From 3b6e0c9402cf8ca8e7daec7f4520685de215e5df Mon Sep 17 00:00:00 2001 From: Karine Deschinkel Date: Thu, 25 Jun 2015 16:18:04 +0200 Subject: [PATCH 1/1] beautiful changes --- PeCO-EO/articleeo.aux | 22 +- PeCO-EO/articleeo.log | 265 +++++----- PeCO-EO/articleeo.pdf | Bin 745343 -> 746264 bytes PeCO-EO/articleeo.tex | 14 +- PeCO-EO/articleeo.tex~ | 1043 ++++++++++++++++++++++------------------ PeCO-EO/reponse.tex | 32 +- 6 files changed, 759 insertions(+), 617 deletions(-) diff --git a/PeCO-EO/articleeo.aux b/PeCO-EO/articleeo.aux index 352fa9e..0d52726 100644 --- a/PeCO-EO/articleeo.aux +++ b/PeCO-EO/articleeo.aux @@ -58,24 +58,23 @@ \citation{ChinhVu} \citation{AMPL} \citation{glpk} +\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Simulation Results}{12}} +\newlabel{tab:EC}{{3}{12}} \citation{ChinhVu} \citation{xu2001geography} \citation{Idrees2} \citation{idrees2014coverage} -\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Simulation Results}{12}} -\newlabel{tab:EC}{{3}{12}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.1}Coverage Ratio}{13}} \newlabel{figure5}{{5}{13}} -\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.2}Active Sensors Ratio}{13}} -\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.3}Energy Consumption}{13}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.2}Active Sensors Ratio}{14}} \newlabel{figure6}{{6}{14}} -\newlabel{figure7}{{7}{14}} -\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.4}Network Lifetime}{15}} -\newlabel{figure8}{{8}{15}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.3}Energy Consumption}{14}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.4}Network Lifetime}{14}} +\newlabel{figure7}{{7}{15}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.5}Impact of $\alpha $ and $\beta $ on PeCO's performance}{15}} +\newlabel{sec:Impact}{{5.2.5}{15}} +\newlabel{figure8}{{8}{16}} \newlabel{figure9}{{9}{16}} -\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.5}Impact of $\alpha $ and $\beta $ on PeCO's performance}{16}} -\newlabel{sec:Impact}{{5.2.5}{16}} -\newlabel{my-labelx}{{4}{16}} \@writefile{toc}{\contentsline {section}{\numberline {6}Conclusion and Future Works}{16}} \newlabel{sec:Conclusion and Future Works}{{6}{16}} \bibstyle{gENO} @@ -85,6 +84,8 @@ \bibcite{berman04}{{3}{2004}{{Berman and Calinescu}}{{}}} \bibcite{cardei2005improving}{{4}{2005}{{Cardei and Du}}{{}}} \bibcite{cardei2005energy}{{5}{2005}{{Cardei et~al.}}{{Cardei, Thai, Li, and Wu}}} +\newlabel{my-labelx}{{4}{17}} +\@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Acknowledgements}{17}} \bibcite{castano2013column}{{6}{2014}{{Casta{\~n}o et~al.}}{{Casta{\~n}o, Rossi, Sevaux, and Velasco}}} \bibcite{Deng2012}{{7}{2012}{{Deng, Jiguo~Yu, and Chen}}{{}}} \bibcite{deschinkel2012column}{{8}{2012}{{Deschinkel}}{{}}} @@ -92,7 +93,6 @@ \bibcite{HeShibo}{{10}{2014}{{He et~al.}}{{He, Gong, Zhang, Chen, and Sun}}} \bibcite{Huang:2003:CPW:941350.941367}{{11}{2005{a}}{{Huang and Tseng}}{{}}} \bibcite{huang2005coverage}{{12}{2005{b}}{{Huang and Tseng}}{{}}} -\@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Acknowledgements}{17}} \bibcite{doi:10.1155/2010/926075}{{13}{2010}{{Hung and Lui}}{{}}} \bibcite{idrees2014coverage}{{14}{2014}{{Idrees et~al.}}{{Idrees, Deschinkel, Salomon, and Couturier}}} \bibcite{Idrees2}{{15}{2015}{{Idrees et~al.}}{{Idrees, Deschinkel, Salomon, and Couturier}}} diff --git a/PeCO-EO/articleeo.log b/PeCO-EO/articleeo.log index 805d083..9dbac05 100644 --- a/PeCO-EO/articleeo.log +++ b/PeCO-EO/articleeo.log @@ -1,11 +1,12 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2015/dev/Debian) (preloaded format=pdflatex 2015.1.24) 25 JUN 2015 14:39 +This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/Debian) (format=pdflatex 2013.9.3) 25 JUN 2015 16:12 entering extended mode restricted \write18 enabled. %&-line parsing enabled. **articleeo.tex (./articleeo.tex -LaTeX2e <2014/05/01> -Babel <3.9l> and hyphenation patterns for 61 languages loaded. +LaTeX2e <2011/06/27> +Babel and hyphenation patterns for english, dumylang, nohyphenation, lo +aded. 