distributed among sensor nodes in each subregion. A sensor node which runs LiCO
protocol repeats periodically four stages: information exchange, leader
election, optimization decision, and sensing. More precisely, the scheduling of
-nodes activities (sleep/wake up duty cycles) is achieved in each subregion by a
+nodes' activities (sleep/wake up duty cycles) is achieved in each subregion by a
leader selected after cooperation between nodes within the same subregion. The
novelty of approach lies essentially in the formulation of a new mathematical
-optimization model based on perimeter coverage level to schedule sensors
+optimization model based on perimeter coverage level to schedule sensors'
activities. Extensive simulation experiments have been performed using OMNeT++,
the discrete event simulator, to demonstrate that LiCO is capable to offer
longer lifetime coverage for WSNs in comparison with some other protocols.
networks of tiny sensors, called Wireless Sensor Networks
(WSN)~\cite{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring
tasks. A WSN consists of small low-powered sensors working together by
-communicating with one another through multihop radio communications. Each node
+communicating with one another through multi-hop radio communications. Each node
can send the data it collects in its environment, thanks to its sensor, to the
user by means of sink nodes. The features of a WSN made it suitable for a wide
range of application in areas such as business, environment, health, industry,
temporal subdivision. On the one hand the area of interest if divided into
several smaller subregions and on the other hand the time line is divided into
periods of equal length. In each subregion the sensor nodes will cooperatively
- choose a leader which will schedule nodes activities, and this grouping of
+ choose a leader which will schedule nodes' activities, and this grouping of
sensors is similar to typical cluster architecture.
\item We propose a new mathematical optimization model. Instead of trying to
cover a set of specified points/targets as in most of the methods proposed in
provide nearly or close to optimal solution since the algorithm has a global
view of the whole network. The disadvantage of a centralized method is obviously
its high cost in communications needed to transmit to a single node, the base
-station which will globally schedule nodes activities, data from all the other
+station which will globally schedule nodes' activities, data from all the other
sensor nodes in the area. The price in communications can be very huge since
long range communications will be needed. In fact the larger the WNS, the higher
the communication and thus energy cost. {\it In order to be suitable for
\caption{Coverage intervals and contributing sensors for sensor node 0.}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
-\begin{tabular}[c]{@{}c@{}}The angle \\ $\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Segment \\ Left (L) or\\ Right (R)\end{tabular} & \begin{tabular}[c]{@{}c@{}}Sensor \\ Node Id\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ Coverage\\ Level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}The Set of Sensors\\ Involved in Interval \\ Coverage\end{tabular}} \\ \hline
-0.0291 & L & 1 & 4 & 0 & 1 & 3 & 4 & \\ \hline
-0.104 & L & 2 & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline
-0.3168 & R & 3 & 4 & 0 & 1 & 4 & 2 & \\ \hline
-0.6752 & R & 4 & 3 & 0 & 1 & 2 & & \\ \hline
-1.8127 & R & 1 & 2 & 0 & 2 & & & \\ \hline
-1.9228 & L & 5 & 3 & 0 & 2 & 5 & & \\ \hline
-2.3959 & L & 6 & 4 & 0 & 2 & 5 & 6 & \\ \hline
-2.4258 & R & 2 & 3 & 0 & 5 & 6 & & \\ \hline
-2.7868 & L & 7 & 4 & 0 & 5 & 6 & 7 & \\ \hline
-2.8358 & L & 8 & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline
