Final corrections

[LiCO.git] / PeCO-EO / articleeo.tex

diff --git a/PeCO-EO/articleeo.tex b/PeCO-EO/articleeo.tex
index 9676c99e0504d0ae6ee3a225c2fa56ad1da56aed..1236ff099c10c9c47e98d1bee2ff3ac799292a5f 100644 (file)
--- a/PeCO-EO/articleeo.tex
+++ b/PeCO-EO/articleeo.tex
@@ -15,7 +15,7 @@
 \title{{\itshape Perimeter-based Coverage Optimization \\
   to Improve Lifetime in Wireless Sensor Networks}}
 
 \title{{\itshape Perimeter-based Coverage Optimization \\
   to Improve Lifetime in Wireless Sensor Networks}}
 

-\author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$
+\author{Ali Kadhum Idrees$^{a,b}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$, and Rapha\"el Couturier $^{a}$

   $^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, \\
   University Bourgogne Franche-Comt\'e, Belfort, France}} \\ 
   $^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}}
   $^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, \\
   University Bourgogne Franche-Comt\'e, Belfort, France}} \\ 
   $^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}}


@@ -48,14 +48,14 @@ coverage for WSNs compared to other protocols.
 \label{sec:introduction}
 
 The continuous progress in Micro  Electro-Mechanical Systems (MEMS) and wireless
 \label{sec:introduction}
 
 The continuous progress in Micro  Electro-Mechanical Systems (MEMS) and wireless

-communication hardware has  given rise to the opportunity of using large networks
+communication hardware has given rise to the opportunity of using large networks

 of      tiny       sensors,      called      Wireless       Sensor      Networks
 (WSN)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring
 tasks.   A  WSN  consists  of  small low-powered  sensors  working  together  by
 communicating with one another through multi-hop radio communications. Each node
 can send the data  it collects in its environment, thanks to  its sensor, to the
 of      tiny       sensors,      called      Wireless       Sensor      Networks
 (WSN)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring
 tasks.   A  WSN  consists  of  small low-powered  sensors  working  together  by
 communicating with one another through multi-hop radio communications. Each node
 can send the data  it collects in its environment, thanks to  its sensor, to the

-user by means of  sink nodes. The features of a WSN makes  it suitable for a wide
-range of applications  in areas such as business,  environment, health, industry,
+user by means of sink nodes. The features  of a WSN makes it suitable for a wide
+range of applications in areas  such as business, environment, health, industry,

 military, and so on~\citep{yick2008wireless}.  Typically, a sensor node contains
 three main components~\citep{anastasi2009energy}: a sensing unit able to measure
 physical,  chemical, or  biological  phenomena observed  in  the environment;  a
 military, and so on~\citep{yick2008wireless}.  Typically, a sensor node contains
 three main components~\citep{anastasi2009energy}: a sensing unit able to measure
 physical,  chemical, or  biological  phenomena observed  in  the environment;  a


@@ -65,13 +65,13 @@ communication unit for data transmission and reception.
 The energy needed  by an active sensor node to  perform sensing, processing, and
 communication is provided by a power supply which is a battery. This battery has
 a limited energy provision and it may  be unsuitable or impossible to replace or
 The energy needed  by an active sensor node to  perform sensing, processing, and
 communication is provided by a power supply which is a battery. This battery has
 a limited energy provision and it may  be unsuitable or impossible to replace or

-recharge  in  most applications. Therefore it is necessary  to deploy WSN with
-high density  in order to  increase reliability  and to exploit  node redundancy
-thanks to energy-efficient activity  scheduling approaches.  Indeed, the overlap
-of sensing  areas can be exploited  to schedule alternatively some  sensors in a
-low power sleep mode and thus save  energy. Overall, the main question that must
-be answered is: how is it possible to extend the lifetime coverage of a WSN as long as possible
-while  ensuring  a   high  level  of  coverage?   These  past   few  years  many
+recharge in most applications. Therefore it is necessary to deploy WSN with high
+density in order  to increase reliability and to exploit  node redundancy thanks
+to  energy-efficient activity  scheduling  approaches.  Indeed,  the overlap  of
+sensing areas can  be exploited to schedule alternatively some  sensors in a low
+power sleep mode and  thus save energy. Overall, the main  question that must be
+answered is: how is it possible to extend the lifetime coverage of a WSN as long
+as possible while ensuring a high level  of coverage?  These past few years many

 energy-efficient mechanisms have been suggested  to retain energy and extend the
 lifetime of the WSNs~\citep{rault2014energy}.
 
 energy-efficient mechanisms have been suggested  to retain energy and extend the
 lifetime of the WSNs~\citep{rault2014energy}.
 