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On & 9.72 \\ + SLEEP & Off & Off & Off & 0.02 \\ + COMPUTATION & On & On & On & 26.83 \\ + \hline + \multicolumn{4}{|l}{Energy needed to send or receive a 2-bit content message} & 0.515 \\ + \hline +\end{tabular} +\end{table} + +The modeling language for Mathematical Programming (AMPL)~\citep{AMPL} is used +to generate the integer 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) \citep{glpk} through a Branch-and-Bound method. + +% No discussion about the execution of GLPK on a sensor ? + +Besides PeCO, three other protocols will be evaluated for comparison +purposes. The first one, called DESK, is a fully distributed coverage algorithm +proposed by \citep{ChinhVu}. The second one, called +GAF~\citep{xu2001geography}, consists in dividing the monitoring area into fixed +squares. Then, during the decision phase, in each square, one sensor is chosen +to remain active during the sensing phase. The last one, the DiLCO +protocol~\citep{Idrees2}, is an improved version of a research work we presented +in~\citep{idrees2014coverage}. Let us notice that PeCO and DiLCO protocols are +based on the same framework. In particular, the choice for the simulations of a +partitioning in 16~subregions was made because it corresponds to the +configuration producing the best results for DiLCO. Of course, this number of subregions sould be adapted according to the size of the area of interest and the number of sensors. + + The protocols are +distinguished from one another by the formulation of the integer program +providing the set of sensors which have to be activated in each sensing +phase. DiLCO protocol tries to satisfy the coverage of a set of primary points, +whereas PeCO protocol objective is to reach a desired level of coverage for each sensor perimeter. In our experimentations, we chose a level of coverage equal to one ($l=1$). -\subsubsection{\bf Coverage Ratio} +\subsubsection{Coverage Ratio} -Figure~\ref{figure5} shows the average coverage ratio for 200 deployed nodes -obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better -coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the 98.76\% -produced by PeCO for the first periods. This is due to the fact that at the -beginning the DiLCO protocol puts to sleep status more redundant sensors (which +Figure~\ref{figure5} shows the average coverage ratio for 200 deployed nodes +obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better +coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the +98.76\% produced by PeCO for the first periods. This is due to the fact that at +the beginning PeCO protocol puts to sleep status more redundant sensors (which slightly decreases the coverage ratio), while the three other protocols activate more sensor nodes. Later, when the number of periods is beyond~70, it clearly appears that PeCO provides a better coverage ratio and keeps a coverage ratio @@ -740,20 +820,17 @@ substantial increase of the coverage performance. \label{figure5} \end{figure} - - - -\subsubsection{\bf Active Sensors Ratio} +\subsubsection{Active Sensors Ratio} Having the less active sensor nodes in each period is essential to minimize the -energy consumption and thus to maximize the network lifetime. Figure~\ref{figure6} -shows the average active nodes ratio for 200 deployed nodes. We observe that -DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen -rounds and DiLCO and PeCO protocols compete perfectly with only 17.92~\% and -20.16~\% active nodes during the same time interval. As the number of periods -increases, PeCO protocol has a lower number of active nodes in comparison with -the three other approaches, while keeping a greater coverage ratio as shown in -Figure \ref{figure5}. +energy consumption and thus to maximize the network lifetime. +Figure~\ref{figure6} shows the average active nodes ratio for 200 deployed +nodes. We observe that DESK and GAF have 30.36~\% and 34.96~\% active nodes for +the first fourteen rounds, and DiLCO and PeCO protocols compete perfectly with +only 17.92~\% and 20.16~\% active nodes during the same time interval. As the +number of periods increases, PeCO protocol has a lower number of active nodes in +comparison with the three other approaches and exhibits a slow decrease, while +keeping a greater coverage ratio as shown in Figure \ref{figure5}. \begin{figure}[h!] \centering @@ -762,82 +839,92 @@ Figure \ref{figure5}. \label{figure6} \end{figure} -\subsubsection{\bf Energy Consumption} - -We studied the effect of the energy consumed by the WSN during the communication, -computation, listening, active, and sleep status for different network densities -and compared it for the four approaches. Figures~\ref{figure7}(a) and (b) -illustrate the energy consumption for different network sizes and for -$Lifetime95$ and $Lifetime50$. The results show that our PeCO protocol is the -most competitive from the energy consumption point of view. As shown in both -figures, PeCO consumes much less energy than the three other methods. One might -think that the resolution of the integer program is too costly in energy, but -the results show that it is very beneficial to lose a bit of time in the -selection of sensors to activate. Indeed the optimization program allows to -reduce significantly the number of active sensors and so the energy consumption -while keeping a good coverage level. +\subsubsection{Energy Consumption} + +The