   They communicate with  each other  by using  multi-hop wireless
communications and cooperate  together to monitor the area  of interest, so that
each  measured data  can be  reported  to a  monitoring center  called sink  for
further analysis~\cite{Sudip03}.

There are  several fields  of application  covering a wide  spectrum for  a WSN,
including    health,    home,    environmental,   military,    and    industrial
applications~\cite{Akyildiz02}. One of  the major scientific research challenges
in WSNs,  which has been  addressed by a  large amount of literature  during the
last few  years, is the design  of energy efficient approaches  for coverage and
connectivity~\cite{conti2014mobile}.     On   the    one    hand   an    optimal
coverage~\cite{Nayak04} is required to  monitor efficiently and continuously the
area of interest and on the other  hand the energy consumption must be as low as
possible,  due   to  the  limited  energy  of   sensors~\cite{Sudip03}  and  the
impossibility or  difficulty to replace and/or recharge  their batteries because
of  the  area  of interest  nature  (such  as  remote, hostile,  or  unpractical
environments)  and the  cost. So,  it is  of  great relevance  for a  WSN to  be
deployed with high density, because  spatial redundancy can then be exploited to
increase the lifetime  of the network. However, turning on  all the sensor nodes
which monitor the same  region at the same time reduces the  the lifetime of the
network. Therefore, to  extend the lifetime of the network, the  main idea is to
take advantage of  the overlapping sensing regions of some  sensor nodes to save
energy by turning off some of them during the sensing phase~\cite{Misra}.

In this paper we concentrate on the area coverage problem with the objective of
maximizing the network lifetime  by using an adaptive scheduling. The area of
interest is divided into subregions  and an activity scheduling for sensor nodes
is planned for each subregion. In fact,  the nodes in a subregion can be seen as
a cluster  where each node sends  sensing data to  the cluster head or  the sink
node.  Furthermore, the  activities in a subregion/cluster can  continue even if
another  cluster stops due  to too  many node  failures.  Our  scheduling scheme
considers  rounds, where  a  round starts  with  a discovery  phase to  exchange
information between sensors  of the subregion, in order to  choose in a suitable
manner a sensor  node to carry out a coverage  strategy.  This coverage strategy
involves the solving of an integer program, which provides the activation of the
sensors for the sensing phase of the current round.

The remainder of the paper is organized as follows. The next section
% Section~\ref{rw}
reviews  the related  work  in  the field. Section~\ref{pd} is devoted to the
DiLCO   protocol  Description.   Section~\ref{cp}  gives   the   coverage  model
formulation   which   is  used   to   schedule   the   activation  of   sensors.
Section~\ref{exp} shows the simulation results obtained using the discrete event
simulator  OMNeT++ \cite{varga}. They  fully demonstrate  the usefulness  of the
proposed approach.  Finally, we give concluding remarks and some suggestions for
future works in Section~\ref{sec:conclusion}.

\fi




















\iffalse

\subsubsection{Active Sensors Ratio} 
 Figure~\ref{fig4} shows the average active nodes ratio for 150 deployed nodes.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.45]{R1/ASR.pdf}  
\caption{The impact of the number of rounds on the active sensors ratio for 150 deployed nodes }
\label{fig4}
\end{figure} 
The results presented in figure~\ref{fig4} show  the increase in the number of subregions led to increase in the number of active nodes. The DiLCO-16 and DiLCO-32 protocols have a larger number of active nodes but it preserve the coverage for a larger number of rounds. The  advantage of the DiLCO-16, and DiLCO-32 protocols are that even if a network is disconnected in one subregion, the other ones usually continues the optimization process, and this extends the lifetime of the network.

\subsubsection{The percentage of stopped simulation runs}
Figure~\ref{fig6} illustrates the percentage of stopped simulation runs per round for 150 deployed nodes. 
\begin{figure}[h!]
\centering
\includegraphics[scale=0.45]{R1/SR.pdf} 
\caption{The percentage of stopped simulation runs compared to the number of rounds for 150 deployed nodes }
\label{fig6}
\end{figure} 

It can be observed that the DiLCO-2  is the approach which stops first because it applied the optimization on only two subregions for the area of interest that is why it is first exhibits network disconnections.
Thus, as explained previously, in case of the DiLCO-16 and DiLCO-32 with several subregions the optimization effectively continues as long as a network in a subregion is still connected. This longer partial coverage optimization participates in extending the network lifetime. 

\fi







\iffalse



\subsection{Performance Comparison for Different Approaches}
After extensive study for our primary point model, we found that  DiLCO protocol  gives better results if the sensor coverage model represented by 9 primary points. Based on the results, which are conducted from previous subsection~\ref{sub1}, we found that Our DiLCO-16, and DiLCO-32 protocols are the best candidates to be compared with other two approches. The first approach, called DESK that proposed by ~\cite{ChinhVu}, which is a full distributed coverage algorithm. The second approach, called GAF ~\cite{xu2001geography}, 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} 
In this experiment, Figure~\ref{fig333} shows  the average coverage ratio for 150 deployed nodes. 
 
\parskip 0pt    
\begin{figure}[h!]
\centering
 \includegraphics[scale=0.45] {R3/CR.pdf} 
\caption{The coverage ratio for 150 deployed nodes}
\label{fig333}
\end{figure} 

It is shown that DESK and GAF provides a
a little better coverage ratio with 99.99\% and 99.91\% against 99.1\% and 99.2\% produced by DiLCO-16 and DiLCO-32 for the lowest number of rounds. This is due to the fact that our DiLCO protocol versions  put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more nodes are active in the case of DESK and GAF.

