Instead of working with a continuous coverage area, we make it discrete by
considering for each sensor a set of points called primary points. Consequently,
we assume that the sensing disk defined by a sensor is covered if all of its
-primary points are covered. The choice of number and locations of primary points
-is the subject of another study not presented here.
+primary points are covered. The choice of number and locations of primary points is the subject of another study not presented here.
%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
$E_{R}$ & 36 Joules\\
$R_s$ & 5~m \\
%\hline
-$W_{\Theta}$ & 1 \\
+$W_{\theta}$ & 1 \\
% [1ex] adds vertical space
%\hline
$W_{U}$ & $|P|^2$
message is obtained by using the equation in ~\cite{raghunathan2002energy} to
calculate the energy cost for transmitting messages and we propose the same
value for receiving the packets. The energy needed to send or receive a 1-bit
-packet is equal to $0.2575~mW$.
+packet is equal to 0.2575~mW.
The initial energy of each node is randomly set in the interval $[500;700]$. A
sensor node will not participate in the next round if its remaining energy is
% New version with global loops on period
\begin{equation*}
\scriptsize
- \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left[ \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T_m} \left( E^{a}_t+E^{s}_t \right) \right]}{\sum\limits_{m=1}^{M_L} T_m},
+ \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left[ \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T_m} \left( E^{a}_t+E^{s}_t \right) \right]}{\sum\limits_{m=1}^{M} T_m},
\end{equation*}
\end{enumerate}
-\section{Results and analysis}
+\subsection{Results and analysis}
-\subsection{Coverage ratio}
+\subsubsection{Coverage ratio}
Figure~\ref{fig3} shows the average coverage ratio for 150 deployed nodes. We
can notice that for the first thirty rounds both DESK and GAF provide a coverage
\label{fig3}
\end{figure}
-\subsection{Active sensors ratio}
+\subsubsection{Active sensors ratio}
It is crucial to have as few active nodes as possible in each round, in order to
minimize the communication overhead and maximize the network
\label{fig4}
\end{figure}
-\subsection{Stopped simulation runs}
+\subsubsection{Stopped simulation runs}
%The results presented in this experiment, is to show the comparison of our MuDiLCO protocol with other two approaches from the point of view the stopped simulation runs per round. Figure~\ref{fig6} illustrates the percentage of stopped simulation
%runs per round for 150 deployed nodes.
\label{fig6}
\end{figure}
-\subsection{Energy consumption} \label{subsec:EC}
+\subsubsection{Energy consumption} \label{subsec:EC}
We measure the energy consumed by the sensors during the communication,
listening, computation, active, and sleep status for different network densities
%In fact, a distributed optimization decision, which produces T rounds, on the subregions is greatly reduced the cost of communications and the time of listening as well as the energy needed for sensing phase and computation so thanks to the partitioning of the initial network into several independent subnetworks and producing T rounds for each subregion periodically.
-\subsection{Execution time}
+\subsubsection{Execution time}
We observe the impact of the network size and of the number of rounds on the
computation time. Figure~\ref{fig77} gives the average execution times in
-seconds (needed to solve optimization problem) for different values of $T$. The
+seconds (needed to solve optimization problem) for different values of $T$. The modeling language for Mathematical Programming (AMPL)~\cite{AMPL} is employed to generate the Mixed Integer Linear Program instance in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method. The
original execution time is computed on a laptop DELL with Intel Core~i3~2370~M
(2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second)
rate equal to 35330. To be consistent with the use of a sensor node with Atmels
%While MuDiLCO-1, 3, and 5 solves the optimization process with suitable execution times to be used on wireless sensor network because it distributed on larger number of small subregions as well as it is used acceptable number of round(s) T. We think that in distributed fashion the solving of the optimization problem to produce T rounds in a subregion can be tackled by sensor nodes. Overall, to be able to deal with very large networks, a distributed method is clearly required.
