-Below, we describe each phase in more details.
-
-\subsection{Information Exchange Phase}
-
-Each sensor node $j$ sends its position, remaining energy $RE_j$, and the number
-of neighbors $NBR_j$ to all wireless sensor nodes in its subregion by using an
-INFO packet (containing information on position coordinates, current remaining
-energy, sensor node ID, number of its one-hop live neighbors) and then waits for
-packets sent by other nodes. After that, each node will have information about
-all the sensor nodes in the subregion. In our model, the remaining energy
-corresponds to the time that a sensor can live in the active mode.
-
-%\subsection{\textbf Working Phase:}
-
-%The working phase works in rounding fashion. Each round include 3 steps described as follow :
-
-\subsection{Leader Election phase}
-
-This step consists in choosing the Wireless Sensor Node Leader (WSNL),
-which will be responsible for executing the coverage algorithm. Each
-subregion in the area of interest will select its own WSNL
-independently for each period. All the sensor nodes cooperate to
-elect a WSNL. The nodes in the same subregion will select the leader
-based on the received informations from all other nodes in the same
-subregion. The selection criteria are, in order of importance: larger
-number of neighbors, larger remaining energy, and then in case of
-equality, larger index. Observations on previous simulations suggest
-to use the number of one-hop neighbors as the primary criterion to
-reduce energy consumption due to the communications.
-
-%the more priority selection factor is the number of $1-hop$ neighbors, $NBR j$, which can minimize the energy consumption during the communication Significantly.
-%The pseudo-code for leader election phase is provided in Algorithm~1.
-
-%Where $E_{th}$ is the minimum energy needed to stay active during the sensing phase. As shown in Algorithm~1, the more priority selection factor is the number of $1-hop$ neighbours, $NBR j$, which can minimize the energy consumption during the communication Significantly.
-
-\subsection{Decision phase}
-
-Each WSNL will solve an integer program to select which cover sets
-will be activated in the following sensing phase to cover the
-subregion to which it belongs. The integer program will produce $T$
-cover sets, one for each round. The WSNL will send an Active-Sleep
-packet to each sensor in the subregion based on the algorithm's
-results, indicating if the sensor should be active or not in each
-round of the sensing phase. The integer program is based on the model
-proposed by \cite{pedraza2006} with some modification, where the
-objective is to find a maximum number of 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 activation of
-sensor $j$ during the 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.
-
-%parler de la limite en energie Et pour un round
-
-For a primary point $p$, let $\alpha_{j,p}$ denote the indicator
-function of whether the point $p$ is covered, that is:
+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. The
+duration of the rounds is a predefined parameter. Round duration should be long
+enough to hide the system control overhead and short enough to minimize the
+negative effects in case of node failures.
+
+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.
+
+At the beginning of each period, each sensor which has enough remaining energy
+($RE_j$) to be alive during at least one round ($E_{R}$ is the amount of energy
+required to be alive during one round) sends (line 3 of
+Algorithm~\ref{alg:MuDiLCO}) its position, remaining energy $RE_j$, and the
+number of neighbors $NBR_j$ to all wireless sensor nodes in its subregion by
+using an INFO packet (containing information on position coordinates, current
+remaining energy, sensor node ID, number of its one-hop live neighbors) and then
+waits for packets sent by other nodes (line 4).
+
+After that, each node will have information about all the sensor nodes in the
+subregion. The nodes in the same subregion will select (line 5) a Wireless
+Sensor Node Leader (WSNL) based on the received information from all other nodes
+in the same subregion. The selection criteria are, in order of importance:
+larger number of neighbors, larger remaining energy, and then in case of
+equality, larger index. Observations on previous simulations suggest to use the
+number of one-hop neighbors as the primary criterion to reduce energy
+consumption due to the communications.
+
+%Each WSNL will solve an integer program to select which cover
+% sets will be activated in the following sensing phase to cover the subregion
+% to which it belongs. $T$ cover sets will be produced, one for each round. The
+% WSNL will send an Active-Sleep packet to each sensor in the subregion based on
+% the algorithm's results, indicating if the sensor should be active or not in
+% each round of the sensing phase.
+\subsection{Multiround Optimization model}
+\label{mom}
+
+As shown in Algorithm~\ref{alg:MuDiLCO} at line 8, the leader (WNSL) will
+execute an optimization algorithm based on an integer program to select the
+cover sets to be activated in the following sensing phase to cover the subregion
+to which it belongs. $T$ cover sets will be produced, one for each round. The
+WSNL will send an Active-Sleep packet to each sensor in the subregion based on
+the algorithm's results (line 10), indicating if the sensor should be active or
+not in each round of the sensing phase.
+
+The integer program is based on the model proposed by \cite{pedraza2006} with
+some modifications, where the objective is to find a maximum number of 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.
+\textcolor{black}{Note that the proposed integer program is an
+ extension of the one formulated in~\cite{idrees2015distributed}, variables are now indexed in
+ addition with the number of round $t$.}
+
+For a primary point $p$, let $\alpha_{j,p}$ denote the indicator function of
+whether the point $p$ is covered, that is:
