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\begin{document}
applications. A sensor network is composed of a large number of tiny
sensing devices deployed in a region of interest. Each device has
processing and wireless communication capabilities, which enable it to
-sense its environment, to compute, to store information and to deliver
+sense its environment, to compute, to store information, and to deliver
report messages to a base station.
%These sensor nodes run on batteries with limited capacities. To achieve a long life of the network, it is important to conserve battery power. Therefore, lifetime optimisation is one of the most critical issues in wireless sensor networks.
One of the main design issues in Wireless Sensor Networks (WSNs) is to
prolong the network lifetime, while achieving acceptable quality of
service for applications. Indeed, sensor nodes have limited resources
-in terms of memory, energy and computational power.
+in terms of memory, energy, and computational power.
Since sensor nodes have limited battery life and without being able to
replace batteries, especially in remote and hostile environments, it
the scheduling strategy for energy-efficient coverage.
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 on
-OMNET++ \cite{varga}. They fully demonstrate the usefulness of 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}.
{\bf Activity scheduling}
-Activitiy scheduling is to schedule the activation and deactivation of
+Activity scheduling is to schedule the activation and deactivation of
sensor nodes. The basic objective is to decide which sensors are in
what states (active or sleeping mode) and for how long, so that the
application coverage requirement can be guaranteed and the network
work~\cite{Cardei:2005:IWS:1160086.1160098}. In~\cite{berman04}, the
authors have formulated the lifetime problem and suggested another
(LP) technique to solve this problem. A centralized solution based on the Garg-K\"{o}nemann
-algorithm~\cite{garg98}, probably near
+algorithm~\cite{garg98}, provably near
the optimal solution, is also proposed.
{\bf Our contribution}
decision is a good compromise between these two conflicting
objectives.
-\item {\bf Which node should make such a decision?} As mentioned in
+\item {\bf Which node should make such a decision?} As mentioned in
\cite{pc10}, both centralized and distributed algorithms have their
own advantages and disadvantages. Centralized coverage algorithms
have the advantage of requiring very low processing power from the
that there is a threshold in terms of network size to switch from a
localized to a centralized algorithm. Indeed the exchange of
messages in large networks may consume a considerable amount of
- energy in a localized approach compared to a centralized one. Our
+ energy in a centralized approach compared to a distributed one. Our
work does not consider only one leader to compute and to broadcast
- the scheduling decision to all the sensors. When the network size
- increases, the network is divided into many subregions and the
+ the scheduling decision to all the sensors. When the network size
+ increases, the network is divided into many subregions and the
decision is made by a leader in each subregion.
\end{itemize}
\subsection{Information exchange phase}
Each sensor node $j$ sends its position, remaining energy $RE_j$, and
-the number of local neighbors $NBR_j$ to all wireless sensor nodes in
+the number of local neighbours $NBR_j$ 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
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
+number of neighbours, larger remaining energy, and then in case of
equality, larger index.
\subsection{Decision phase}
sensing in the round (1 if yes and 0 if not);
\item $\Theta_{p}$ : {\it overcoverage}, the number of sensors minus
one that are covering the primary point $p$;
-\item $U_{p}$ : {\it undercoverage}, indicates whether or not the principal point
+\item $U_{p}$ : {\it undercoverage}, indicates whether or not the primary point
$p$ is being covered (1 if not covered and 0 if covered).
\end{itemize}
sleeping node will use 0.002 joules. Each sensor node will not
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 $w_{U}=|P^2|$.
+$R_s=5~m$, $w_{\Theta}=1$, and $w_{U}=|P^2|$.