effect of the energy consumed by the WSN during the communication, +computation, listening, active, and sleep status is studied for different +network densities and the four approaches compared. Figures~\ref{figure7}(a) +and (b) illustrate the energy consumption for different network sizes and for +$Lifetime95$ and $Lifetime50$. The results show that PeCO protocol is the most +competitive from the energy consumption point of view. As shown by both figures, +PeCO consumes much less energy than the other methods. One might think that the +resolution of the integer program is too costly in energy, but the results show +that it is very beneficial to lose a bit of time in the selection of sensors to +activate. Indeed the optimization program allows to reduce significantly the +number of active sensors and so the energy consumption while keeping a good +coverage level. Let us notice that the energy overhead when increasing network +size is the lowest with PeCO. \begin{figure}[h!] \centering \begin{tabular}{@{}cr@{}} - \includegraphics[scale=0.475]{figure7a.eps} & \raisebox{2.75cm}{(a)} \\ - \includegraphics[scale=0.475]{figure7b.eps} & \raisebox{2.75cm}{(b)} + \includegraphics[scale=0.5]{figure7a.eps} & \raisebox{2.75cm}{(a)} \\ + \includegraphics[scale=0.5]{figure7b.eps} & \raisebox{2.75cm}{(b)} \end{tabular} \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.} \label{figure7} \end{figure} +\subsubsection{Network Lifetime} - -\subsubsection{\bf Network Lifetime} - -We observe the superiority of PeCO and DiLCO protocols in comparison with the -two other approaches in prolonging the network lifetime. In -Figures~\ref{figure8}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for -different network sizes. As highlighted by these figures, the lifetime -increases with the size of the network, and it is clearly largest for DiLCO -and PeCO protocols. For instance, for a network of 300~sensors and coverage -ratio greater than 50\%, we can see on Figure~\ref{figure8}(b) that the lifetime -is about twice longer with PeCO compared to DESK protocol. The performance -difference is more obvious in Figure~\ref{figure8}(b) than in -Figure~\ref{figure8}(a) because the gain induced by our protocols increases with - time, and the lifetime with a coverage over 50\% is far longer than with -95\%. +We observe the superiority of both PeCO and DiLCO protocols in comparison with +the two other approaches in prolonging the network lifetime. In +Figures~\ref{figure8}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for +different network sizes. As can be seen in these figures, the lifetime +increases with the size of the network, and it is clearly largest for DiLCO and +PeCO protocols. For instance, for a network of 300~sensors and coverage ratio +greater than 50\%, we can see on Figure~\ref{figure8}(b) that the lifetime is +about twice longer with PeCO compared to DESK protocol. The performance +difference is more obvious in Figure~\ref{figure8}(b) than in +Figure~\ref{figure8}(a) because the gain induced by our protocols increases with +time, and the lifetime with a coverage over 50\% is far longer than with 95\%. \begin{figure}[h!] \centering \begin{tabular}{@{}cr@{}} - \includegraphics[scale=0.475]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\ - \includegraphics[scale=0.475]{figure8b.eps} & \raisebox{2.75cm}{(b)} + \includegraphics[scale=0.5]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\ + \includegraphics[scale=0.5]{figure8b.eps} & \raisebox{2.75cm}{(b)} \end{tabular} - \caption{Network Lifetime for (a)~$Lifetime_{95}$ \\ - and (b)~$Lifetime_{50}$.} + \caption{Network Lifetime for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.} \label{figure8} \end{figure} - - -Figure~\ref{figure9} compares the lifetime coverage of our protocols for -different coverage ratios. We denote by Protocol/50, Protocol/80, Protocol/85, -Protocol/90, and Protocol/95 the amount of time during which the network can -satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$ -respectively, where the term Protocol refers to DiLCO or PeCO. Indeed there are applications -that do not require a 100\% coverage of the area to be monitored. PeCO might be -an interesting method since it achieves a good balance between a high level -coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three -lower coverage ratios, moreover the improvements grow with the network -size. DiLCO is better for coverage ratios near 100\%, but in that case PeCO is -not ineffective for the smallest network sizes. +Figure~\ref{figure9} compares the lifetime coverage of DiLCO and PeCO protocols +for different coverage ratios. We denote by Protocol/50, Protocol/80, +Protocol/85, Protocol/90, and Protocol/95 the amount of time during