region) of interest to be monitored, while simultaneously preventing as much
as possible a network failure due to battery-depleted nodes. In this paper we
propose a protocol, called Distributed Lifetime Coverage Optimization protocol
- (DiLCO), which maintains the coverage and improves the lifetime of a wireless
+ (DiLCO), which maintains the coverage and improves the lifetime of a wireless
sensor network. First, we partition the area of interest into subregions using
a classical divide-and-conquer method. Our DiLCO protocol is then distributed
- on the sensor nodes in each subregion in a second step. To fulfill our
- objective, the proposed protocol combines two effective techniques: a leader
+ on the sensor nodes in each subregion in a second step. To fulfill our
+ objective, the proposed protocol combines two effective techniques: a leader
election in each subregion, followed by an optimization-based node activity
- scheduling performed by each elected leader. This two-step process takes
+ scheduling performed by each elected leader. This two-step process takes
place periodically, in order to choose a small set of nodes remaining active
for sensing during a time slot. Each set is built to ensure coverage at a low
- energy cost, allowing to optimize the network lifetime.
- %More precisely, a
- %period consists of four phases: (i)~Information Exchange, (ii)~Leader
- %Election, (iii)~Decision, and (iv)~Sensing.
- The decision process, which
+ energy cost, allowing to optimize the network lifetime. %More precisely, a
+ %period consists of four phases: (i)~Information Exchange, (ii)~Leader
+ %Election, (iii)~Decision, and (iv)~Sensing. The decision process, which
results in an activity scheduling vector, is carried out by a leader node
- through the solving of an integer program.
- {\color{red} Simulations are conducted using the discret event simulator OMNET++.
- We refer to the characterictics of a Medusa II sensor for the energy consumption and the time computation.
- In comparison with two other existing methods, our approach is able to increase the WSN lifetime and provides
- improved coverage performance. }}
-
+ through the solving of an integer program.
+% MODIF - BEGIN
+ Simulations are conducted using the discret event simulator
+ OMNET++. We refer to the characterictics of a Medusa II sensor for
+ the energy consumption and the computation time. In comparison with
+ two other existing methods, our approach is able to increase the WSN
+ lifetime and provides improved coverage performance. }
+% MODIF - END
\onecolumn \maketitle \normalsize \vfill
an integer program. The resulting activation vector is broadcast by a leader
to every node of its subregion.
-{\color{red} Our previous paper ~\cite{idrees2014coverage} relies almost exclusively on the framework of the DiLCO approach and the coverage problem formulation.
-In this paper we strengthen our simulations by taking into account the characteristics of a Medusa II sensor ~\cite{raghunathan2002energy} to measure the energy consumption and the computation time.
-We have implemented two other existing approaches (a distributed one DESK ~\cite{ChinhVu} and a centralized one GAF ~\cite{xu2001geography}) in order to compare their performances with our approach.
-We also focus on performance analysis based on the number of subregions. }
-
+% MODIF - BEGIN
+Our previous paper ~\cite{idrees2014coverage} relies almost exclusively on the
+framework of the DiLCO approach and the coverage problem formulation. In this
+paper we made more realistic simulations by taking into account the
+characteristics of a Medusa II sensor ~\cite{raghunathan2002energy} to measure
+the energy consumption and the computation time. We have implemented two other
+existing approaches (a distributed one, DESK ~\cite{ChinhVu}, and a centralized
+one called GAF ~\cite{xu2001geography}) in order to compare their performances
+with our approach. We also focus on performance analysis based on the number of
+subregions. }
+% MODIF - END
The remainder of the paper continues with Section~\ref{sec:Literature Review}
where a review of some related works is presented. The next section describes
\section{\uppercase{Coverage problem formulation}}
\label{cp}
-{\color{red}
+% MODIF - BEGIN
We formulate the coverage optimization problem with an integer program.
The objective function consists in minimizing the undercoverage and the overcoverage of the area as suggested in \cite{pedraza2006}.
-The area coverage problem is transformed to the coverage of a fraction of points called primary points.
+The area coverage problem is expressed as the coverage of a fraction of points called primary points.
Details on the choice and the number of primary points can be found in \cite{idrees2014coverage}. The set of primary points is denoted by $P$
and the set of sensors by $J$. As we consider a boolean disk coverage model, we use the boolean indicator $\alpha_{jp}$ which is equal to 1 if the primary point $p$ is in the sensing range of the sensor $j$. The binary variable $X_j$ represents the activation or not of the sensor $j$. So we can express the number of active sensors that cover the primary point $p$ by $\sum_{j \in J} \alpha_{jp} * X_{j}$. We deduce the overcoverage denoted by $\Theta_p$ of the primary point $p$ :
\begin{equation}
\end{array} \right.
\label{eq14}
\end{equation}
-There is, of course, a relationship between the three variables $X_j$, $\Theta_p$ and $U_p$ which can be formulated as follows :
+There is, of course, a relationship between the three variables $X_j$, $\Theta_p$, and $U_p$ which can be formulated as follows :
\begin{equation}
\sum_{j \in J} \alpha_{jp} X_{j} - \Theta_{p}+ U_{p} =1, \forall p \in P
\end{equation}
-If the point $p$ is not covered, $U_p=1$, $\sum_{j \in J} \alpha_{jp} X_{j}=0$ and $\Theta_{p}=0$ by defintion, so the equality is satisfied.
+If the point $p$ is not covered, $U_p=1$, $\sum_{j \in J} \alpha_{jp} X_{j}=0$ and $\Theta_{p}=0$ by definition, so the equality is satisfied.
On the contrary, if the point $p$ is covered, $U_p=0$, and $\Theta_{p}=\left( \sum_{j \in J} \alpha_{jp} X_{j} \right)- 1$.
\noindent Our coverage optimization problem can then be formulated as follows:
\begin{equation} \label{eq:ip2r}
The objective function is a weighted sum of overcoverage and undercoverage. The goal is to limit the overcoverage in order to activate a minimal number of sensors while simultaneously preventing undercoverage. Both weights $w_\theta$ and $w_U$ must be carefully chosen in
order to guarantee that the maximum number of points are covered during each
period.
-}
+% MODIF - END
