\cite{pedraza2006} where the objective is to maximize the number of cover
sets.}
-% ***** Part which must be rewritten - Start
-% Start of Ali's papers catalog => there's no link between them or with our work
-% (use of subregions; optimization based method; etc.)
-\iffalse
-Diongue and Thiare~\cite{diongue2013alarm} proposed an energy aware sleep
-scheduling algorithm for lifetime maximization in wireless sensor networks
-(ALARM). The proposed approach permits to schedule redundant nodes according to
-the weibull distribution. This work did not analyze the ALARM scheme under the
-coverage problem.
-Shi et al.~\cite{shi2009} modeled the Area Coverage Problem (ACP), which will be
-changed into a set coverage problem. By using this model, they proposed an
-Energy-Efficient central-Scheduling greedy algorithm, which can reduces energy
-consumption and increases network lifetime, by selecting a appropriate subset of
-sensor nodes to support the networks periodically.
-
-In ~\cite{chenait2013distributed}, the authors presented a coverage-guaranteed
-distributed sleep/wake scheduling scheme so ass to prolong network lifetime
-while guaranteeing network coverage. This scheme mitigates scheduling process to
-be more stable by avoiding useless transitions between states without affecting
-the coverage level required by the application.
-
-The work in~\cite{cheng2014achieving} presented a unified sensing architecture
-for duty cycled sensor networks, called uSense, which comprises three ideas:
-Asymmetric Architecture, Generic Switching and Global Scheduling. The objective
-is to provide a flexible and efficient coverage in sensor networks.
-
-In~\cite{ling2009energy}, the lifetime of a sensor node is divided into
-epochs. At each epoch, the base station deduces the current sensing coverage
-requirement from application or user request. It then applies the heuristic
-algorithm in order to produce the set of active nodes which take the mission of
-sensing during the current epoch. After that, the produced schedule is sent to
-the sensor nodes in the network.
-
-% What is the link between the previous work and this paragraph about DiLCO ?
-
-
-
-Yang et al.~\cite{yang2014energy} investigated full area coverage problem under
-the probabilistic sensing model in the sensor networks. They have studied the
-relationship between the coverage of two adjacent points mathematically and then
-convert the problem of full area coverage into point coverage problem. They
-proposed $\varepsilon$-full area coverage optimization (FCO) algorithm to select
-a subset of sensors to provide probabilistic area coverage dynamically so as to
-extend the network lifetime.
-
-The work proposed by \cite{qu2013distributed} considers the coverage problem in
-WSNs where each sensor has variable sensing radius. The final objective is to
-maximize the network coverage lifetime in WSNs.
-\fi
-% Same remark, no link with the two previous citations...
-
-
-% ***** Part which must be rewritten - End
-
-\iffalse
-
-Some algorithms have been developed in ~\cite{yang2014energy,ChinhVu,vashistha2007energy,deschinkel2012column,shi2009,qu2013distributed,ling2009energy,xin2009area,cheng2014achieving,ling2009energy} to solve the area coverage problem so as to preserve coverage and prolong the network lifetime.
-
-
-Yang et al.~\cite{yang2014energy} investigated full area coverage problem
-under the probabilistic sensing model in the sensor networks. They have studied the relationship between the
-coverage of two adjacent points mathematically and then convert the problem of full area coverage into point coverage problem. They proposed $\varepsilon$-full area coverage optimization (FCO) algorithm to select a subset
-of sensors to provide probabilistic area coverage dynamically so as to extend the network lifetime.
-
-
-Vu et al.~\cite{ChinhVu} proposed a localized and distributed greedy algorithm named DESK for generating non-disjoint cover sets which provide the k-area coverage for the whole network.
-
-
-Qu et al.~\cite{qu2013distributed} developed a distributed algorithm using adjustable sensing sensors
-for maintaining the full coverage of such sensor networks. The
-algorithm contains two major parts: the first part aims at
-providing $100\%$ coverage and the second part aims at saving
-energy by decreasing the sensing radius.