-\subsection{Network lifetime}
+\subsubsection{Network lifetime}
The next two figures, Figures~\ref{fig8}(a) and \ref{fig8}(b), illustrate the
network lifetime for different network sizes, respectively for $Lifetime_{95}$
The activity scheduling in each subregion works in periods, where each period
consists of four phases: (i) Information Exchange, (ii) Leader Election, (iii)
Decision Phase to plan the activity of the sensors over $T$ rounds, (iv) Sensing
-Phase itself divided into T rounds.
+Phase itself divided into $T$ rounds.
Simulations results show the relevance of the proposed protocol in terms of
lifetime, coverage ratio, active sensors ratio, energy consumption, execution
--- /dev/null
+\documentclass[14]{article}
+
+\usepackage{color}
+\usepackage{times}
+\usepackage{titlesec}
+\usepackage{pifont}
+%\usepackage[T1]{fontenc}
+%\usepackage[latin1]{inputenc}
+
+\renewcommand{\labelenumii}{\labelenumi\arabic{enumii}}
+%\titleformat*{\section}{\Large\bfseries}
+
+%\title{Response to the reviewers of \bf "Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks"}
+%\author{Ali Kadhum Idrees, Karine Deschinkela, Michel Salomon and Raphael Couturier}
+
+\begin{document}
+
+\begin{flushright}
+\today
+\end{flushright}%
+
+\vspace{-0.5cm}\hspace{-2cm}FEMTO-ST Institute, UMR 6714 CNRS
+
+\hspace{-2cm}University Bourgogne Franche-Comt\'e
+
+\hspace{-2cm}IUT Belfort-Montb\'eliard, BP 527, 90016 Belfort Cedex, France.
+
+\bigskip
+
+\begin{center}
+Detailed changes and addressed issues in the revision of the article
+
+``Multiround Distributed Lifetime Coverage Optimization \\
+ Protocol in Wireless Sensor Networks''\\
+
+
+by Ali Kadhum Idrees, Karine Deschinkel, Michel Salomon, and Raph\"ael Couturier
+
+\medskip
+
+\end{center}
+Dear Editor and Reviewers,
+
+First of all, we would like to thank you very much for your kind help to improve
+our article named: `` Multiround Distributed Lifetime Coverage Optimization
+Protocol in Wireless Sensor Networks
+''. We highly appreciate the detailed valuable
+comments of the reviewers on our article. The suggestions are quite helpful for
+us and we incorporate them in the revised article. We are happy to submit to you
+a revised version that considers most of your remarks and suggestions to improve
+the quality of our article.
+
+As below, we would like to clarify some of the points raised by the reviewers
+and we hope the reviewers and the editors will be satisfied by our responses to
+the comments and the revision for the original manuscript.
+
+
+
+\section*{Response to Reviewer No. 1 Comments}
+
+The paper entitled "Multiround Distributed Lifetime Coverage Optimization
+Protocol in Wireless Sensor Networks" introduces MuDiLCO, a distributed protocol
+to enhance the use of WSN by splitting the network lifetime into periods, and by
+breaking each sensing activity of a period into a series of rounds. A sensor
+called the leader is elected, and based on local data, solves a Mixed Integer
+Linear Program in order to schedule the activity of its neighbors over the
+sensing rounds of the current period.
+
+The contribution of this paper is interesting, but probably needs to be deepened
+in order to reach the standards of a publication in Ad Hoc Networks.\\
+
+
+\noindent\textcolor{black}{\textbf{MAJOR COMMENTS:}} \\
+
+\noindent {\bf 1.} Page 6, Section 3.2
+The author didn't explain how subregions are created. This is an important
+point, as clustering may have a significant impact on solution quality. Not only
+the size of the subregion should be discussed and analyzed, but also the
+clustering strategy.\\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} }}\\
+
+
+\noindent {\bf 2.} Page 8
+The objective function (5) of the Mixed Integer Linear Program appears to be
+very questionable. Indeed overcoverage and undercoverage may compensate each
+other, so the same objective value may represent two incomparable situations. It
+seems that the semantic of the objective function is not well defined, as one
+may wonder what exactly is (quantitatively speaking) the problem objective.
+Coverage breach is obviously an issue in WSN, but why penalizing overcoverage? A
+two-phase approach where breach is minimized first, and then overcoverage is
+minimized would probably make more sense.
