\item Sensors scheduling algorithm implementation, i.e. centralized or
distributed/localized algorithms.
\item The objective of sensor coverage, i.e. to maximize the network lifetime or
- to minimize the number of sensors during the sensing period.
+ to minimize the number of sensors during a sensing round.
\item The homogeneous or heterogeneous nature of the nodes, in terms of sensing
or communication capabilities.
\item The node deployment method, which may be random or deterministic.
responsibility of sensing and communication.
Some other approaches (outside the scope of our work) do not consider a
-synchronized and predetermined period of time where the sensors are active or
-not. Indeed, each sensor maintains its own timer and its wake-up time is
-randomized \cite{Ye03} or regulated \cite{cardei2005maximum} over time.
+synchronized and predetermined time-slot where the sensors are active or not.
+Indeed, each sensor maintains its own timer and its wake-up time is randomized
+\cite{Ye03} or regulated \cite{cardei2005maximum} over time.
The MuDiLCO protocol (for Multiround Distributed Lifetime Coverage Optimization
protocol) presented in this paper is an extension of the approach introduced
the residual energy levels and feedback from the sink for scheduling the
activity of their neighbors. This feedback mechanism reduces the randomness in
scheduling that would otherwise occur due to the absence of location
-information. In \cite{ChinhVu}, the author have proposed a novel distributed
+information. In \cite{ChinhVu}, the author have proposed a novel distributed
heuristic, called Distributed Energy-efficient Scheduling for k-coverage (DESK),
which ensures that the energy consumption among the sensors is balanced and the
lifetime maximized while the coverage requirement is maintained. This heuristic
% set cover responsible for the sensing task.
%For each round a set of sensors (said a cover set) is responsible for the sensing task.
-This protocol is reliable against an unexpected node failure, 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.
+%This protocol is reliable against an unexpected node failure, because it works in periods.
%%RC : why? I am not convinced
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,
will be temporarily affected: only during the period of sensing until a new
period starts.
%%RC so if there are at least one failure per period, the coverage is bad...
+%%MS if we want to be reliable against many node failures we need to have an
+%% overcoverage...
The energy consumption and some other constraints can easily be taken into
account, since the sensors can update and then exchange their information
%%RC why W_{\theta} is not defined (only one sentence)? How to define in practice Wtheta and Wu?
-
\begin{itemize}
\item $X_{t,j}$: indicates whether or not the sensor $j$ is actively sensing
during the round $t$ (1 if yes and 0 if not);
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 $W_{\theta}$ very
+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 $W_{\theta}$ very
large compared to $W_U$.
%The Active-Sleep packet includes the schedule vector with the number of rounds that should be applied by the receiving sensor node during the sensing phase.
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, the general case will be
-denoted by MuDiLCO-T and we will make comparisons with two other methods. The
-first method, called DESK and proposed by \cite{ChinhVu}, is a full distributed
-coverage algorithm. The second method, called GAF~\cite{xu2001geography},
-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.
+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{ChinhVu},
+is a full distributed coverage algorithm. The second method, called
+GAF~\cite{xu2001geography}, 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.
Some preliminary experiments were performed to study the choice of the number of
subregions which subdivide 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-T protocol more robust against random
-network disconnection due to node failures. However, too much subdivisions
+lifetime. Moreover, it makes the MuDiLCO protocol more robust against random
+network disconnection due to node failures. However, too much subdivisions
reduces the advantage of the optimization. In fact, there is a balance between
the benefit from the optimization and the execution time needed to solve
-it. Therefore, we have set the number of subregions to 16 rather than 32.
+it. Therefore, we have set the number of subregions to 16 rather than 32.
\subsection{Energy model}
seen as the total energy consumed by the sensors during the $Lifetime_{95}$ or
$Lifetime_{50}$ divided by the number of rounds. EC can be computed as
follows:
- \begin{equation*}
-\scriptsize
-\mbox{EC} = \frac{\sum\limits_{m=1}^{M_L} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +
- \sum\limits_{t=1}^{T_L} \left( E^{a}_t+E^{s}_t \right)}{T_L},
-\end{equation*}
+ % New version with global loops on period
+ \begin{equation*}
+ \scriptsize
+ \mbox{EC} = \frac{\sum\limits_{m=1}^{M_L} \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},
+ \end{equation*}
+
+
+% Old version with loop on round outside the loop on period
+% \begin{equation*}
+% \scriptsize
+% \mbox{EC} = \frac{\sum\limits_{m=1}^{M_L} \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T_L} \left( E^{a}_t+E^{s}_t \right)}{T_L},
+% \end{equation*}
+
+% Ali version
%\begin{equation*}
%\scriptsize
%\mbox{EC} = \frac{\mbox{$\sum\limits_{d=1}^D E^c_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D %E^l_d$}}{\mbox{$D$}} + \frac{\mbox{$\sum\limits_{d=1}^D E^a_d$}}{\mbox{$D$}} + %\frac{\mbox{$\sum\limits_{d=1}^D E^s_d$}}{\mbox{$D$}}.
%\end{equation*}
-where $M_L$ and $T_L$ are respectively the number of periods and rounds during
-$Lifetime_{95}$ or $Lifetime_{50}$. The total energy consumed by the sensors
-(EC) comes through taking into consideration four main energy factors. The first
-one , denoted $E^{\scriptsize \mbox{com}}_m$, represent the energy consumption
-spent by all the nodes for wireless communications during period $m$.