-2.9184 & R & 5 & 4 & 0 & 6 & 7 & 8 & \\ \hline
-3.3301 & R & 7 & 3 & 0 & 6 & 8 & & \\ \hline
-3.9464 & L & 9 & 4 & 0 & 6 & 8 & 9 & \\ \hline
-4.767 & R & 6 & 3 & 0 & 8 & 9 & & \\ \hline
-4.8425 & L & 3 & 4 & 0 & 3 & 8 & 9 & \\ \hline
-4.9072 & R & 8 & 3 & 0 & 3 & 9 & & \\ \hline
-5.3804 & L & 4 & 4 & 0 & 3 & 4 & 9 & \\ \hline
-5.9157 & R & 9 & 3 & 0 & 3 & 4 & & \\ \hline
+\begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\ level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in interval coverage\end{tabular}} \\ \hline
+0.0291 & 1L & 2L & 4 & 0 & 1 & 3 & 4 & \\ \hline
+0.104 & 2L & 3R & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline
+0.3168 & 3R & 4R & 4 & 0 & 1 & 4 & 2 & \\ \hline
+0.6752 & 4R & 1R & 3 & 0 & 1 & 2 & & \\ \hline
+1.8127 & 1R & 5L & 2 & 0 & 2 & & & \\ \hline
+1.9228 & 5L & 6L & 3 & 0 & 2 & 5 & & \\ \hline
+2.3959 & 6L & 2R & 4 & 0 & 2 & 5 & 6 & \\ \hline
+2.4258 & 2R & 7L & 3 & 0 & 5 & 6 & & \\ \hline
+2.7868 & 7L & 8L & 4 & 0 & 5 & 6 & 7 & \\ \hline
+2.8358 & 8L & 5R & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline
+2.9184 & 5R & 7R & 4 & 0 & 6 & 7 & 8 & \\ \hline
+3.3301 & 7R & 9R & 3 & 0 & 6 & 8 & & \\ \hline
+3.9464 & 9R & 6R & 4 & 0 & 6 & 8 & 9 & \\ \hline
+4.767 & 6R & 3L & 3 & 0 & 8 & 9 & & \\ \hline
+4.8425 & 3L & 8R & 4 & 0 & 3 & 8 & 9 & \\ \hline
+4.9072 & 8R & 4L & 3 & 0 & 3 & 9 & & \\ \hline
+5.3804 & 4L & 9R & 4 & 0 & 3 & 4 & 9 & \\ \hline
+5.9157 & 9R & 1L & 3 & 0 & 3 & 4 & & \\ \hline
\end{tabular}
\label{my-label}
%The optimization algorithm that used by LiCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1.
-In LiCO protocol, scheduling of sensor nodes activities is formulated with an
+In LiCO protocol, scheduling of sensor nodes' activities is formulated with an
integer program based on coverage intervals. The formulation of the coverage
optimization problem is detailed in~section~\ref{cp}. Note that when a sensor
node has a part of its sensing range outside the WSN sensing field, as in
%\label{ex5pcm}
%\end{figure}
-% MICHEL TO BE CONTINUED FROM HERE
-
\subsection{The Main Idea}
-\noindent The area of interest can be divided into smaller areas called subregions and
-then our protocol will be implemented in each subregion simultaneously. LiCO protocol works into periods fashion as shown in figure~\ref{fig2}.
-\begin{figure}[ht!]
+
+\noindent The WSN area of interest is, in a first step, divided into regular
+homogeneous subregions using a divide-and-conquer algorithm. In a second step
+our protocol will be executed in a distributed way in each subregion
+simultaneously to schedule nodes' activities for one sensing period.
+
+As shown in figure~\label{fig2}, node activity scheduling is produced by our
+protocol in a periodic manner. Each period is divided into 4 stages: Information
+(INFO) Exchange, Leader Election, Decision (the result of an optimization
+problem), and Sensing. For each period there is exactly one set cover
+responsible for the sensing task. Protocols based on a periodic scheme, like
+LiCO, are more robust against an unexpected node failure. On the one hand, if
+node failure is discovered before taking the decision, the corresponding sensor
+node will not be considered by the optimization algorithm, and, on the other
+hand, if the sensor failure happens after the decision, the sensing task of the
+network will be temporarily affected: only during the period of sensing until a
+new period starts, since a new set cover will take charge of the sensing task in
+the next period. 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 (INFO Exchange, Leader Election, and Decision)
+are energy consuming, even for nodes that will not join the set cover to monitor
+the area.
+
+\begin{figure}[t!]