which the +network can satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, +$90\%$, and $95\%$ respectively, where the term Protocol refers to DiLCO or +PeCO. Indeed there are applications that do not require a 100\% coverage of the +area to be monitored. PeCO might be an interesting method since it achieves a +good balance between a high level coverage ratio and network lifetime. PeCO +always outperforms DiLCO for the three lower coverage ratios, moreover the +improvements grow with the network size. DiLCO is better for coverage ratios +near 100\%, but in that case PeCO is not ineffective for the smallest network +sizes. \begin{figure}[h!] -\centering \includegraphics[scale=0.5]{figure9.eps} +\centering \includegraphics[scale=0.55]{figure9.eps} \caption{Network lifetime for different coverage ratios.} \label{figure9} \end{figure} +\subsubsection{Impact of $\alpha$ and $\beta$ on PeCO's performance} +\label{sec:Impact} + +Table~\ref{my-labelx} shows network lifetime results for different values of +$\alpha$ and $\beta$, and a network size equal to 200 sensor nodes. On the one +hand, the choice of $\beta \gg \alpha$ prevents the overcoverage, and so limit +the activation of a large number of sensors, but as $\alpha$ is low, some areas +may be poorly covered. This explains the results obtained for {\it Lifetime50} +with $\beta \gg \alpha$: a large number of periods with low coverage ratio. On +the other hand, when we choose $\alpha \gg \beta$, we favor the coverage even if +some areas may be overcovered, so high coverage ratio is reached, but a large +number of sensors are activated to achieve this goal. Therefore network +lifetime is reduced. The choice $\alpha=0.6$ and $\beta=0.4$ seems to achieve +the best compromise between lifetime and coverage ratio. That explains why we +have chosen this setting for the experiments presented in the previous +subsections. -\subsubsection{\bf Impact of $\alpha$ and $\beta$ on PeCO's performance} -Table~\ref{my-labelx} shows network lifetime results for the different values of $\alpha$ and $\beta$, and for a network size equal to 200 sensor nodes. The choice of $\beta \gg \alpha$ prevents the overcoverage, and so limit the activation of a large number of sensors, but as $\alpha$ is low, some areas may be poorly covered. This explains the results obtained for {\it Lifetime50} with $\beta \gg \alpha$: a large number of periods with low coverage ratio. With $\alpha \gg \beta$, we priviligie the coverage even if some areas may be overcovered, so high coverage ratio is reached, but a large number of sensors are activated to achieve this goal. Therefore network lifetime is reduced. The choice $\alpha=0.6$ and $\beta=0.4$ seems to achieve the best compromise between lifetime and coverage ratio. %As can be seen in Table~\ref{my-labelx}, it is obvious and clear that when $\alpha$ decreased and $\beta$ increased by any step, the network lifetime for $Lifetime_{50}$ increased and the $Lifetime_{95}$ decreased. Therefore, selecting the values of $\alpha$ and $\beta$ depend on the application type used in the sensor nework. In PeCO protocol, $\alpha$ and $\beta$ are chosen based on the largest value of network lifetime for $Lifetime_{95}$. \begin{table}[h] @@ -865,16 +952,32 @@ $\alpha$ & $\beta$ & $Lifetime_{50}$ & $Lifetime_{95}$ \\ \hline \section{Conclusion and Future Works} \label{sec:Conclusion and Future Works} -In this paper we have studied the problem of Perimeter-based Coverage Optimization in WSNs. We have designed a new protocol, called Perimeter-based Coverage Optimization, which schedules nodes' activities (wake up and sleep stages) with the objective of maintaining a good coverage ratio while maximizing the network lifetime. This protocol is applied in a distributed way in regular subregions obtained after partitioning the area of interest in a preliminary step. It works in periods and -is based on the resolution of an integer program to select the subset of sensors operating in active status 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. - - -We have carried out several simulations to evaluate the proposed protocol. The simulation results show that PeCO is more energy-efficient than other approaches, with respect to lifetime, coverage ratio, active sensors ratio, and energy consumption. - -We plan to extend our framework so that the schedules are planned for multiple sensing periods. We also want to improve our integer program to take into account heterogeneous sensors from both energy and node characteristics point of views. Finally, it would be interesting to implement our protocol using a sensor-testbed to evaluate it in real world applications. +In this paper we have studied the problem of perimeter coverage optimization in +WSNs. We have designed a new protocol, called Perimeter-based Coverage +Optimization, which schedules nodes' activities (wake up and sleep stages) with +the objective of maintaining a good coverage ratio while maximizing the network +lifetime. This protocol is applied in a distributed way in regular subregions +obtained after partitioning the area of interest in a preliminary step. It works +in periods and is based on the resolution of an integer program to select the +subset of sensors operating in active status 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. Several simulations have +been carried out to evaluate the proposed protocol. The simulation results show +that PeCO is more energy-efficient than other approaches, with respect to +lifetime, coverage ratio, active sensors ratio, and energy consumption. + +We plan to extend our framework so that the schedules are planned for multiple +sensing periods. We also want to improve the integer program to take into +account heterogeneous sensors from both energy and node characteristics point of +views. Finally, it would be interesting to implement PeCO protocol using a +sensor-testbed to evaluate it in real world applications. + + +\subsection{Acknowledgements} +The authors are deeply grateful to the anonymous reviewers for their constructive advice, which improved the technical quality of the paper. As a Ph.D. student, Ali Kadhum IDREES would like to gratefully acknowledge the University of Babylon - Iraq for financial support and Campus France for the received support. This work is also partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01). \bibliographystyle{gENO} \bibliography{biblio} %articleeo - \end{document} diff --git a/PeCO-EO/reponse.tex b/PeCO-EO/reponse.tex index b00dd1d..e99e712 100644 --- a/PeCO-EO/reponse.tex +++ b/PeCO-EO/reponse.tex @@ -23,7 +23,7 @@ \hspace{-2cm}University of Franche-Comt\'e -\hspace{-2cm}IUT Belfort-Montbéliard, BP 527, 90016 Belfort Cedex, France. +\hspace{-2cm}IUT Belfort-Montb\'eliard, BP 527, 90016 Belfort Cedex, France. \bigskip @@ -75,14 +75,14 @@ decisions was not discussed. \\ \noindent {\bf 4.} The definitions of the undercoverage and overcoverage variables are not clear. I suggest adding some information about these values, since without it, you cannot understand how M and V are computed for the optimization problem. \\ -\textcolor{blue}{\textbf{\textsc{Answer:} The perimeter of each sensor may be cut in parts called coverage intervals (CI). The level of coverage of one CI is defined as the number of active sensors neighbours covering this part of the perimeter. If a given level of coverage $l$ is required for one sensor, the sensor is said to be undercovered (respectively overcovered) if the level of coverage of one of its CI is less (respectively greater) than $l$. In other terms, we define undercoverage and overcoverage through the use of variables $M_{i}^{j}$ and $V_{i}^{j}$ for one sensor $j$ and its coverage interval $i$. If the sensor $j$ is undercovered, there exists at least one of its CI (say $i$) for which the number of active sensors (denoted by $l^{i}$) covering this part of the perimeter is less than $l$ and in this case : $M_{i}^{j}=l-l^{i}$, $V_{i}^{j}=0$. In the contrary, if the sensor $j$ is overcovered, there exists at least one of its CI (say $i$) for which the number of active sensors (denoted by $l^{i}$) covering this part of the perimeter is greater than $l$ and in this case : $M_{i}^{j}=0$, $V_{i}^{j}=l^{i}-l$. }}\\ +\textcolor{blue}{\textbf{\textsc{Answer:} The perimeter of each sensor may be cut in parts called coverage intervals (CI). The level of coverage of one CI is defined as the number of active sensors neighbours covering this part of the perimeter. If a given level of coverage $l$ is required for one sensor, the sensor is said to be undercovered (respectively overcovered) if the level of coverage of one of its CI is less (respectively greater) than $l$. In other terms, we define undercoverage and overcoverage through the use of variables $M_{i}^{j}$ and $V_{i}^{j}$ for one sensor $j$ and its coverage interval $i$. If the sensor $j$ is undercovered, there exists at least one of its CI (say $i$) for which the number of active sensors (denoted by $l^{i}$) covering this part of the perimeter is less than $l$ and in this case : $M_{i}^{j}=l-l^{i}$, $V_{i}^{j}=0$. In the contrary, if the sensor $j$ is overcovered, there exists at least one of its CI (say $i$) for which the number of active sensors (denoted by $l^{i}$) covering this part of the perimeter is greater than $l$ and in this case : $M_{i}^{j}=0$, $V_{i}^{j}=l^{i}-l$. This explanation has been added at the end of section~4. }}\\ \noindent {\bf 5.} Can you mathematically justify how you chose the values of alpha and beta? This is not very clear. I would suggest possibly adding more results showing how the algorithm performs with different alphas and betas. \\ -\textcolor{blue}{\textbf{\textsc{Answer:} The choice of alpha and beta should be made according to the needs of the application. Alpha should be enough large to prevent undercoverage and so to reach the highest possible coverage ratio. Beta should be enough large to prevent overcoverage and so to activate a minimum number of sensors. The values of $\alpha_{i}^{j}$ can be identical for all coverage intervals $i$ of one sensor $j$ in order to express that the perimeter of each sensor should be uniformly covered, but $\alpha_{i}^{j}$ values can be differenciated between sensors to force some regions to be better covered than others. The choice of $\beta \gg \alpha$ prevents the overcoverage, and so limit the activation of a large number of sensors, but as $\alpha$ is low, some areas may be poorly covered. This explains the results obtained for {\it Lifetime50} with $\beta \gg \alpha$: a large number of periods with low coverage ratio. With $\alpha \gg \beta$, we priviligie the coverage even if some areas may be overcovered, so high coverage ratio is reached, but a large number of sensors are activated to achieve this goal. Therefore network lifetime is reduced. The choice $\alpha=0.6$ and $\beta=0.4$ seems to achieve the best compromise between lifetime and coverage ratio. }}\\ +\textcolor{blue}{\textbf{\textsc{Answer:} The choice of alpha and beta should be made according to the needs of the application. Alpha should be enough large to prevent undercoverage and so to reach the highest possible coverage ratio. Beta should be enough large to prevent overcoverage and so to activate a minimum number of sensors. The values of $\alpha_{i}^{j}$ can be identical for all coverage intervals $i$ of one sensor $j$ in order to express that the perimeter of each sensor should be uniformly covered, but $\alpha_{i}^{j}$ values can be differenciated between sensors to force some regions to be better covered than others. The choice of $\beta \gg \alpha$ prevents the overcoverage, and so limit the activation of a large number of sensors, but as $\alpha$ is low, some areas may be poorly covered. This explains the results obtained for {\it Lifetime50} with $\beta \gg \alpha$: a large number of periods with low coverage ratio. With $\alpha \gg \beta$, we favor the coverage even if some areas may be overcovered, so high coverage ratio is reached, but a large number of sensors are activated to achieve this goal. Therefore network lifetime is reduced. The choice $\alpha=0.6$ and $\beta=0.4$ seems to achieve the best compromise between lifetime and coverage ratio. This discussion about the impact of the values of alpha and beta on the protocol performance is added as subsection 5.2.5. }}\\ @@ -90,7 +90,7 @@ very clear. I would suggest possibly adding more results showing how the algorit However, the clarity in the literature review is a little off. Some of the descriptions of the method s used are very vague and do not bring out their key contributions. Some references are not consistent and I suggest using the journals template to adjust them for overall consistency. \\ -\textcolor{blue}{\textbf{\textsc{Answer:} }}\\ +\textcolor{blue}{\textbf{\textsc{Answer:} References have been carefully checked and seem to be consistent with the journal template. In section "related works" we refer to papers dealing with coverage and lifetime in WSN. Each paragraph of this section discusses the literature related to a particular aspect of the problem : 1.Type of coverage, 2.Type of scheme, 3.Centralized versus Distributed, 4. Optimization method. At the end of each paragraph we position our method.}}\\ @@ -146,7 +146,7 @@ s used are very vague and do not bring out their key contributions. Some referen \noindent { \ding{90} Lots of English and grammar mistakes. I recommend rereading the paper line by line and adjusting the sentences that do not make sense.} \\ -\textcolor{blue}{\textbf{\textsc{Answer:} ?????? relecture par Ingrid }}.\\ +\textcolor{blue}{\textbf{\textsc{Answer:} The paper has been carefully reread, and the readability of the paper (English) has been improved. }}\\ @@ -159,13 +159,13 @@ The paper entitled "Perimeter-based Coverage Optimization to Improve Lifetime in \noindent {\bf 1.