\label{ch6:sec:01}
The most important problem in a Wireless Sensor Network (WSN) is to optimize the
-use of its limited energy provision, so that it can fulfill its monitoring task
+use of its limited energy provision so that it can fulfill its monitoring task
as long as possible. Among known available approaches that can be used to
improve power management, lifetime coverage optimization provides activity
scheduling which ensures sensing coverage while minimizing the energy cost. In
\subsection{Assumptions and Models}
\label{ch6:sec:02:01}
-PeCO protocol uses the same assumptions and network model that presented in chapter 4, section \ref{ch4:sec:02:01}.
+The PeCO protocol uses the same assumptions and network model that presented in chapter 4, section \ref{ch4:sec:02:01}.
The PeCO protocol uses the same perimeter-coverage model as Huang and
Tseng in~\cite{ref133}. It can be expressed as follows: a sensor is
-said to be perimeter covered if all the points on its perimeter are covered by
+said to be a perimeter covered if all the points on its perimeter are covered by
at least one sensor other than itself. They proved that a network area is
$k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).
\end{table}
-In the PeCO protocol, the scheduling of the 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{ch6:sec:03}. Note that when a sensor
-node has a part of its sensing range outside the WSN sensing field, as in
-Figure~\ref{ex4pcm}, the maximum coverage level for this arc is set to $\infty$
-and the corresponding interval will not be taken into account by the
-optimization algorithm.
+In the PeCO protocol, the scheduling of the sensor nodes' activities is formulated as an integer program based on coverage intervals. The formulation of the coverage optimization problem is detailed in~section~\ref{ch6:sec:03}. Note that when a sensor node has a part of its sensing range outside the WSN sensing field, as in Figure~\ref{ex4pcm}, the maximum coverage level for this arc is set to $\infty$ and the corresponding interval will not be taken into account by the optimization algorithm.
\begin{figure}[h!]
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~\ref{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
-PeCO, are more robust against an unexpected node failure. On the one hand, if
-a node failure is discovered before taking the decision, the corresponding sensor
-node will not be considered by the optimization algorithm. 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.
+As shown in Figure~\ref{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 PeCO, are more robust against an unexpected node failure. On the one hand, if a node failure is discovered before taking the decision, the corresponding sensor
+node will not be considered by the optimization algorithm. 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
collect position coordinates, remaining energy, sensor node ID, and the number
of their 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 numbers of neighbors, larger remaining
+leader, in order of priority, are larger numbers 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.
lifetime, the objective is to activate a minimal number of sensors in each
period to ensure the desired coverage level. As the number of alive sensors
decreases, it becomes impossible to reach the desired level of coverage for all
-coverage intervals. Therefore we use variables $M^j_i$ and $V^j_i$ as a measure
+coverage intervals. Therefore, we use variables $M^j_i$ and $V^j_i$ as a measure
of the deviation between the desired number of active sensors in a coverage
interval and the effective number. And we try to minimize these deviations,
first to force the activation of a minimal number of sensors to ensure the
desired coverage level, and if the desired level cannot be completely satisfied,
to reach a coverage level as close as possible to the desired one.
-
Our coverage optimization problem can then be mathematically expressed as follows:
%Objective:
\begin{equation} %\label{eq:ip2r}
relative importance of satisfying the associated level of coverage. For example,
weights associated with coverage intervals of a specified part of a region may
be given by a relatively larger magnitude than weights associated with another
-region. This kind of integer program is inspired from the model developed for
+region. This kind of an integer program is inspired from the model developed for
brachytherapy treatment planning for optimizing dose distribution
\cite{0031-9155-44-1-012}. The integer program must be solved by the leader in
each subregion at the beginning of each sensing phase, whenever the environment