@@ -88,13 +88,13 @@ This paper makes the following contributions :
   architecture.
 \item A new  mathematical optimization model is proposed.  Instead  of trying to
   cover a set of specified points/targets as  in most of the methods proposed in
   architecture.
 \item A new  mathematical optimization model is proposed.  Instead  of trying to
   cover a set of specified points/targets as  in most of the methods proposed in

-  the literature, we formulate a mixed-integer program based on the perimeter coverage of
-  each sensor.  The  model involves integer variables to  capture the deviations
-  between  the actual  level  of coverage  and the  required  level.  Hence,  an
-  optimal  schedule will  be  obtained by  minimizing a  weighted  sum of  these
-  deviations.
+  the literature,  we formulate a  mixed-integer program based on  the perimeter
+  coverage of each sensor.  The model  involves integer variables to capture the
+  deviations  between the  actual  level  of coverage  and  the required  level.
+  Hence, an  optimal schedule will be  obtained by minimizing a  weighted sum of
+  these deviations.

 \item Extensive  simulation experiments are  conducted using the  discrete event
 \item Extensive  simulation experiments are  conducted using the  discrete event

-  simulator  OMNeT++, to  demonstrate the  efficiency of  our protocol.  We have
+  simulator OMNeT++,  to demonstrate  the efficiency of  our protocol.   We have

   compared  the  PeCO  protocol  to  two approaches  found  in  the  literature:
   DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to our previous
   protocol DiLCO published in~\citep{Idrees2}. DiLCO  uses the same framework as
   compared  the  PeCO  protocol  to  two approaches  found  in  the  literature:
   DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to our previous
   protocol DiLCO published in~\citep{Idrees2}. DiLCO  uses the same framework as


@@ -125,12 +125,12 @@ to  the objective  of coverage  for a  finite number  of discrete  points called
 targets,   and   barrier  coverage~\citep{HeShibo,kim2013maximum}   focuses   on
 preventing  intruders   from  entering   into  the   region  of   interest.   In
 \citep{Deng2012} authors  transform the  area coverage  problem into  the target
 targets,   and   barrier  coverage~\citep{HeShibo,kim2013maximum}   focuses   on
 preventing  intruders   from  entering   into  the   region  of   interest.   In
 \citep{Deng2012} authors  transform the  area coverage  problem into  the target

-coverage one, taking into account the  intersection points among disks of sensors
-nodes    or   between    disks   of    sensor   nodes    and   boundaries.     In
-\citep{Huang:2003:CPW:941350.941367}  authors prove  that if  the perimeters  of the
-sensors are sufficiently  covered it will be  the case for the  whole area. They
-provide an algorithm in $O(nd~log~d)$  time to compute the perimeter-coverage of
-each sensor. $d$ denotes  the maximum number of sensors that  are neighbors to a
+coverage one, taking into account the intersection points among disks of sensors
+nodes   or    between   disks    of   sensor    nodes   and    boundaries.    In
+\citep{huang2005coverage} authors  prove that if  the perimeters of  the sensors
+are sufficiently covered it will be the case for the whole area. They provide an
+algorithm  in  $O(nd~log~d)$ time  to  compute  the perimeter-coverage  of  each
+sensor.  $d$ denotes  the maximum  number  of sensors  that are  neighbors to  a

 sensor, and  $n$ is the  total number  of sensors in  the network. {\it  In PeCO
   protocol, instead  of determining the level  of coverage of a  set of discrete
   points, our optimization model is  based on checking the perimeter-coverage of
 sensor, and  $n$ is the  total number  of sensors in  the network. {\it  In PeCO
   protocol, instead  of determining the level  of coverage of a  set of discrete
   points, our optimization model is  based on checking the perimeter-coverage of


