X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/ThesisAli.git/blobdiff_plain/1e6c973630b57cc7cf78232de0f9c8b3bf0d334b..5b873620b230517c1592c89c4c8dd5dba2818339:/CHAPITRE_05.tex?ds=inline

diff --git a/CHAPITRE_05.tex b/CHAPITRE_05.tex
index 95ad64d..733232c 100644
--- a/CHAPITRE_05.tex
+++ b/CHAPITRE_05.tex
@@ -53,9 +53,9 @@ period  after  Information~Exchange  and  Leader~Election phases,  in  order to
 \end{figure} 
 
 
-This protocol minimizes the impact of unexpected node failure (not due to batteries running out of energy), because it works in periods. On the one hand, if a node failure is detected before making the decision, the node will not participate during this phase. On the other hand, if the node failure occurs after the decision, the sensing  task of the network will be temporarily affected:  only during  the period of sensing until a new period starts.
+%This protocol minimizes the impact of unexpected node failure (not due to batteries running out of energy), because it works in periods. On the one hand, if a node failure is detected before making the decision, the node will not participate during this phase. On the other hand, if the node failure occurs after the decision, the sensing  task of the network will be temporarily affected:  only during  the period of sensing until a new period starts.
 
-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 (Information  Exchange, Leader  Election, and  Decision) are energy  consuming for some  nodes, even  when they  do not  join the  network to monitor the area.
+%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 (Information  Exchange, Leader  Election, and  Decision) are energy  consuming for some  nodes, even  when they  do not  join the  network to monitor the area.
 
  
 
@@ -106,16 +106,11 @@ The  energy consumption  and some other constraints  can easily  be  taken into
 \label{ch5:sec:03}
 
 
-According to Algorithm~\ref{alg:MuDiLCO}, the integer program is based on the model
-proposed by  \cite{ref156} with some modifications, where  the objective of our model is
-to find  a maximum number of non-disjoint cover sets. 
+%According to Algorithm~\ref{alg:MuDiLCO}, the integer program is based on the model proposed by  \cite{ref156} with some modifications, where  the objective of our model is to find  a maximum number of non-disjoint cover sets. 
 %To fulfill this  goal, the authors proposed an integer  program which forces undercoverage and overcoverage of  targets to  become minimal  at  the same  time.  They  use binary  variables $x_{jl}$ to indicate if  sensor $j$ belongs to cover set $l$. In our model, 
-We consider binary variables $X_{t,j}$ to determine the  possibility of activating
-sensor $j$ during round $t$ of  a given sensing phase.  We also consider primary
-points as targets.  The set of primary points is denoted by  $P$ and the set of
-sensors by  $J$. Only sensors  able to  be alive during  at least one  round are
-involved in the integer program.
+%We consider binary variables $X_{t,j}$ to determine the  possibility of activating sensor $j$ during round $t$ of  a given sensing phase.  We also consider primary points as targets.  The set of primary points is denoted by  $P$ and the set of sensors by  $J$. Only sensors  able to  be alive during  at least one  round are involved in the integer program.
 
+We extend the mathematical formulation given in section \ref{ch4:sec:03} to take into account multiple rounds.
 
 For a  primary point  $p$, let $\alpha_{j,p}$  denote the indicator  function of
 whether the point $p$ is covered, that is
@@ -200,22 +195,10 @@ U_{t,p} \in \lbrace0,1\rbrace, \hspace{10 mm}\forall p \in P, t = 1,\dots,T  \la
   covered).
 \end{itemize}
 
-The first group  of constraints indicates that some primary  point $p$ should be
-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
-alive during  the selected rounds knowing  that $E_{th}$ is the amount of energy
-required to be alive during one round.
+%The first group  of constraints indicates that some primary  point $p$ should be 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 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
-points in order to activate a  minimum number of sensors.  Second we prevent the
-absence  of  monitoring  on  some  parts  of the  subregion  by  minimizing  the
-undercoverage.  The weights  $W_\theta$ and $W_U$ must be  properly chosen so as
-to guarantee that the maximum number of points are covered during each round. 
-%% MS W_theta is smaller than W_u => problem with the following sentence
-In our simulations, priority is given  to the coverage by choosing $W_{U}$ very
-large compared to $W_{\theta}$.
+%There  are two main  objectives.  First,  we limit  the overcoverage  of primary points in order to activate a  minimum number of sensors.  Second we prevent the absence  of  monitoring  on  some  parts  of the  subregion  by  minimizing  the undercoverage.  The weights  $W_\theta$ and $W_U$ must be  properly chosen so as to guarantee that the maximum number of points are covered during each round.  In our simulations, priority is given  to the coverage by choosing $W_{U}$ very large compared to $W_{\theta}$.
 
 
  
@@ -327,9 +310,8 @@ rounds, and thus should extend the network lifetime.
 %\subsection{Active sensors ratio} 
 %\label{ch5:sec:03:02:02}
 
-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
-lifetime. Figure~\ref{fig4}  presents the active  sensor ratio for  150 deployed
+%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 lifetime. 
+Figure~\ref{fig4}  presents the active  sensor ratio for  150 deployed
 nodes all along the network lifetime. It appears that up to round thirteen, DESK
 and GAF have  respectively 37.6\% and 44.8\% of nodes  in active mode, whereas
 MuDiLCO clearly  outperforms them  with only 23.7\%  of active nodes.  After the
@@ -360,7 +342,6 @@ emphasize that the  simulation continues as long as a network  in a subregion is
 \label{fig6}
 \end{figure} 
 
-
  
 \item {{\bf Energy consumption}} \label{subsec:EC} 
 %\subsection{Energy consumption} 
