Update by Ali

diff --git a/CHAPITRE_05.tex b/CHAPITRE_05.tex
index ff828167a3fdab08abd125db4e141c902e05480f..a49a28a1dc45b81084c0a95112bfe0a5b74831c2 100755 (executable)
--- a/CHAPITRE_05.tex
+++ b/CHAPITRE_05.tex
@@ -39,7 +39,7 @@ task. Each sensor node in the subregion will
 receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
 sleep for  each round of the sensing  phase.  Algorithm~\ref{alg:MuDiLCO}, which
 will be  executed by each node  at the beginning  of a period, explains  how the
 receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
 sleep for  each round of the sensing  phase.  Algorithm~\ref{alg:MuDiLCO}, which
 will be  executed by each node  at the beginning  of a period, explains  how the

-Active-Sleep packet is obtained. In this way a multiround optimization  process is performed  during each
+Active-Sleep packet is obtained. In this way, a multiround optimization  process is performed  during each

 period  after  Information~Exchange  and  Leader~Election phases,  in  order  to
 produce $T$ cover sets that will take the mission of sensing for $T$ rounds.
 \begin{figure}[ht!]
 period  after  Information~Exchange  and  Leader~Election phases,  in  order  to
 produce $T$ cover sets that will take the mission of sensing for $T$ rounds.
 \begin{figure}[ht!]


@@ -51,9 +51,9 @@ produce $T$ cover sets that will take the mission of sensing for $T$ rounds.
 
 This protocol minimizes the impact of unexpected node failure (not due to batteries running out of energy), because it works in periods. 
 
 
 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 to this phase, and, 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.
+On the one hand, if a node failure is detected before making the decision, the node will not participate during this phase, and, 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.

 
  
 
 
  
 


@@ -117,7 +117,7 @@ involved in the integer program.
 
 
 For a  primary point  $p$, let $\alpha_{j,p}$  denote the indicator  function of
 
 
 For a  primary point  $p$, let $\alpha_{j,p}$  denote the indicator  function of

-whether the point $p$ is covered, that is:
+whether the point $p$ is covered, that is

 \begin{equation}
 \alpha_{j,p} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
 \alpha_{j,p} = \left \{ 
 \begin{array}{l l}


@@ -128,7 +128,7 @@ whether the point $p$ is covered, that is:
 %\label{eq12} 
 \end{equation}
 The number of  active sensors that cover the  primary point $p$ during
 %\label{eq12} 
 \end{equation}
 The number of  active sensors that cover the  primary point $p$ during

-round $t$ is equal to $\sum_{j \in J} \alpha_{j,p} * X_{t,j}$ where:
+round $t$ is equal to $\sum_{j \in J} \alpha_{j,p} * X_{t,j}$ where

 \begin{equation}
 X_{t,j} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
 X_{t,j} = \left \{ 
 \begin{array}{l l}


@@ -137,7 +137,7 @@ X_{t,j} = \left \{
 \end{array} \right.
 %\label{eq11} 
 \end{equation}
 \end{array} \right.
 %\label{eq11} 
 \end{equation}

-We define the Overcoverage variable $\Theta_{t,p}$ as:
+We define the Overcoverage variable $\Theta_{t,p}$ as

 \begin{equation}
  \Theta_{t,p} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
  \Theta_{t,p} = \left \{ 
 \begin{array}{l l}


@@ -150,7 +150,7 @@ We define the Overcoverage variable $\Theta_{t,p}$ as:
 More  precisely, $\Theta_{t,p}$  represents the  number of  active  sensor nodes
 minus  one  that  cover  the  primary  point $p$  during  round  $t$.   The
 Undercoverage variable  $U_{t,p}$ of the primary  point $p$ during  round $t$ is
 More  precisely, $\Theta_{t,p}$  represents the  number of  active  sensor nodes
 minus  one  that  cover  the  primary  point $p$  during  round  $t$.   The
 Undercoverage variable  $U_{t,p}$ of the primary  point $p$ during  round $t$ is

-defined by:
+defined by

 \begin{equation}
 U_{t,p} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
 U_{t,p} = \left \{ 
 \begin{array}{l l}


@@ -160,7 +160,7 @@ U_{t,p} = \left \{
 \label{eq14} 
 \end{equation}
 
 \label{eq14} 
 \end{equation}
 

-Our coverage optimization problem can then be formulated as follows:
+Our coverage optimization problem can then be formulated as follows

 \begin{equation}
  \min \sum_{t=1}^{T} \sum_{p=1}^{P} \left(W_{\theta}* \Theta_{t,p} + W_{U} * U_{t,p}  \right)  \label{eq15} 
 \end{equation}
 \begin{equation}
  \min \sum_{t=1}^{T} \sum_{p=1}^{P} \left(W_{\theta}* \Theta_{t,p} + W_{U} * U_{t,p}  \right)  \label{eq15} 
 \end{equation}


@@ -213,7 +213,7 @@ 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
 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
+In our simulations, priority is given  to the coverage by choosing $W_{U}$ very

 large compared to $W_{\theta}$.
 
 
 large compared to $W_{\theta}$.
 