@@ -162,22 +162,22 @@ algorithms~\citep{ChinhVu,qu2013distributed,yangnovel}  each  sensor decides  of
 its own  activity scheduling after  an information exchange with  its neighbors.
 The main interest of such an approach  is to avoid long range communications and
 thus to reduce the energy dedicated to the communications.  Unfortunately, since
 its own  activity scheduling after  an information exchange with  its neighbors.
 The main interest of such an approach  is to avoid long range communications and
 thus to reduce the energy dedicated to the communications.  Unfortunately, since

-each node has information on its immediate neighbors only  (usually the one-hop
-ones),  it may  make a  bad  decision leading  to a  global suboptimal  solution.
+each node has  information on its immediate neighbors only  (usually the one-hop
+ones),  it may  make a  bad decision  leading to  a global  suboptimal solution.

 Conversely,                                                          centralized
 algorithms~\citep{cardei2005improving,zorbas2010solving,pujari2011high}   always
 Conversely,                                                          centralized
 algorithms~\citep{cardei2005improving,zorbas2010solving,pujari2011high}   always

-provide nearly optimal solutions since  the algorithm has  a global
-view of the whole network. The disadvantage of a centralized method is obviously
-its high cost  in communications needed to  transmit to a single  node, the base
-station which will globally schedule nodes'  activities, data from all the other
-sensor nodes in  the area.  The price  in communications can be  huge since long
-range communications will be needed. In fact  the larger the WSN, the higher the
+provide nearly  optimal solutions since the  algorithm has a global  view of the
+whole network.  The disadvantage of a  centralized method is obviously  its high
+cost in  communications needed to  transmit to a  single node, the  base station
+which will globally  schedule nodes' activities, data from all  the other sensor
+nodes in  the area.  The  price in communications can  be huge since  long range
+communications  will be  needed. In  fact  the larger  the WSN,  the higher  the

 communication  energy  cost.  {\it  In  order  to  be suitable  for  large-scale
 communication  energy  cost.  {\it  In  order  to  be suitable  for  large-scale

-  networks,  in the PeCO  protocol  the area  of interest  is  divided into  several
+  networks, in  the PeCO protocol the  area of interest is  divided into several

   smaller subregions, and in each one, a  node called the leader is in charge of
   smaller subregions, and in each one, a  node called the leader is in charge of

-  selecting the  active sensors for the  current period.  Thus the PeCO  protocol is
-  scalable and a globally distributed method,  whereas it is centralized in each
-  subregion.}
+  selecting the active  sensors for the current period.  Thus  the PeCO protocol
+  is scalable  and a globally distributed  method, whereas it is  centralized in
+  each subregion.}

 
 Various coverage scheduling algorithms have been developed these past few years.
 Many of  them, dealing with  the maximization of the  number of cover  sets, are
 
 Various coverage scheduling algorithms have been developed these past few years.
 Many of  them, dealing with  the maximization of the  number of cover  sets, are


@@ -202,20 +202,20 @@ The  authors   in  \citep{Idrees2}  propose  a   Distributed  Lifetime  Coverage
 Optimization (DiLCO)  protocol, which  maintains the  coverage and  improves the
 lifetime  in WSNs.   It is  an  improved version  of a  research work  presented
 in~\citep{idrees2014coverage}.  First, the area  of interest is partitioned into
 Optimization (DiLCO)  protocol, which  maintains the  coverage and  improves the
 lifetime  in WSNs.   It is  an  improved version  of a  research work  presented
 in~\citep{idrees2014coverage}.  First, the area  of interest is partitioned into

-subregions using a divide-and-conquer method. The DiLCO protocol is then distributed
-on the  sensor nodes  in each  subregion in  a second  step. Hence this protocol
-combines two  techniques: a leader  election in  each subregion, followed  by an
-optimization-based   node  activity   scheduling  performed   by  each   elected
+subregions  using  a  divide-and-conquer  method. The  DiLCO  protocol  is  then
+distributed on the sensor  nodes in each subregion in a  second step. Hence this
+protocol combines two techniques: a  leader election in each subregion, followed
+by  an optimization-based  node activity  scheduling performed  by each  elected