} The protocol framework is not described in details. In particular, the spatial and temporal subdivision (page 2, line 11) that is at the core of PeCO, is not described nor justified in much detail. How to implement an efficient spatial subdivision? On page 10, line 11, the number of subdivisions is said to be equal to 16, but the clustering algorithm used is not mentioned. Is this number dependent of the size of the sensing area? Of the number of sensors? Of the sensing range? The proposed protocol cannot be adopted by practitioners if such an important step is not documented. Temporal subdivision suffers from the same lack of description and justification: why should time intervals have the same duration? If they have the same duration, how should this common duration should be chosen? \\ -\textcolor{blue}{\textbf{\textsc{Answer:} Spatial and temporal choices of subdivision are not the topics of the paper. In the study, we assume that the deployment of sensors is almost uniformly over the region. So we only need to fix a regular division of the region into subregions to make the problem tractable. The subdivision is made such that the number of hops between any pairs of sensors inside a subregion is less than or equal to 3. Concerning the choice of the sensing period duration, it is correlated with the types of applications, with the amount of initial energy in sensors batteries and also with the duration of the exchange phase. All applications do not have the same requirements of Quality of Service. Here information exchange is executed every hour but the length of the sensing period could be reduced and adapted dynamically. On the one hand a small sensing period would allow to be more reliable but would have higher communication costs. On the other hand the choice of a long duration may cause problems in case of nodes failure during the sensing period.}}\\ +\textcolor{blue}{\textbf{\textsc{Answer:} Spatial and temporal choices of subdivision are not the topics of the paper. In the study, we assume that the deployment of sensors is almost uniformly over the region. So we only need to fix a regular division of the region into subregions to make the problem tractable. The subdivision is made such that the number of hops between any pairs of sensors inside a subregion is less than or equal to 3. Concerning the choice of the sensing period duration, it is correlated with the types of applications, with the amount of initial energy in sensors batteries and also with the duration of the exchange phase. All applications do not have the same requirements of Quality of Service. Here information exchange is executed every hour but the length of the sensing period could be reduced and adapted dynamically. On the one hand a small sensing period would allow to be more reliable but would have higher communication costs. On the other hand the choice of a long duration may cause problems in case of nodes failure during the sensing period. Explanation has been given throughout the paper. In particular the sensing duration is discussed in section 5.1.}}\\ \noindent {\bf 2.}Page 9, Section 4, is the Perimeter-based coverage problem NP-hard? This question is important for justifying the use of a Mixed Integer Linear Programming model. \\ \textcolor{blue}{\textbf{\textsc{Answer:} The perimeter scheduling coverage problem is NP-hard in general, it has been proved - in the paper entitled "Perimeter Coverage Scheduling in Wireless Sensor Networks Using Sensors with a Single Continuous Cover Range" from Ka-Shun Hung and King-Shan Lui (EURASIP Journal on Wireless Communications and Networking 2010, 2010:926075 doi:10.1155/2010/926075). In this paper, authors study the coverage of the perimeter of a large object requiring to be monitored. In our study, the large object to be monitored is the sensor itself (or more precisely its sensing area). }}\\ + in the paper entitled "Perimeter Coverage Scheduling in Wireless Sensor Networks Using Sensors with a Single Continuous Cover Range" from Ka-Shun Hung and King-Shan Lui (EURASIP Journal on Wireless Communications and Networking 2010, 2010:926075 doi:10.1155/2010/926075). In this paper, authors study the coverage of the perimeter of a large object requiring to be monitored. In our study, the large object to be monitored is the sensor itself (or more precisely its sensing area). This point has been highlighted at the beginning of section 4. }}\\ \noindent {\bf 3.} Page 9, the major problem with the present paper is, in my opinion, the objective function of the Mixed Integer Linear Program (2). It is not described in the paper, and looks like an attempt to address a multiobjective problem (like minimizing overcoverage and undercoverage). However, using a weighted sum is well known not to be an efficient way to address biobjective problems. The introduction of various performance metrics in Section 5.1 also suggests that the authors have not decided exactly which objective function to use, and compare their protocols against competitors without mentioning the exact purpose of each of them. If the performance metrics list given in Section 5.1 is exhaustive, then the authors should mention at the beginning of the paper what are the aims of the protocol, and explain how the protocol is built to optimize these objectives. \\ @@ -175,7 +175,7 @@ The paper entitled "Perimeter-based Coverage Optimization to Improve Lifetime in \noindent {\bf 4.