Update by Ali

[ThesisAli.git] / CHAPITRE_05.tex

diff --git a/CHAPITRE_05.tex b/CHAPITRE_05.tex
index 91014fb9ba229257a060435a5450f0267123a523..714ecd7520b60575188f9d1963b297c21dc14cec 100644 (file)
--- a/CHAPITRE_05.tex
+++ b/CHAPITRE_05.tex
@@ -90,7 +90,7 @@ The  energy consumption  and some other constraints  can easily  be  taken into
   \BlankLine
   %\emph{Initialize the sensor node and determine it's position and subregion} \; 
   
   \BlankLine
   %\emph{Initialize the sensor node and determine it's position and subregion} \; 
   

-  \If{ $RE_j \geq E_{R}$ }{
+  \If{ $RE_j \geq E_{th}$ }{

       \emph{$s_j.status$ = COMMUNICATION}\;
       \emph{Send $INFO()$ packet to other nodes in the subregion}\;
       \emph{Wait $INFO()$ packet from other nodes in the subregion}\; 
       \emph{$s_j.status$ = COMMUNICATION}\;
       \emph{Send $INFO()$ packet to other nodes in the subregion}\;
       \emph{Wait $INFO()$ packet from other nodes in the subregion}\; 


@@ -199,7 +199,7 @@ Subject to
 \end{equation}
 
 \begin{equation}
 \end{equation}
 
 \begin{equation}

-  \sum_{t=1}^{T}  X_{t,j}   \leq  \lfloor {RE_{j}/E_{R}} \rfloor \hspace{6 mm} \forall j \in J, t = 1,\dots,T
+  \sum_{t=1}^{T}  X_{t,j}   \leq  \lfloor {RE_{j}/E_{th}} \rfloor \hspace{6 mm} \forall j \in J, t = 1,\dots,T

   \label{eq144} 
 \end{equation}
 
   \label{eq144} 
 \end{equation}
 


@@ -232,7 +232,7 @@ covered by at least  one sensor and, if it is not  always the case, overcoverage
 and undercoverage  variables help balancing the restriction  equations by taking
 positive values. The constraint  given by equation~(\ref{eq144}) guarantees that
 the sensor has enough energy ($RE_j$  corresponds to its remaining energy) to be
 and undercoverage  variables help balancing the restriction  equations by taking
 positive values. The constraint  given by equation~(\ref{eq144}) guarantees that
 the sensor has enough energy ($RE_j$  corresponds to its remaining energy) to be

-alive during  the selected rounds knowing  that $E_{R}$ is the  amount of energy
+alive during  the selected rounds knowing  that $E_{th}$ is the  amount of energy

 required to be alive during one round.
 
 There  are two main  objectives.  First,  we limit  the overcoverage  of primary
 required to be alive during one round.
 
 There  are two main  objectives.  First,  we limit  the overcoverage  of primary


@@ -290,7 +290,7 @@ Network size &  50, 100, 150, 200 and 250~nodes   \\
 Initial energy  & 500-700~joules  \\  
 %\hline
 Sensing time for one round & 60 Minutes \\
 Initial energy  & 500-700~joules  \\  
 %\hline
 Sensing time for one round & 60 Minutes \\

-$E_{R}$ & 36 Joules\\
+$E_{th}$ & 36 Joules\\

 $R_s$ & 5~m   \\     
 %\hline
 $W_{\Theta}$ & 1   \\
 $R_s$ & 5~m   \\     
 %\hline
 $W_{\Theta}$ & 1   \\


@@ -317,7 +317,7 @@ it. Therefore, we have set the number of subregions to 16 rather than 32.
 
 We used the modeling language and the optimization solver which are mentioned in chapter 4, section \ref{ch4:sec:04:02}. In addition, we employed an energy consumption model, which is presented in chapter 4, section \ref{ch4:sec:04:03}. 
 
 
 We used the modeling language and the optimization solver which are mentioned in chapter 4, section \ref{ch4:sec:04:02}. In addition, we employed an energy consumption model, which is presented in chapter 4, section \ref{ch4:sec:04:03}. 
 

-%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 less than  $E_{R}=36~\mbox{Joules}$, the minimum  energy needed for the  node to stay alive  during one round.  This value has  been computed by  multiplying the energy consumed in  active state (9.72 mW) by the time in second  for one round (3600 seconds). According to the  interval of initial energy, a sensor may be alive during at most 20 rounds.
+%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 less than  $E_{th}=36~\mbox{Joules}$, the minimum  energy needed for the  node to stay alive  during one round.  This value has  been computed by  multiplying the energy consumed in  active state (9.72 mW) by the time in second  for one round (3600 seconds). According to the  interval of initial energy, a sensor may be alive during at most 20 rounds.

 
 \subsection{Metrics}
 \label{ch5:sec:04:02}
 
 \subsection{Metrics}
 \label{ch5:sec:04:02}