 leader. The proposed DiLCO protocol is  a periodic protocol where each period is
 decomposed into 4  phases: information exchange, leader  election, decision, and
 sensing. The  simulations show that DiLCO  is able to increase  the WSN lifetime
 and provides  improved coverage performance.  {\it  In the PeCO protocol,  a new
   mathematical optimization model is proposed. Instead  of trying to cover a set
 leader. The proposed DiLCO protocol is  a periodic protocol where each period is
 decomposed into 4  phases: information exchange, leader  election, decision, and
 sensing. The  simulations show that DiLCO  is able to increase  the WSN lifetime
 and provides  improved coverage performance.  {\it  In the PeCO protocol,  a new
   mathematical optimization model is proposed. Instead  of trying to cover a set

-  of  specified points/targets  as in  the DiLCO protocol,  we formulate  an integer
-  program based on the perimeter coverage of each sensor. The model involves integer
-  variables to capture  the deviations between the actual level  of coverage and
-  the required level. The idea is that an optimal scheduling will be obtained by
-  minimizing a weighted sum of these deviations.}
+  of specified points/targets as in the  DiLCO protocol, we formulate an integer
+  program based  on the perimeter  coverage of  each sensor. The  model involves
+  integer  variables to  capture  the  deviations between  the  actual level  of
+  coverage and the  required level. The idea is that  an optimal scheduling will
+  be obtained by minimizing a weighted sum of these deviations.}

   
 \section{ The P{\scshape e}CO Protocol Description}
 \label{sec:The PeCO Protocol Description}
   
 \section{ The P{\scshape e}CO Protocol Description}
 \label{sec:The PeCO Protocol Description}


@@ -741,14 +741,14 @@ approach.
 \subsection{Simulation Results}
 
 In  order  to  assess and  analyze  the  performance  of  our protocol  we  have
 \subsection{Simulation Results}
 
 In  order  to  assess and  analyze  the  performance  of  our protocol  we  have

-implemented the PeCO  protocol in OMNeT++~\citep{varga} simulator.   The simulations
-were run  on a DELL laptop  with an Intel Core~i3~2370~M  (1.8~GHz) processor (2
-cores) whose MIPS  (Million Instructions Per Second) rate is  equal to 35330. To
-be consistent  with the  use of  a sensor  node based  on Atmels  AVR ATmega103L
-microcontroller (6~MHz)  having a MIPS rate  equal to 6, the  original execution
-time  on  the  laptop  is multiplied  by  2944.2  $\left(\frac{35330}{2}  \times
-\frac{1}{6} \right)$.  Energy  consumption is calculated according  to the power
-consumption  values,  in  milliWatt  per  second,  given  in  Table~\ref{tab:EC}.
+implemented  the   PeCO  protocol   in  OMNeT++~\citep{varga}   simulator.   The
+simulations were  run on a  DELL laptop  with an Intel  Core~i3~2370~M (1.8~GHz)
+processor (2 cores)  whose MIPS (Million Instructions Per Second)  rate is equal
+to 35330.  To be consistent with  the use of a  sensor node based on  Atmels AVR
+ATmega103L microcontroller (6~MHz)  having a MIPS rate equal to  6, the original
+execution  time on  the laptop  is multiplied  by 2944.2  $\left(\frac{35330}{2}
+\times \frac{1}{6} \right)$.  Energy consumption  is calculated according to the
+power consumption values, in milliWatt  per second, given in Table~\ref{tab:EC},

 based on the energy model proposed in \citep{ChinhVu}.
 
 \begin{table}[h]
 based on the energy model proposed in \citep{ChinhVu}.
 
 \begin{table}[h]


@@ -780,7 +780,7 @@ consuming and more efficient, or implement a lightweight heuristic. For example,
 for  a WSN  of 200  sensor nodes,  a leader  node has  to deal  with constraints
 induced  by about  12 sensor  nodes.  In  that case,  to solve  the optimization
 problem  a memory  consumption of  more  than 1~MB  can be  observed with  GLPK,
 for  a WSN  of 200  sensor nodes,  a leader  node has  to deal  with constraints
 induced  by about  12 sensor  nodes.  In  that case,  to solve  the optimization
 problem  a memory  consumption of  more  than 1~MB  can be  observed with  GLPK,

-whereas less than 300~kB would be needed with CPLEX.
+whereas less than 300~KB would be needed with CPLEX.