 


@@ -276,17 +276,11 @@ $W_{U}$ & $|P|^2$
 % is used to refer this table in the text
 \end{table}
   
 % is used to refer this table in the text
 \end{table}
   

-Our protocol  is declined into  four versions: MuDiLCO-1,  MuDiLCO-3, MuDiLCO-5,
-and  MuDiLCO-7, corresponding  respectively to  $T=1,3,5,7$ ($T$  the  number of
-rounds in one sensing period).  In  the following, we will make comparisons with
-two other methods. The first method, called DESK and proposed by \cite{DESK},
-is  a   full  distributed  coverage   algorithm.   The  second   method,  called
+Our protocol  is declined into  four versions: MuDiLCO-1,  MuDiLCO-3, MuDiLCO-5, and  MuDiLCO-7, corresponding  respectively to  $T=1,3,5,7$ ($T$  the  number of rounds in one sensing period).  In  the following, we will make comparisons with two other methods. The first method, called DESK and proposed by \cite{DESK}, is  a   fully  distributed  coverage   algorithm.   The  second   method is called

 GAF~\cite{GAF}, consists in dividing  the region into fixed squares.
 GAF~\cite{GAF}, consists in dividing  the region into fixed squares.

-During the decision  phase, in each square, one sensor is  then chosen to remain
-active during the sensing phase time.
+During the decision  phase, in each square, one sensor is  then chosen to remain active during the sensing phase time.

 
 

-Some preliminary experiments were performed in chapter 4 to study the choice of the number of
-subregions  which subdivides  the  sensing field,  considering different  network
+Some preliminary experiments were performed in chapter 4 to study the choice of the number of subregions  which subdivides  the  sensing field,  considering different  network

 sizes. They show that as the number of subregions increases, so does the network
 lifetime. Moreover,  it makes  the MuDiLCO protocol  more robust  against random
 network  disconnection due  to node  failures.  However,  too  many subdivisions
 sizes. They show that as the number of subregions increases, so does the network
 lifetime. Moreover,  it makes  the MuDiLCO protocol  more robust  against random
 network  disconnection due  to node  failures.  However,  too  many subdivisions


@@ -380,13 +374,13 @@ which is a little bit better than the one of MuDiLCO.
 
 This is due  to the fact that, in comparison with  MuDiLCO which uses optimization
 to put in  SLEEP status redundant sensors, more sensor  nodes remain active with
 
 This is due  to the fact that, in comparison with  MuDiLCO which uses optimization
 to put in  SLEEP status redundant sensors, more sensor  nodes remain active with

-DESK and GAF.   As a consequence, when the number of  rounds increases, a larger
+DESK and GAF. As a consequence, when the number of  rounds increases, a larger

 number of node failures  can be observed in DESK and GAF,  resulting in a faster
 decrease of the coverage ratio.   Furthermore, our protocol allows to maintain a
 coverage ratio  greater than  50\% for far  more rounds.  Overall,  the proposed
 sensor  activity scheduling based  on optimization  in MuDiLCO  maintains higher
 coverage ratios of the  area of interest for a larger number  of rounds. It also
 number of node failures  can be observed in DESK and GAF,  resulting in a faster
 decrease of the coverage ratio.   Furthermore, our protocol allows to maintain a
 coverage ratio  greater than  50\% for far  more rounds.  Overall,  the proposed
 sensor  activity scheduling based  on optimization  in MuDiLCO  maintains higher
 coverage ratios of the  area of interest for a larger number  of rounds. It also

-means that MuDiLCO saves more energy,  with less dead nodes, at most for several
+means that MuDiLCO saves more energy,  with fewer dead nodes, at most for several

 rounds, and thus should extend the network lifetime.
 
 \begin{figure}[ht!]
 rounds, and thus should extend the network lifetime.
 
 \begin{figure}[ht!]