-
-Shi et al.~\cite{shi2009} modeled the Area Coverage Problem (ACP), which will be changed into a set coverage
-problem. By using this model, they are proposed an Energy-Efficient central-Scheduling greedy algorithm, which can reduces energy consumption and increases network lifetime, by selecting a appropriate subset of sensor nodes to support the networks periodically.
-
-The work in~\cite{cheng2014achieving} presented a unified sensing architecture for duty cycled sensor networks, called uSense, which comprises three ideas: Asymmetric Architecture, Generic Switching and Global Scheduling. The objective is to provide a flexible and efficient coverage in sensor networks.
-
- In~\cite{ling2009energy}, the lifetime of
-a sensor node is divided into epochs. At each epoch, the
-base station deduces the current sensing coverage requirement
-from application or user request. It then applies the heuristic algorithm in order to produce the set of active nodes which take the mission of sensing during the current epoch. After that, the produced schedule is sent to the sensor nodes in the network.
-\fi
-
-\iffalse
-
-The work in ~\cite{vu2009delaunay} considered the area coverage problem for variable sensing radii in WSNs by improving the energy balancing heuristic proposed in ~\cite{wang2007energy} so that the area of interest can be full covered using Delaunay triangulation structure.
-
-Diongue and Thiare~\cite{diongue2013alarm} proposed an energy aware sleep scheduling algorithm for lifetime maximization in wireless sensor networks (ALARM). The proposed approach permits to schedule redundant nodes according to the weibull distribution. This work did not analyze the ALARM scheme under the coverage problem.
-
-
-In~\cite{xin2009area}, the authors proposed a circle intersection localized coverage algorithm
-to maintain connectivity based on loose connectivity critical condition
-. By using the connected coverage node set, it can maintain network
-connection in the case which loose condition is not meet.
-The authors in ~\cite{vashistha2007energy} addressed the full area coverage problem using information
-coverage. They are proposed a low-complexity heuristic algorithm to obtain full area information covers (FAIC), which they refer to as Grid Based FAIC (GB-FAIC) algorithm. Using these FAICs, they are obtained the optimal schedule for applying the sensing activity of sensor nodes in order to
-achieve increased sensing lifetime of the network.
-
-
-
-
-
-
-In \cite{xu2001geography}, Xu et al. proposed a Geographical Adaptive Fidelity (GAF) algorithm, which uses geographic location information to divide the area of interest into fixed square grids. Within each grid, it keeps only one node staying awake to take the responsibility of sensing and communication.
-
-The main contributions of our DiLCO Protocol can be summarized as follows:
-(1) The distributed optimization over the subregions in the area of interest,
-(2) The distributed dynamic leader election at each period by each sensor node in the subregion,
-(3) The primary point coverage model to represent each sensor node in the network,
-(4) The activity scheduling based optimization on the subregion, which are based on the primary point coverage model to activate as less number as possible of sensor nodes to take the mission of the coverage in each subregion, and (5) The improved energy consumption model.
-\fi
-\iffalse
-The work presented in~\cite{luo2014parameterized,tian2014distributed} tries to solve the target coverage problem so as to extend the network lifetime since it is easy to verify the coverage status of discreet target.
-%Je ne comprends pas la phrase ci-dessus
-The work proposed in~\cite{kim2013maximum} considers the barrier-coverage problem in WSNs. The final goal is to maximize the network lifetime such that any penetration of the intruder is detected.
-%inutile de parler de ce papier car il concerne barrier coverage
-In \cite{ChinhVu}, the authors propose a localized and distributed greedy algorithm named DESK for generating non-disjoint cover sets which provide the k-coverage for the whole network.
-Our Work in~\cite{idrees2014coverage} proposes a coverage optimization protocol to improve the lifetime in heterogeneous energy wireless sensor networks. In this work, the coverage protocol distributed in each sensor node in the subregion but the optimization take place over the the whole subregion. We are considered only distributing the coverage protocol over two subregions.