-$E^{\scriptsize \mbox{list}}_m$, the next factor, corresponds to the energy
-consumed by the sensors in LISTENING status before receiving the decision to go
-active or sleep in period $m$. $E^{\scriptsize \mbox{comp}}_m$ refers to the
-energy needed by all the leader nodes to solve the integer program during a
-period. Finally, $E^a_t$ and $E^s_t$ indicate the energy consummed by the whole
-network in round $t$.
+% Old version -> where $M_L$ and $T_L$ are respectively the number of periods and rounds during
+%$Lifetime_{95}$ or $Lifetime_{50}$.
+% New version
+where $M_L$ is the number of periods and $T_m$ the number of rounds in a
+period~$m$, both during $Lifetime_{95}$ or $Lifetime_{50}$. The total energy
+consumed by the sensors (EC) comes through taking into consideration four main
+energy factors. The first one , denoted $E^{\scriptsize \mbox{com}}_m$,
+represent the energy consumption spent by all the nodes for wireless
+communications during period $m$. $E^{\scriptsize \mbox{list}}_m$, the next
+factor, corresponds to the energy consumed by the sensors in LISTENING status
+before receiving the decision to go active or sleep in period $m$.
+$E^{\scriptsize \mbox{comp}}_m$ refers to the energy needed by all the leader
+nodes to solve the integer program during a period. Finally, $E^a_t$ and $E^s_t$
+indicate the energy consummed by the whole network in round $t$.
%\item {Network Lifetime:} we have defined the network lifetime as the time until all
%nodes have been drained of their energy or each sensor network monitoring an area has become disconnected.
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
-which is a little bit better than the one of MuDiLCO-T.
-%%RC : need to uniformize MuDiLCO or MuDiLCO-T?
-
+which is a little bit better than the one of MuDiLCO.
+%%RC : need to uniformize MuDiLCO or MuDiLCO-T?
+%%MS : MuDiLCO everywhere
%%RC maybe increase the size of the figure for the reviewers, no?
-
-This is due to the fact
-that in comparison with MuDiLCO-T that 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 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-T
-saves more energy, with less dead nodes, at most for several rounds, and thus
-should extend the network lifetime.
+This is due to the fact that in comparison with MuDiLCO that 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
+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
+rounds, and thus should extend the network lifetime.
\begin{figure}[ht!]
\centering
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 status, whereas
-MuDiLCO-T clearly outperforms them with only 24.8\% of active nodes. After the
-thirty fifth round, MuDiLCO-T exhibits larger number 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 number 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-T activates the available
+activated many nodes at the beginning. Anyway, MuDiLCO activates the available
nodes in a more efficient manner.
\begin{figure}[ht!]
per round for 150 deployed nodes. This figure gives the breakpoint for each of
the methods. DESK stops first, after around 45~rounds, because it consumes the
more energy by turning on a large number of redundant nodes during the sensing
-phase. GAF stops secondly for the same reason than DESK. MuDiLCO-T overcomes
+phase. GAF stops secondly for the same reason than DESK. MuDiLCO overcomes
DESK and GAF because the optimization process distributed on several subregions
leads to coverage preservation and so extends the network lifetime. Let us
emphasize that the simulation continues as long as a network in a subregion is
\label{fig7}
\end{figure}
-The results show that MuDiLCO-T is the most competitive from the energy
+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
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 result in more and more redundant nodes that can be
-deactivated and thus save energy. Compared to the other approaches, our
-MuDiLCO-T 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 bee observed for MuDiLCO-7
-in case of $Lifetime_{95}$ with large wireless sensor networks results from the
+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 bee 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 subsection \ref{subsec:EC} devoted to the
energy consumption, since network lifetime and energy consumption are directly
\label{fig8}
\end{figure}
-% By choosing the best suited nodes, for each round, by optimizing the coverage and lifetime of the network to cover the area of interest with a maximum number rounds and by letting the other nodes sleep in order to be used later in next rounds, our MuDiLCO-T protocol efficiently prolonges the network lifetime.
+% By choosing the best suited nodes, for each round, by optimizing the coverage and lifetime of the network to cover the area of interest with a maximum number rounds and by letting the other nodes sleep in order to be used later in next rounds, our MuDiLCO protocol efficiently prolonges the network lifetime.
-%In Figure~\ref{fig8}, Comparison shows that our MuDiLCO-T protocol, which are used distributed optimization on the subregions with the ability of producing T rounds, is the best one because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. It also means that distributing the protocol in each sensor node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
+%In Figure~\ref{fig8}, Comparison shows that our MuDiLCO protocol, which are used distributed optimization on the subregions with the ability of producing T rounds, is the best one because it is robust to network disconnection during the network lifetime as well as it consume less energy in comparison with other approaches. It also means that distributing the protocol in each sensor node and subdividing the sensing field into many subregions, which are managed independently and simultaneously, is the most relevant way to maximize the lifetime of a network.
%We see that our MuDiLCO-7 protocol results in execution times that quickly become unsuitable for a sensor network as well as the energy consumption seems to be huge because it used a larger number of rounds T during performing the optimization decision in the subregions, which is led to decrease the network lifetime. On the other side, our MuDiLCO-1, 3, and 5 protocol seems to be more efficient in comparison with other approaches because they are prolonged the lifetime of the network more than DESK and GAF.