@@ -409,9 +403,7 @@ and GAF have  respectively 37.6\% and 44.8\% of nodes  in ACTIVE status, whereas
 MuDiLCO clearly  outperforms them  with only 24.8\%  of active nodes.  After the
 thirty-fifth round, MuDiLCO exhibits larger numbers of active nodes, which agrees
 with  the  dual  observation  of  higher  level  of  coverage  made  previously.
 MuDiLCO clearly  outperforms them  with only 24.8\%  of active nodes.  After the
 thirty-fifth round, MuDiLCO exhibits larger numbers of active nodes, which agrees
 with  the  dual  observation  of  higher  level  of  coverage  made  previously.

-Obviously, in  that case DESK  and GAF have  less active nodes, since  they have
-activated many nodes  at the beginning. Anyway, MuDiLCO  activates the available
-nodes in a more efficient manner.
+Obviously, in  that case, DESK and GAF have fewer active nodes since they have activated many nodes  in the beginning. Anyway, MuDiLCO  activates the available nodes in a more efficient manner.

 
 \begin{figure}[ht!]
 \centering
 
 \begin{figure}[ht!]
 \centering


@@ -468,16 +460,8 @@ network sizes, for $Lifetime_{95}$ and $Lifetime_{50}$.
 \end{figure}
 
 
 \end{figure}
 
 

-The  results  show  that  MuDiLCO  is  the  most  competitive  from  the  energy
-consumption point of view.  The  other approaches have a high energy consumption
-due  to activating a  larger number  of redundant  nodes as  well as  the energy
-consumed during  the different  status of the  sensor node. Among  the different
-versions of our protocol, the MuDiLCO-7  one consumes more energy than the other
-versions. This is  easy to understand since the bigger the  number of rounds and
-the number of  sensors involved in the integer program are,  the larger the time
-computation to solve the optimization problem is. To improve the performances of
-MuDiLCO-7, we  should increase the  number of subregions  in order to  have less
-sensors to consider in the integer program.
+The  results  show  that  MuDiLCO  is  the  most  competitive  from  the  energy consumption point of view.  The  other approaches have a high energy consumption due  to activating a  larger number  of redundant  nodes, as  well as  the energy consumed during  the different  status of the  sensor node. Among  the different versions of our protocol, the MuDiLCO-7  one consumes more energy than the other versions. This is  easy to understand since the bigger the  number of rounds and
+the number of  sensors involved in the integer program is  the larger the time computation to solve the optimization problem is. To improve the performances of MuDiLCO-7, we  should increase the  number of subregions  in order to  have fewer sensors to consider in the integer program.

 
 
 
 
 
 


@@ -498,16 +482,8 @@ seconds (needed to solve optimization problem) for different values of $T$. The
 \label{fig77}
 \end{figure} 
 
 \label{fig77}
 \end{figure} 
 

-As expected,  the execution time increases  with the number of  rounds $T$ taken
-into account to schedule the sensing phase. The times obtained for $T=1,3$
-or $5$ seem bearable, but for $T=7$ they become quickly unsuitable for a sensor
-node, especially when  the sensor network size increases.   Again, we can notice
-that if we want  to schedule the nodes activities for a  large number of rounds,
-we need to choose a relevant number of subregions in order to avoid a complicated
-and cumbersome optimization.  On the one hand, a large value  for $T$ permits to
-reduce the  energy-overhead due  to the three  pre-sensing phases, on  the other
-hand  a leader  node may  waste a  considerable amount  of energy  to  solve the
-optimization problem.
+As expected,  the execution time increases  with the number of  rounds $T$ taken into account to schedule the sensing phase. The times obtained for $T=1,3$ or $5$ seem bearable, but for $T=7$ they become quickly unsuitable for a sensor node, especially when  the sensor network size increases.   Again, we can notice that if we want  to schedule the nodes activities for a  large number of rounds,
+we need to choose a relevant number of subregions in order to avoid a complicated and cumbersome optimization.  On the one hand, a large value  for $T$ permits to reduce the  energy overhead due  to the three  pre-sensing phases, on  the other hand  a leader  node may  waste a  considerable amount  of energy  to  solve the optimization problem.

