X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/JournalMultiPeriods.git/blobdiff_plain/2bf5c08bf09601e4ef8ee0277c15eb82a654a8fa..82c1d57498033e9e0d5b86bd387ca04e71c60399:/article.tex

diff --git a/article.tex b/article.tex
index f156c36..16831f3 100644
--- a/article.tex
+++ b/article.tex
@@ -521,8 +521,7 @@ active nodes.
 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
@@ -859,7 +858,7 @@ Sensing time for one round & 60 Minutes \\
 $E_{R}$ & 36 Joules\\
 $R_s$ & 5~m   \\     
 %\hline
-$W_{\Theta}$ & 1   \\
+$W_{\theta}$ & 1   \\
 % [1ex] adds vertical space
 %\hline
 $W_{U}$ & $|P|^2$
@@ -948,7 +947,7 @@ and 24~bits  respectively.  The  value of energy  spent to send  a 1-bit-content
 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
@@ -1011,7 +1010,7 @@ network, and $R$ is the total number of subregions in the network.
   % 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*}
 
 
@@ -1057,9 +1056,9 @@ indicate the energy consumed by the whole network in round $t$.
 
 \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
@@ -1085,7 +1084,7 @@ rounds, and thus should extend the network lifetime.
 \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
@@ -1106,7 +1105,7 @@ nodes in a more efficient manner.
 \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. 
 
@@ -1128,7 +1127,7 @@ still connected.
 \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
@@ -1162,11 +1161,11 @@ sensors to consider in the integer program.
 %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
@@ -1195,7 +1194,7 @@ optimization problem.
 
 %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 $Lifetime_{95}$
@@ -1252,7 +1251,7 @@ scheduling.
 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