-
-The work presented in ~\cite{Zhang} focuses on a distributed clustering method, which aims to extend the network lifetime, while the coverage is ensured.
-
-The work proposed by \cite{qu2013distributed} considers the coverage problem in WSNs where each sensor has variable sensing radius. The final objective is to maximize the network coverage lifetime in WSNs.
-
-
-
-Casta{\~n}o et al.~\cite{castano2013column} proposed a multilevel approach based on column generation (CG) to extend the network lifetime with connectivity and coverage constraints. They are included two heuristic methods within the CG framework so as to accelerate the solution process.
-In \cite{diongue2013alarm}, diongue is proposed an energy Aware sLeep scheduling AlgoRithm for lifetime maximization in WSNs (ALARM) algorithm for coverage lifetime maximization in wireless sensor networks. ALARM is sensor node scheduling approach for lifetime maximization in WSNs in which it schedule redundant nodes according to the weibull distribution taking into consideration frequent nodes failure.
-Yu et al.~\cite{yu2013cwsc} presented a connected k-coverage working sets construction
-approach (CWSC) to maintain k-coverage and connectivity. This approach try to select the minimum number of connected sensor nodes that can provide k-coverage ($k \geq 1$).
-In~\cite{cheng2014achieving}, the authors are presented a unified sensing architecture for duty cycled sensor networks, called uSense, which comprises three ideas: Asymmetric Architecture, Generic Switching and Global Scheduling. The objective is to provide a flexible and efficient coverage in sensor networks.
-
-In~\cite{yang2013energy}, the authors are investigated full area coverage problem
-under the probabilistic sensing model in the sensor networks. %They are designed $\varepsilon-$full area coverage optimization (FCO) algorithm to select a subset of sensors to provide probabilistic area coverage dynamically so as to extend the network lifetime.
-In \cite{xu2001geography}, Xu et al. proposed a Geographical Adaptive Fidelity (GAF) algorithm, which uses geographic location information to divide the area of interest into fixed square grids. Within each grid, it keeps only one node staying awake to take the responsibility of sensing and communication.
-
-The main contributions of our DiLCO Protocol can be summarized as follows:
-(1) The distributed optimization over the subregions in the area of interest,
-(2) The distributed dynamic leader election at each round by each sensor node in the subregion,
-(3) The primary point coverage model to represent each sensor node in the network,
-(4) The activity scheduling based optimization on the subregion, which are based on the primary point coverage model to activate as less number as possible of sensor nodes to take the mission of the coverage in each subregion,
-(5) The improved energy consumption model.
-
-\fi
\section{\uppercase{Description of the DiLCO protocol}}
\label{sec:The DiLCO Protocol Description}
techniques: network leader election and sensor activity scheduling for coverage
preservation and energy conservation, applied periodically to efficiently
maximize the lifetime in the network.
-\iffalse The main features of our DiLCO protocol: i)It divides the area of
-interest into subregions by using divide-and-conquer concept, ii)It requires
-only the information of the nodes within the subregion, iii) it divides the
-network lifetime into rounds, iv)It based on the autonomous distributed decision
-by the nodes in the subregion to elect the Leader, v)It apply the activity
-scheduling based optimization on the subregion, vi) it achieves an energy
-consumption balancing among the nodes in the subregion by selecting different
-nodes as a leader during the network lifetime, vii) It uses the optimization to
-select the best representative set of sensors in the subregion by optimize the
-coverage and the lifetime over the area of interest, viii)It uses our proposed
-primary point coverage model, which represent the sensing range of the sensor as
-a set of points, which are used by the our optimization algorithm, ix) It uses a
-simple energy model that takes communication, sensing and computation energy
-consumptions into account to evaluate the performance of our protocol.
-\fi
+
\subsection{Assumptions and models}
primary points are covered. Obviously, the approximation of coverage is more or
less accurate according to the number of primary points.