\centering
-\includegraphics[width=85mm]{Model.pdf}
+\includegraphics[width=80mm]{Model.pdf}
\caption{LiCO protocol}
\label{fig2}
\end{figure}
-Each period is divided into 4 stages: Information (INFO) Exchange, Leader Election, Optimization Decision, and Sensing. For each period there is exactly one set cover responsible for the sensing task. LiCO is more powerful against an unexpected node failure because it works in periods. On the one hand, if the node failure is discovered before taking the decision of the optimization algorithm, the sensor node would not involved to current stage, and, on the other hand, if the sensor failure takes place after the decision, the sensing task of the network will be temporarily affected: only during the period of sensing until a new period starts, since a new set cover will take charge of the sensing task in the next period. 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 (INFO Exchange, Leader Election, and Decision) are energy consuming for some sensor nodes, even when they do not join the network to monitor the area.
-
-We define two types of packets to be used by LiCO protocol.
+We define two types of packets to be used by LiCO protocol:
%\begin{enumerate}[(a)]
\begin{itemize}
-\item INFO packet: sent by each sensor node to all the nodes inside a same subregion for information exchange.
-\item ActiveSleep packet: sent by the leader to all the nodes in its subregion to inform them to be Active or Sleep during the sensing phase.
+\item INFO packet: sent by each sensor node to all the nodes inside a same
+ subregion for information exchange.
+\item ActiveSleep packet: sent by the leader to all the nodes in its subregion
+ to transmit to them their respective status (stay Active or go Sleep) during
+ sensing phase.
\end{itemize}
%\end{enumerate}
-There are five status for each sensor node in the network :
+Five status are possible for a sensor node in the network:
%\begin{enumerate}[(a)]
\begin{itemize}
-\item LISTENING: Sensor is waiting for a decision (to be active or not)
-\item COMPUTATION: Sensor applies the optimization process as leader
-\item ACTIVE: Sensor is active
-\item SLEEP: Sensor is turned off
-\item COMMUNICATION: Sensor is transmitting or receiving packet
+\item LISTENING: waits for a decision (to be active or not);
+\item COMPUTATION: executes the optimization algorithm as leader to
+ determine the activities scheduling;
+\item ACTIVE: node is sensing;
+\item SLEEP: node is turned off;
+\item COMMUNICATION: transmits or recevives packets.
\end{itemize}
%\end{enumerate}
%Below, we describe each phase in more details.
\subsection{LiCO Protocol Algorithm}
-The pseudo-code for LiCO Protocol is illustrated as follows:
+The pseudocode implementing the protocol on a node is given below. More
+precisely, Algorithm~\label{alg:LiCO} gives a brief description of the protocol
+applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
\begin{algorithm}[h!]
% \KwIn{all the parameters related to information exchange}
\If{ $RE_k \geq E_{th}$ }{
\emph{$s_k.status$ = COMMUNICATION}\;
- \emph{Send $INFO()$ packet to other nodes in the subregion}\;
- \emph{Wait $INFO()$ packet from other nodes in the subregion}\;
+ \emph{Send $INFO()$ packet to other nodes in subregion}\;
+ \emph{Wait $INFO()$ packet from other nodes in subregion}\;
\emph{Update K.CurrentSize}\;
\emph{LeaderID = Leader election}\;
\If{$ s_k.ID = LeaderID $}{
% \emph{ Determine the segment points using perimeter coverage model}\;
}
- \If{$ (s_k.ID $ is the same Previous Leader) AND (K.CurrentSize = K.PreviousSize)}{
+ \If{$ (s_k.ID $ is the same Previous Leader) And (K.CurrentSize = K.PreviousSize)}{
\emph{ Use the same previous cover set for current sensing stage}\;
}
\Else{
- \emph{ Update $a^j_{ik}$ and prepare data to Algorithm}\;
+ \emph{Update $a^j_{ik}$; prepare data for IP~Algorithm}\;
\emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$)}\;
\emph{K.PreviousSize = K.CurrentSize}\;
}
\end{algorithm}
-\noindent Algorithm 1 gives a brief description of the protocol applied by each sensor node (denoted by $s_k$ for a sensor node indexed by $k$). In this algorithm, the K.CurrentSize and K.PreviousSize refer to the current size and the previous size of sensor nodes still alive in the subregion respectively.