+ \\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} }}\\
+
+
+
+\noindent {\bf 3.} Page 9
+In the MILP formulation, it is possible that some point p is never covered at
+all, which means that some part of the area to monitor may never be monitored by
+the WSN. The authors are referred to "alpha-coverage to extend network lifetime
+on wireless sensor networks", Optim. Lett. 7, No. 1, 157-172 (2013) by Gentilli
+et al to enforce a constraint on the minimum coverage of each point. \\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} }}\\
+
+
+\noindent {\bf 4.} Page 13
+The criterion "Energy Consumption" is the average consumption per round. But the
+duration of a round is a feature that can be arbitrarily set in the algorithm.
+Computing the average energy consumption per unit of time over the network
+lifetime would be better, as it is independent from the number and duration of
+rounds. \\
+
+\textcolor{blue}{\textbf{\textsc{Answer :} }}
+
+
+
+\noindent {\bf 5.} Page 15-18
+Figures 2-6 mention four different versions of MuDiLCO. The performance of these
+different versions should be analyzed with more details for each figure.
+Alternatively, the authors may remove some versions of MuDiLCO if they do not
+bring any valuable insight. \\
+
+
+\textcolor{blue}{\textbf{\textsc{Answer :} }}
+
+
+\noindent {\bf 6.} Page 19 (most major point)
+The authors state that solving the Mixed Integer Linear Program is
+time-consuming, and use this point for explaining why MuDiLCO-7 is not as
+efficient as other versions. Why not using a heuristic (or a metaheuristic) for
+addressing the problem instead of using an exact solver? A straightforward and
+easily implementable idea to cut CPU time would be to return the best feasible
+solution found by the solver after a given time threshold for example. Doing so
+is very likely to save time and energy, and to improve the results of MuDiLCO-7
+in particular. \\
+
+
+\textcolor{blue}{\textbf{\textsc{Answer :} }}
+
+
+\bigskip
+
+\noindent\textcolor{black}{\textbf{MINOR COMMENTS:}} \\
+
+\noindent {\ding{90} Page 2
+The paragraph that begins with "The remainder of the paper is organized as
+follows" should mention the content of Section 5. } \\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed. Section 5 is included as a subsection 4.4 within section 4. }}\\
+
+\noindent {\ding{90} Page 3
+The sentence "the centralized approaches usually suffer from the scalability
+problem, making them less competitive as the network size increase" should
+probably be tempered: heuristics and metaheuristics can handle very large and
+centralized problems (even if exact approaches can't), and these approaches are
+very popular in WSN. } \\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} }}\\
+
+\noindent {\ding{90} Page 5
+"The choice of number and locations of primary points is the subject of another
+study not presented here". The authors should provide at least one reference
+about the aforementioned study. } \\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} }}\\
+
+\noindent {\ding{90} Page 6, Figure 1:
+All rounds seem to have the same duration. This should be stated explicitly, and
+justified (in column generation based approaches, "rounds" to not have the same
+duration). } \\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} }}\\
+
+\noindent {\ding{90} Page 11 in Table 1
+$W_\Theta$ should be replaced with $W_\theta$
+ } \\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
+
+\noindent {\ding{90} Page 12
+Don't italicize "mW" in "equal to 02575 mW" } \\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
+
+\noindent {\ding{90} Page 14
+ML is not defined (see the denominator of the large, unnumbered formula that
+defines EC). } \\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
+
+\noindent {\ding{90} Page 19 Section 6
+
+"Sensing phase itself divided into T rounds" -> T should be italic. }
+\\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
+
+\noindent {\ding{90} Page 18 Section 5.5
+The name of the solver used to solve the Mixed Integer Linear Program should be
+given. } \\
+
+\textcolor{blue}{\textbf{\textsc{Answer:} Right, fixed }}.\\
+
+
+We are very grateful to the reviewers who, by their recommendations, allowed us
+to improve the quality of our article.
+\begin{flushright}
+Best regards\\
+The authors
+\end{flushright}
+
+
+
+\end{document}