-\iffalse
-By knowing the position (point center: ($p_x,p_y$)) of a wireless
-sensor node and its $R_s$, we calculate the primary points directly
-based on the proposed model. We use these primary points (that can be
-increased or decreased if necessary) as references to ensure that the
-monitored region of interest is covered by the selected set of
-sensors, instead of using all the points in the area.
-
-\indent We can calculate the positions of the selected primary
-points in the circle disk of the sensing range of a wireless sensor
-node (see figure~\ref{fig1}) as follows:\\
-$(p_x,p_y)$ = point center of wireless sensor node\\
-$X_1=(p_x,p_y)$ \\
-$X_2=( p_x + R_s * (1), p_y + R_s * (0) )$\\
-$X_3=( p_x + R_s * (-1), p_y + R_s * (0)) $\\
-$X_4=( p_x + R_s * (0), p_y + R_s * (1) )$\\
-$X_5=( p_x + R_s * (0), p_y + R_s * (-1 )) $\\
-$X_6= ( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (0)) $\\
-$X_7=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (0))$\\
-$X_8=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
-$X_9=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{-\sqrt{2}}{2})) $\\
-$X_{10}=( p_x + R_s * (\frac{-\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
-$X_{11}=( p_x + R_s * (\frac{\sqrt{2}}{2}), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
-$X_{12}=( p_x + R_s * (0), p_y + R_s * (\frac{\sqrt{2}}{2})) $\\
-$X_{13}=( p_x + R_s * (0), p_y + R_s * (\frac{-\sqrt{2}}{2})) $.
-
- \begin{figure}[h!]
-\centering
- \begin{multicols}{3}
-\centering
-%\includegraphics[scale=0.20]{fig21.pdf}\\~ ~ ~ ~ ~(a)
-%\includegraphics[scale=0.20]{fig22.pdf}\\~ ~ ~ ~ ~(b)
-\includegraphics[scale=0.25]{principles13.pdf}%\\~ ~ ~ ~ ~(c)
-%\includegraphics[scale=0.10]{fig25.pdf}\\~ ~ ~(d)
-%\includegraphics[scale=0.10]{fig26.pdf}\\~ ~ ~(e)
-%\includegraphics[scale=0.10]{fig27.pdf}\\~ ~ ~(f)
-\end{multicols}
-\caption{Wireless Sensor Node represented by 13 primary points}
-%\caption{Wireless Sensor Node represented by (a)5, (b)9 and (c)13 primary points respectively}
-\label{fig1}
-\end{figure}
-
-\fi
\subsection{Main idea}
\label{main_idea}
not. Alternately, if the sensor is not the leader, it will wait for the
Active-Sleep packet to know its state for the coming sensing phase.
-\iffalse
-\subsubsection{Information Exchange Phase}
-
-Each sensor node $j$ sends its position, remaining energy $RE_j$, and
-the number of neighbors $NBR_j$ to all wireless sensor nodes in
-its subregion by using an INFO packet and then listens to the packets
-sent from other nodes. After that, each node will have information
-about all the sensor nodes in the subregion. In our model, the
-remaining energy corresponds to the time that a sensor can live in the
-active mode.
-
-\subsubsection{Leader Election Phase}
-This step includes choosing the Wireless Sensor Node Leader (WSNL),
-which will be responsible for executing the coverage algorithm. Each
-subregion in the area of interest will select its own WSNL
-independently for each round. All the sensor nodes cooperate to
-select WSNL. The nodes in the same subregion will select the leader
-based on the received information from all other nodes in the same
-subregion. The selection criteria in order of priority are: larger
-number of neighbors, larger remaining energy, and then in case of
-equality, larger index.
-
-\subsubsection{Decision phase}
-The WSNL will solve an integer program (see section~\ref{cp}) to
-select which sensors will be activated in the following sensing phase
-to cover the subregion. WSNL will send Active-Sleep packet to each
-sensor in the subregion based on the algorithm's results.