-Initially, the sensor node checks its remaining energy $RE_k$, which must be greater than a threshold $E_{th}$ in order to participate in the current period. Each sensor node determines its position and its subregion based Embedded GPS or Location Discovery Algorithm. After that, all the sensors collect position coordinates, remaining energy, sensor node id, and the number of its one-hop live neighbors during the information exchange. The sensors inside a same region cooperate to elect a leader. The selection criteria for the leader in order of priority are: larger number of neighbors, larger remaining energy, and then in case of equality, larger index. Thereafter the leader collects information to formulate and solve the integer program which allows to construct the set of active sensors in the sensing stage.
-
+\noindent In this algorithm, K.CurrentSize and K.PreviousSize refer to the
+current size and the previous size of the subnetwork in the subregion
+respectively. That means the number of sensor nodes which are still
+alive. Initially, the sensor node checks its remaining energy $RE_k$, which must
+be greater than a threshold $E_{th}$ in order to participate in the current
+period. Each sensor node determines its position and its subregion using an
+embedded GPS or a location discovery algorithm. After that, all the sensors
+collect position coordinates, remaining energy, sensor node ID, and the number
+of its one-hop live neighbors during the information exchange. The sensors
+inside a same region cooperate to elect a leader. The selection criteria for the
+leader, in order of priority, are: larger number of neighbors, larger remaining
+energy, and then in case of equality, larger index. Once chosen, the leader
+collects information to formulate and solve the integer program which allows to
+construct the set of active sensors in the sensing stage.
%After the cooperation among the sensor nodes in the same subregion, the leader will be elected in distributed way, where each sensor node and based on it's information decide who is the leader. The selection criteria for the leader in order of priority are: larger number of neighbors, larger remaining energy, and then in case of equality, larger index. Thereafter, if the sensor node is leader, it will execute the perimeter-coverage model for each sensor in the subregion in order to determine the segment points which would be used in the next stage by the optimization algorithm of the LiCO protocol. Every sensor node is selected as a leader, it is executed the perimeter coverage model only one time during it's life in the network.
% The leader has the responsibility of applying the integer program algorithm (see section~\ref{cp}), which provides a set of sensors planned to be active in the sensing stage. As leader, it will send an Active-Sleep packet to each sensor in the same subregion to inform it if it has to be active or not. On the contrary, if the sensor is not the leader, it will wait for the Active-Sleep packet to know its state for the sensing stage.
+% MICHEL TO BE CONTINUED
\section{Lifetime Coverage problem formulation}
+
\label{cp}
In this section, the coverage model is mathematically formulated.
For convenience, the notations are described first.
\noindent $I_j :$ the set of coverage intervals (CI) for sensor $j$.\\
\noindent $I_j$ refers to the set of intervals which have been defined for each sensor $j$ in section~\ref{sec:The LiCO Protocol Description}.
\noindent For a coverage interval $i$, let $a^j_{ik}$ denote the indicator function of whether the sensor $k$ is involved in the coverage interval $i$ of sensor $j$, that is:
-
\begin{equation}
a^j_{ik} = \left \{
\begin{array}{lll}
-\noindent Our coverage optimization problem can be mathematically formulated as follows: \\
+\noindent Our coverage optimization problem can be mathematically formulated as follows:
%Objective:
-
\begin{equation} \label{eq:ip2r}
\left \{
\begin{array}{ll}
\section{\uppercase{Conclusion and Future Works}}
\label{sec:Conclusion and Future Works}
In this paper we have studied the problem of lifetime coverage optimization in
-WSNs. We designed a protocol LiCO that schedules node activities (wakeup and sleep) with the objective of maintaining a good coverage ratio while maximizing the network lifetime. This protocol is applied on each subregion of the area of interest. It works in periods and is based on the resolution of an integer program to select the subset of sensors operating in active mode for each period. Our work is original in so far as it proposes for the first time an integer program scheduling the activation of sensors based on their perimeter coverage level instead of using a set of targets/points to be covered.
+WSNs. We designed a protocol LiCO that schedules node' activities (wakeup and sleep) with the objective of maintaining a good coverage ratio while maximizing the network lifetime. This protocol is applied on each subregion of the area of interest. It works in periods and is based on the resolution of an integer program to select the subset of sensors operating in active mode for each period. Our work is original in so far as it proposes for the first time an integer program scheduling the activation of sensors based on their perimeter coverage level instead of using a set of targets/points to be covered.