We evaluate the efficiency of our approach by using some performance
metrics such as: coverage ratio, number of active nodes ratio, energy
\parskip 0pt
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.55]{TheCoverageRatio150.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.5]{TheCoverageRatio150g.eps} %\\~ ~ ~(a)
\caption{The impact of the number of rounds on the coverage ratio for 150 deployed nodes}
\label{fig3}
\end{figure}
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. This point is assessed through the Active Sensors
-Ratio, which is defined as follows:
+Ratio (ASR), which is defined as follows:
\begin{equation*}
\scriptsize
\mbox{ASR}(\%) = \frac{\mbox{Number of active sensors
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.55]{TheActiveSensorRatio150.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.5]{TheActiveSensorRatio150g.eps} %\\~ ~ ~(a)
\caption{The impact of the number of rounds on the active sensors ratio for 150 deployed nodes }
\label{fig4}
\end{figure}
\subsection{The impact of the number of rounds on the energy saving ratio}
In this experiment, we consider a performance metric linked to energy.
-This metric, called Energy Saving Ratio, is defined by:
+This metric, called Energy Saving Ratio (ESR), is defined by:
\begin{equation*}
\scriptsize
\mbox{ESR}(\%) = \frac{\mbox{Number of alive sensors during this round}}
%\centering
% \begin{multicols}{6}
\centering
-\includegraphics[scale=0.55]{TheEnergySavingRatio150.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.5]{TheEnergySavingRatio150g.eps} %\\~ ~ ~(a)
\caption{The impact of the number of rounds on the energy saving ratio for 150 deployed nodes}
\label{fig5}
\end{figure}
performing one, since it takes longer to have the two subregion networks
simultaneously disconnected.
-\subsection{The number of stopped simulation runs}
+\subsection{The percentage of stopped simulation runs}
-We will now study the number of simulations which stopped due to
+We will now study the percentage of simulations which stopped due to
network disconnections per round for each of the three approaches.
-Figure~\ref{fig6} illustrates the average number of stopped simulation
+Figure~\ref{fig6} illustrates the percentage of stopped simulation
runs per round for 150 deployed nodes. It can be observed that the
simple heuristic is the approach which stops first because the nodes
are randomly chosen. Among the two proposed strategies, the
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.55]{TheNumberofStoppedSimulationRuns150.eps}
-\caption{The number of stopped simulation runs compared to the number of rounds for 150 deployed nodes }
+\includegraphics[scale=0.5]{TheNumberofStoppedSimulationRuns150g.eps}
+\caption{The percentage of stopped simulation runs compared to the number of rounds for 150 deployed nodes }
\label{fig6}
\end{figure}
average number of rounds to define a metric allowing a fair comparison
between networks having different densities.
-Figure~\ref{fig7} illustrates the Energy Consumption for the different
+Figure~\ref{fig7} illustrates the energy consumption for the different
network sizes and the three approaches. The results show that the
strategy with two leaders is the most competitive from the energy
consumption point of view. A centralized method, like the strategy
\begin{figure}[h!]
\centering
-\includegraphics[scale=0.55]{TheEnergyConsumption.eps}
+\includegraphics[scale=0.5]{TheEnergyConsumptiong.eps}
\caption{The energy consumption}
\label{fig7}
\end{figure}
%\centering
% \begin{multicols}{6}
\centering
-\includegraphics[scale=0.5]{TheNetworkLifetime.eps} %\\~ ~ ~(a)
+\includegraphics[scale=0.5]{TheNetworkLifetimeg.eps} %\\~ ~ ~(a)
\caption{The network lifetime }
\label{fig8}
\end{figure}
independently and simultaneously, is the most relevant way to maximize
the lifetime of a network.
-\section{Conclusion and Future Works}
+\section{Conclusion and future works}
\label{sec:conclusion}
In this paper, we have addressed the problem of the coverage and the lifetime
problems, one per subregion, that can be solved more easily.
In future work, we plan to study and propose a coverage protocol which
-computes all active sensor schedules in a single round, using
+computes all active sensor schedules in one time, using
optimization methods such as swarms optimization or evolutionary
-algorithms. This single round will still consists of 4 phases, but the
+algorithms. 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 round is far more
+The computation of all cover sets in one time is far more
difficult, but will reduce the communication overhead.
-
% use section* for acknowledgement
%\section*{Acknowledgment}