-
-
-\subsubsection{Sensing phase}
-
-Active sensors in the round will execute their sensing task to preserve maximal
-coverage in the region of interest. We will assume that the cost of keeping a
-node awake (or asleep) for sensing task is the same for all wireless sensor
-nodes in the network. Each sensor will receive an Active-Sleep packet from WSNL
-informing it to stay awake or to go to sleep for a time equal to the period of
-sensing until starting a new round. Algorithm 1, which will be executed by each
-node at the beginning of a round, explains how the Active-Sleep packet is
-obtained.
-
-\fi
-
-
-\iffalse
-\subsection{DiLCO protocol Algorithm}
-we first show the pseudo-code of DiLCO protocol, which is executed by each
-sensor in the subregion and then describe it in more detail. \fi
+
+
+
\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)}
+
\BlankLine
%\emph{Initialize the sensor node and determine it's position and subregion} \;
\Else{
\emph{$s_j.status$ = LISTENING}\;
\emph{Wait $ActiveSleep()$ packet from the Leader}\;
- % \emph{After receiving Packet, Retrieve the schedule and the $T$ rounds}\;
+
\emph{Update $RE_j $}\;
}
% }
\end{algorithm}
-\iffalse
-The DiLCO protocol work in rounds and executed at each sensor node in the network, each sensor node can still sense data while being in
-LISTENING mode. Thus, by entering the LISTENING mode at the beginning of each round,
-sensor nodes still executing sensing task while participating in the leader election and decision phases. More specifically, The DiLCO protocol algorithm works as follow:
-Initially, the sensor node check it's remaining energy in order to participate in the current round. Each sensor node determines it's position and it's subregion based Embedded GPS or Location Discovery Algorithm. After that, All the sensors collect position coordinates, current remaining energy, sensor node id, and the number of its one-hop live neighbors during the information exchange. It stores this information into a list L.
-The sensor node enter in listening mode waiting to receive ActiveSleep packet from the leader to take the decision. Each sensor node will execute the Algorithm~1 to know who is the leader. After that, if the sensor node is leader, It will execute the integer program algorithm ( see section~\ref{cp}) to optimize the coverage and the lifetime in it's subregion. After the decision, the optimization approach will select the set of sensor nodes to take the mission of coverage during the sensing phase. The leader will send ActiveSleep packet to each sensor node in the subregion to inform him to it's status during the period of sensing, either Active or sleep until the starting of next round. Based on the decision, the leader as other nodes in subregion, either go to be active or go to be sleep during current sensing phase. the other nodes in the same subregion will stay in listening mode waiting the ActiveSleep packet from the leader. After finishing the time period for sensing, all the sensor nodes in the same subregion will start new round by executing the DiLCO protocol and the lifetime in the subregion will continue until all the sensor nodes are died or the network becomes disconnected in the subregion.
-\fi
-
-
\section{\uppercase{Coverage problem formulation}}
\label{cp}
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 rounds.
+most 20 periods.
In the simulations, we introduce the following performance metrics to evaluate
the efficiency of our approach:
%there are $51 \times 26~ = ~ 1326$ points in total.
% Therefore, for our simulations, the error in the coverage calculation is less than ~ 1 $\% $.
-\iffalse
-\item{{\bf Number of Active Sensors Ratio(ASR)}:} It is important to have as few active nodes as possible in each round,
-in order to minimize the communication overhead and maximize the
-network lifetime. The Active Sensors Ratio is defined as follows:
-\begin{equation*}
-\scriptsize
-\mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$A_r^t$}}{\mbox{$S$}} \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, $S$ is the total number of sensors in the network, and $R$ is the total number of the subregions in the network.
-
-\fi
\item {{\bf Energy Consumption}:} energy consumption (EC) can be seen as the
total amount of energy consumed by the sensors during $Lifetime_{95}$ or
by the whole network in the sensing phase (active and sleeping nodes).