 
 Besides  PeCO,   three  other  protocols   will  be  evaluated   for  comparison
 purposes. The first one, called DESK,  is a fully distributed coverage algorithm
 
 Besides  PeCO,   three  other  protocols   will  be  evaluated   for  comparison
 purposes. The first one, called DESK,  is a fully distributed coverage algorithm


@@ -789,17 +789,17 @@ 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
 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 the 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
+in~\citep{idrees2014coverage}. Let us  notice that the 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
 configuration producing  the best results for  DiLCO. Of course, this  number of

-subregions should be adapted according to the  size of the area  of interest and
+subregions should 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
 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. The DiLCO protocol tries to satisfy the coverage of
-a set of primary  points, whereas the objective of the PeCO protocol is  to reach a desired
-level of coverage for each sensor perimeter. In our experimentations, we chose a
-level of coverage equal to one ($l=1$).
+activated  in each  sensing  phase.  The DiLCO  protocol  tries  to satisfy  the
+coverage of a set of primary points,  whereas the objective of the PeCO protocol
+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{Coverage Ratio}
 
 
 \subsubsection{Coverage Ratio}
 


@@ -807,9 +807,9 @@ 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
 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  and  PeCO protocols  put more  redundant
-sensors to  sleep  status  (which slightly  decreases the  coverage  ratio), while  the two  other
-protocols  activate more  sensor nodes.  Later, when  the number  of periods  is
+the beginning the  DiLCO and PeCO protocols put more  redundant sensors to sleep
+status  (which slightly  decreases  the  coverage ratio),  while  the two  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 greater than 50\% for longer periods (15 more compared to
 DiLCO, 40 more compared to DESK). The  energy saved by PeCO in the early periods
 beyond~70, it  clearly appears that  PeCO provides  a better coverage  ratio and
 keeps a coverage ratio greater than 50\% for longer periods (15 more compared to
 DiLCO, 40 more compared to DESK). The  energy saved by PeCO in the early periods


@@ -848,7 +848,7 @@ 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
 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 the PeCO protocol is the most
+$Lifetime_{95}$ and $Lifetime_{50}$.  The results show  that the 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
 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


@@ -872,7 +872,7 @@ size is the lowest with PeCO.
 
 We observe the  superiority of both the PeCO and DiLCO  protocols in comparison with
 the   two   other  approaches   in   prolonging   the  network   lifetime.    In
 
 We observe the  superiority of both the 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
+Figures~\ref{figure8}(a) and  (b), $Lifetime_{95}$  and $Lifetime_{50}$ 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 larger for the DiLCO and
 PeCO protocols.  For  instance, for a network of 300~sensors  and coverage ratio
 different  network  sizes.  As  can  be  seen  in  these figures,  the  lifetime
 increases with the size of the network,  and it is clearly larger for the DiLCO and
 PeCO protocols.  For  instance, for a network of 300~sensors  and coverage ratio


@@ -916,17 +916,17 @@ sizes.
 
 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
 
 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 also limits
-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 ahigh  coverage ratio is reached,  but a large
-number  of  sensors are  activated  to  achieve  this goal.   Therefore the  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.
+hand,  the choice  of $\beta  \gg \alpha$  prevents the  overcoverage, and  also
+limits 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
+$Lifetime_{50}$ 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 a high coverage ratio is
+reached,  but a  large number  of sensors  are activated  to achieve  this goal.
+Therefore  the  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.

 
 %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 $Lifetime_{95}$.
 
 
 %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 $Lifetime_{95}$.
 


@@ -973,18 +973,17 @@ 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
 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 the  PeCO protocol  using a
+views.  Finally, it would be interesting  to implement the PeCO protocol using a

 sensor-testbed to evaluate it in real world applications.
 
 sensor-testbed to evaluate it in real world applications.
 

-
-\subsection*{Acknowledgements}
+\subsection*{Acknowledgments}

 The  authors  are   deeply  grateful  to  the  anonymous   reviewers  for  their
 constructive advice,  which improved the  technical quality  of the paper.  As a
 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
+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
 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).
-
+(contract ANR-11-LABX-01-01).  
+ 

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