 
 
 
 
 
 


@@ -515,20 +491,10 @@ optimization problem.
 %\subsection{Network lifetime}
 %\label{ch5:sec:03:02:06}
 
 %\subsection{Network lifetime}
 %\label{ch5:sec:03:02:06}
 

-The next  two figures,  Figures~\ref{fig8}(a) and \ref{fig8}(b),  illustrate the
-network lifetime  for different network sizes,  respectively for $Lifetime_{95}$
-and  $Lifetime_{50}$.  Both  figures show  that the  network  lifetime increases
-together with the  number of sensor nodes, whatever the  protocol, thanks to the
-node  density  which  results in  more  and  more  redundant  nodes that  can  be
-deactivated and thus save energy.  Compared to the other approaches, our MuDiLCO
-protocol  maximizes the  lifetime of  the network.   In particular  the  gain in
-lifetime for a  coverage over 95\% is greater than 38\%  when switching from GAF
-to MuDiLCO-3.  The  slight decrease that can be observed  for MuDiLCO-7 in case
-of  $Lifetime_{95}$  with  large  wireless  sensor  networks  results  from  the
-difficulty  of the optimization  problem to  be solved  by the  integer program.
+The next  two figures,  Figures~\ref{fig8}(a) and \ref{fig8}(b),  illustrate the network lifetime  for different network sizes,  respectively for $Lifetime_{95}$ and  $Lifetime_{50}$.  Both  figures show  that the  network  lifetime increases together with the  number of sensor nodes, whatever the  protocol, thanks to the node  density  which  results in  more  and  more  redundant  nodes that  can  be deactivated and thus save energy.  Compared to the other approaches, our MuDiLCO
+protocol  maximizes the  lifetime of  the network.   In particular,  the  gain in lifetime for a  coverage over 95\% is greater than 38\%  when switching from GAF to MuDiLCO-3.  The  slight decrease that can be observed  for MuDiLCO-7 in case of  $Lifetime_{95}$  with  large  wireless  sensor  networks  results  from  the difficulty  of the optimization  problem to  be solved  by the  integer program.

 This  point was  already noticed  in \ref{subsec:EC} devoted  to the
 This  point was  already noticed  in \ref{subsec:EC} devoted  to the

-energy consumption,  since network lifetime and energy  consumption are directly
-linked.
+energy consumption,  since network lifetime and energy  consumption are directly linked.

 
 
 \begin{figure}[h!]
 
 
 \begin{figure}[h!]


@@ -552,30 +518,12 @@ linked.
 \section{Conclusion}
 \label{ch5:sec:04}
 
 \section{Conclusion}
 \label{ch5:sec:04}
 

-We have addressed  the problem of the coverage and of the lifetime optimization in
-wireless  sensor networks.  This is  a key  issue as  sensor nodes  have limited
-resources in terms of memory, energy, and computational power. To cope with this
-problem,  the field  of sensing  is divided  into smaller  subregions  using the
-concept  of divide-and-conquer  method, and  then  we propose  a protocol  which
-optimizes coverage  and lifetime performances in each  subregion.  Our protocol,
-called MuDiLCO (Multiround  Distributed Lifetime Coverage Optimization) combines
-two  efficient   techniques:  network   leader  election  and   sensor  activity
-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.
-
-Simulations  results show the  relevance of  the proposed  protocol in  terms of
-lifetime, coverage  ratio, active  sensors ratio, energy  consumption, execution
-time. Indeed,  when dealing with  large wireless sensor networks,  a distributed
-approach, like  the one we  propose, allows to  reduce the difficulty of  a single
-global optimization problem by partitioning it in many smaller problems, one per
-subregion, that can be solved  more easily. Nevertheless, results also show that
-it is not possible to plan the activity of sensors over too many rounds, because
-the resulting optimization problem leads to too high resolution times and thus to
-an excessive energy consumption.
+We have addressed  the problem of the coverage and of the lifetime optimization in wireless  sensor networks.  This is  a key  issue as  sensor nodes  have limited resources in terms of memory, energy, and computational power. To cope with this problem,  the field  of sensing  is divided  into smaller  subregions  using the concept  of divide-and-conquer  method, and  then  we propose  a protocol  which optimizes coverage  and lifetime performances in each  subregion.  Our protocol,
+called MuDiLCO (Multiround  Distributed Lifetime Coverage Optimization) combines two  efficient   techniques:  network   leader  election  and   sensor  activity 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.
+
+Simulations  results show the  relevance of  the proposed  protocol in  terms of lifetime, coverage  ratio, active  sensors ratio, energy  consumption, execution time. Indeed,  when dealing with  large wireless sensor networks,  a distributed approach, like  the one we  propose, allows to  reduce the difficulty of  a single global optimization problem by partitioning it into many smaller problems, one per subregion, that can be solved  more easily. Nevertheless, results also show that it is not possible to plan the activity of sensors over too many rounds because the resulting optimization problem leads to too high-resolution times and thus to an excessive energy consumption.