Moreover, when the number of rounds increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, Our DiLCO-16 and DiLCO-32 protocols maintains almost a good coverage. This is because it optimize the coverage and the lifetime in wireless sensor network by selecting the best representative sensor nodes to take the reponsibilty of coverage during the sensing phase and this will leads to continue for a larger number of rounds and prolonging the network lifetime; although some nodes are dead, sensor activity scheduling of our protocol chooses other nodes to ensure the coverage of the area of interest. 

\iffalse

\subsubsection{Active Sensors Ratio} 
It is important to have as few active nodes as possible in each round,
in  order to  minimize the energy consumption and maximize the network lifetime. Figure~\ref{fig444} shows the average active nodes ratio for 150 deployed nodes. 

\begin{figure}[h!]
\centering
\includegraphics[scale=0.45]{R3/ASR.pdf}  
\caption{The active sensors ratio for 150 deployed nodes }
\label{fig444}
\end{figure} 

The results presented in figure~\ref{fig444} show the superiority of the proposed DiLCO-16 and DiLCO-32 protocols, in comparison with the other approaches.  We can observe that DESK and GAF have 37.5 \% and 44.5 \% active nodes and our DiLCO-16 and DiLCO-32 protocols competes perfectly with only 17.4 \%, 24.8 \% and 26.8 \%  active nodes for the first 14 rounds. Then as the number of rounds increases our DiLCO-16 and DiLCO-32 protocols have larger number of active nodes in comparison with DESK and GAF, especially from round $35^{th}$ because they give a better coverage ratio than other approaches. We see that the DESK and GAF have less number of active nodes beginning at the rounds $35^{th}$ and $32^{th}$ because there are many nodes are died due to the high energy consumption by the redundant nodes during the sensing phase. 

\subsubsection{The percentage of stopped simulation runs}
The results presented in this experiment, is to show the comparison of our DiLCO-16 and DiLCO-32 protocols with other two approaches from the point of view the stopped simulation runs per round.
Figure~\ref{fig666} illustrates the percentage of stopped simulation
runs per round for 150 deployed nodes. 
\begin{figure}[h!]
\centering
\includegraphics[scale=0.45]{R3/SR.pdf} 
\caption{The percentage of stopped simulation runs compared to the number of rounds for 150 deployed nodes }
\label{fig666}
\end{figure} 
It can be observed that the DESK is the approach, which stops first because it consumes more energy for communication as well as it turn on a large number of redundant nodes during the sensing phase. Our DiLCO-16 and DiLCO-32 protocols have less stopped simulation runs in comparison with DESK and GAF because it distributed the optimization on several subregions in order to optimize the coverage and the lifetime of the network by activating a less number of nodes during the sensing phase leading to extend the network lifetime and coverage preservation.The optimization effectively continues as long as a network in a subregion is still connected.

\fi

\subsubsection{The Energy Consumption}
In this experiment, we study the effect of the energy consumed by the wireless sensor network during the communication, computation, listening, active, and sleep modes for different network densities and compare it with other approaches. Figures~\ref{fig3EC95} and ~\ref{fig3EC50} illustrate the energy consumption for different network sizes for $Lifetime95$ and $Lifetime50$. 

\begin{figure}[h!]
\centering
\includegraphics[scale=0.45]{R3/EC95.pdf} 
\caption{The Energy Consumption with $95\%-Lifetime$}
\label{fig3EC95}
\end{figure} 

\begin{figure}[h!]
\centering
\includegraphics[scale=0.45]{R3/EC50.pdf} 
\caption{The Energy Consumption with $Lifetime50$}
\label{fig3EC50}
\end{figure} 

The results show that our DiLCO-16 and DiLCO-32 protocols are 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 modes of sensor nodes. In fact,  a distributed  method on the subregions greatly reduces the number of communications and the time of listening so thanks to the partitioning of the initial network into several independent subnetworks. 

\subsubsection{The Network Lifetime}
In this experiment, we are observed the superiority of our DiLCO-16 and DiLCO-32 protocols against other two approaches in prolonging the network lifetime. In figures~\ref{fig3LT95} and \ref{fig3LT50}, network lifetime, $Lifetime95$ and $Lifetime50$ respectively, are illustrated for different network sizes.  

\begin{figure}[h!]
\centering
\includegraphics[scale=0.45]{R3/LT95.pdf}  
\caption{The Network Lifetime for $Lifetime95$}
\label{fig3LT95}
\end{figure}


\begin{figure}[h!]
\centering
\includegraphics[scale=0.45]{R3/LT50.pdf}  
\caption{The Network Lifetime for $Lifetime50$}
\label{fig3LT50}
\end{figure} 

As highlighted by figures~\ref{fig3LT95} and \ref{fig3LT50}, the network lifetime obviously
increases when the size of the network increases, with our DiLCO-16 and DiLCO-32 protocols
that leads to maximize the lifetime of the network compared with other approaches. 
By choosing the best suited nodes, for each round, by optimizing the coverage and lifetime of the network to cover the area of interest and by letting the other ones sleep in order to be used later in next rounds, our DiLCO-16 and DiLCO-32 protocols efficiently prolonges the network lifetime. 
Comparison shows that our DiLCO-16 and DiLCO-32 protocols, which are used distributed optimization over the subregions, is the best one because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. It also means that distributing the algorithm in each node and subdividing the sensing field into many subregions, which are managed
independently and simultaneously, is the most relevant way to maximize the lifetime of a network.

\fi