}Page 11 Section 5.2, the sensor nodes are said to be based on Atmels AVR ATmega103L microcontroller. If I am not mistaken, these devices have 128 KBytes of memory, and I didn't find any clue that they can run an operating system like Linux. This point is of primary importance for the proposed protocol, since GLPK (a C API) is supposed to be executed by the cluster leader. In addition to that, GLPK requires a non negligible amount of memory to run properly, and the Atmels AVR ATmega103L microcontroller might be insufficient for that purpose. The authors are urged to provide references of previous works showing that these technical constraints are not preventing their protocol to be implemented on the aforementioned microcontroller. Then, on page 13, in Section "5.2.3 Energy Consumption", the estimation of $E_p^{com}$ for the considered microcontroller seems quite challenging and should be carefully documented. Indeed, this is a key point in providing a fair comparison of PeCO with its competitors. \\ -\textcolor{blue}{\textbf{\textsc{Answer:} +\textcolor{blue}{\textbf{\textsc{Answer 1:} To implement PeCO on real sensors nodes with limited memories capacities, we can act on : \begin{itemize} \item the solver : GLPK is memory consuming for the resolution of integer programming (IP) compared with other commercial solvers like CPLEX\textregistered. Commercial solvers generally outperform open source solvers (See the report : "Analysis of commercial and free and open source @@ -194,18 +194,22 @@ where $S$ denotes the number of sensors in the subregion, $I$ the average number Total number & S & I & GLPK IP & GLPK LP & nodes&CPLEX\\ of nodes &&&&relaxation &B\&B tree &\\ \hline -100 & 6.25& 5&0.2 Mb & 0.2 Mb &1 & 64 Kb\\ +100 & 6.25& 5&0.2 MB & 0.2 Mb &1 & 64 kB\\ \hline -200 & 12.5& 11&1.7 Mb & 1.6 Mb &1 & 281 Kb\\ +200 & 12.5& 11&1.7 MB & 1.6 Mb &1 & 281 kB\\ \hline -300 &18.5 & 17&3.6 Mb & 3.5 Mb & 3 &644 Kb\\ +300 &18.5 & 17&3.6 MB & 3.5 Mb & 3 &644 kB\\ \hline \end{tabular} \\ -It is noteworthy that the difference of memory used with GLPK between the resolution of the IP and its LP-relaxation is very weak (not more than 0.1 Mb). The size of the branch and bound tree dos not exceed 3 nodes. This result leads one to believe that the memory use with CPLEX\textregistered for solving the IP would be very close to that for the LP-relaxation, that is to say around 100 Kb for a subregion containing $S=10$ sensors. Moreover the IP seems to have some specifities that encourage us to develop our own solver (coefficents matrix is very sparse) or to use an existing heuristic to find good approximate solutions (Reference : "A feasibility pump heuristic for general mixed-integer problems", Livio Bertacco and Matteo Fischetti and Andrea Lodi, Discrete Optimization, issn 1572-5286). +It is noteworthy that the difference of memory used with GLPK between the resolution of the IP and its LP-relaxation is very weak (not more than 0.1 MB). The size of the branch and bound tree dos not exceed 3 nodes. This result leads one to believe that the memory use with CPLEX\textregistered for solving the IP would be very close to that for the LP-relaxation, that is to say around 100 Kb for a subregion containing $S=10$ sensors. Moreover the IP seems to have some specifities that encourage us to develop our own solver (coefficents matrix is very sparse) or to use an existing heuristic to find good approximate solutions (Reference : "A feasibility pump heuristic for general mixed-integer problems", Livio Bertacco and Matteo Fischetti and Andrea Lodi, Discrete Optimization, issn 1572-5286). \item the subdivision of the region of interest. To make the resolution of integer programming tractable by a leader sensor, we need to limit the number of nodes in each subregion (the number of variables and constraints of the integer programming is directly depending on the number of nodes and neigbors). It is therefore necessary to adapt the subdvision according to the number of sensors deployed in the area and their sensing range (impact on the number of coverage intervals). -\end{itemize}}}\\ - +\end{itemize} +A discussion about memory consumption has been added in section 5.2}} +\bigskip +\textcolor{blue}{\textbf{\textsc{Answer 2:} +In section 5.2 we give a table with the power consumption values which are used to compute the energy consumption. These ones are based on the energy model of (Vu et al. 2006). +}} -- 2.39.5