-\iffalse
-\item {{\bf Execution Time}:} a sensor node has limited energy resources and
- computing power, therefore it is important that the proposed algorithm has the
- shortest possible execution time. The energy of a sensor node must be mainly
- used for the sensing phase, not for the pre-sensing ones.
-
-\item {{\bf Stopped simulation runs}:} A simulation ends when the sensor network
- becomes disconnected (some nodes are dead and are not able to send information
- to the base station). We report the number of simulations that are stopped due
- to network disconnections and for which round it occurs.
-\fi
\end{itemize}
%\end{enumerate}
\label{fig3}
\end{figure}
-%As shown in the figure ~\ref{fig3}, as the number of subregions increases, the coverage preservation for area of interest increases for a larger number of periods. Coverage ratio decreases when the number of periods increases due to dead nodes. Although some nodes are dead,
-%thanks to DiLCO-8, DiLCO-16 and DiLCO-32 protocols, other nodes are preserved to ensure the coverage. Moreover, when we have a dense sensor network, it leads to maintain the coverage for a larger number of rounds. DiLCO-8, DiLCO-16 and DiLCO-32 protocols are
-%slightly more efficient than other protocols, because they subdivides
-%the area of interest into 8, 16 and 32~subregions if one of the subregions becomes disconnected, the coverage may be still ensured in the remaining subregions.%
\subsubsection{Energy consumption}
the larger level of coverage ($95\%$) in the case of our protocol, the subdivision
in $16$~subregions seems to be the most appropriate.
-% with our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols
-% that leads to the larger lifetime improvement in comparison with other approaches. By choosing the best
-% suited nodes, for each round, to cover the area of interest and by
-% letting the other ones sleep in order to be used later in next rounds. Comparison shows that our DiLCO-16/50, DiLCO-32/50, DiLCO-16/95 and DiLCO-32/95 protocols, which are used distributed optimization over the subregions, are 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 protocol 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.
+
\section{\uppercase{Conclusion and future work}}
\label{sec:Conclusion and Future Works}
context a subdivision in $16$~subregions seems to be the most relevant. The
optimal number of subregions will be investigated in the future.
-\iffalse
-\noindent In this paper, we have addressed the problem of the coverage and the lifetime
-optimization in wireless sensor networks. This is a key issue as
-sensor nodes have limited resources in terms of memory, energy and
-computational power. To cope with this problem, the field of sensing
-is divided into smaller subregions using the concept of divide-and-conquer method, and then a DiLCO protocol for optimizing the coverage and lifetime performances in each subregion.
-The proposed protocol combines two efficient techniques: network
-leader election and sensor activity scheduling, where the challenges
-include how to select the most efficient leader in each subregion and
-the best representative active nodes that will optimize the network lifetime
-while taking the responsibility of covering the corresponding
-subregion. The network lifetime in each subregion is divided into
-rounds, each round consists of four phases: (i) Information Exchange,
-(ii) Leader Election, (iii) an optimization-based Decision in order to
-select the nodes remaining active for the last phase, and (iv)
-Sensing. The simulations show the relevance of the proposed DiLCO
-protocol in terms of lifetime, coverage ratio, active sensors ratio, energy consumption, execution time, and the number of stopped simulation runs due to network disconnection. Indeed, when
-dealing with large and dense wireless sensor networks, a distributed
-approach like the one we are proposed allows to reduce the difficulty of a
-single global optimization problem by partitioning it in many smaller
-problems, one per subregion, that can be solved more easily.
-
-In future work, we plan to study and propose a coverage optimization protocol, which
-computes all active sensor schedules in one time, using
-optimization methods. \iffalse The round will still consist of 4 phases, but the
- decision phase will compute the schedules for several sensing phases
- which, aggregated together, define a kind of meta-sensing phase.
-The computation of all cover sets in one time is far more
-difficult, but will reduce the communication overhead. \fi
-\fi
+
\section*{\uppercase{Acknowledgements}}
