-The limited resources in WSNs have been addressed, and one of the main challenges in WSNs is the limited power resource. For this reason, there are extensive researches have been proposed in order to prolong the network lifetime by means of designing and implementing energy-efficient protocols. The reason for these large number of proposed protocols to maximize the network lifetime is the difficulty and sometime impossibility to replace or recharge the batteries of wireless sensor nodes especially in the large WSN and hostile environment. The authors have been defined the network lifetime in different contexts and use it as a metric to evaluate the performance of their protocols. Based on the previous proposed works in prolonging the network lifetime;Various definitions exist for the lifetime of a sensor network~\cite{ref92,ref93} such as:~\textbf{(i)} is the time spent by WSN until the death of the first wireless sensor node ( or cluster head ) in the network due to its energy depletion.~\textbf{(ii)} is the time spent by WSN and has at least a specific set $\beta$ of alive sensor nodes in WSN.~\textbf{(iii)} is the time spent by WSN until the death of all wireless sensor nodes in WSN because they have been depleted of their energy.~\textbf{(iv)} for k-coverage is the time spent by WSN in covering the area of interest by at least $k$ sensor nodes.~\textbf{(v)} for 100 $\%$ coverage is the time spent by WSN in covering each target or the whole area by at least one sensor node.~\textbf{(vi)} for $\alpha$-coverage: the total time by which at least $\alpha$ part of the sensing field is covered by at least one node; or is the time spent by WSN until the coverage ratio becomes less than a predetermined threshold $\alpha$.
-~\textbf{(vii)} the working time spent by the system before either the coverage ratio or delivery ratio become less than a predetermined threshold.~\textbf{(viii)} the number of the successful data gathering trips.~\textbf{(ix)} the number of sent packets.~\textbf{(x)} the percentage of wireless sensor nodes that have a route to the sink.~\textbf{(xi)} the prediction of the total period of time during which the probability of ensuring the connectivity and k-coverage concurrently is at least $\alpha$.~\textbf{(xii)} the time spent by WSN until loosing the connectivity or the coverage.~\textbf{(xiii)} the time spent by WSN until acceptable event detection ratio is not acceptable in the network.~\textbf{(xiv)} the time spent by WSN and the application requirement has been met.
+\indent The limited resources in WSNs have been addressed, and one of the main challenges in WSNs is the limited power resource. For this reason, extensive researches have been proposed in order to prolong the network lifetime by means of designing and implementing energy-efficient protocols. The reason for these large number of proposed protocols to maximize the network lifetime is the difficulty and sometime impossibility to replace or recharge the batteries of wireless sensor nodes especially in the large WSN and hostile environment.
+
+\indent The authors have defined the network lifetime in different contexts and use it as a metric to evaluate the performance of their protocols. Based on the previous proposed works in prolonging the network lifetime, Various definitions are exist for the lifetime of a sensor network~\cite{ref92,ref93} such as:
+%~\textbf{(i)}
+\begin{enumerate} [i.]
+
+\item The time spent by WSN until the death of the first wireless sensor node ( or cluster head ) in the network due to its energy depletion~\cite{ref162,ref163}.
+\item The time spent by WSN and has at least a specific set $\beta$ of alive sensor nodes in WSN~\cite{ref164,ref165}.
+\item The time spent by WSN until the death of all wireless sensor nodes in WSN because they have been depleted their energy~\cite{ref166}.
+\item For k-coverage, is the time spent by WSN in covering the area of interest by at least $k$ sensor nodes~\cite{DESK}.
+\item For 100 $\%$ coverage is the time spent by WSN in covering each target or the whole area by at least one sensor node~\cite{ref167}.
+\item For $\alpha$-coverage: the total time by which at least $\alpha$ part of the sensing field is covered by at least one node~\cite{ref168}; or is the time spent by WSN until the coverage ratio becomes less than a predetermined threshold $\alpha$~\cite{ref169}.
+\item The working time spent by the system before either the coverage ratio or delivery ratio become less than a predetermined threshold~\cite{ref170}.
+\item The number of the successful data gathering trips~\cite{ref173}.
+\item The number of sent packets~\cite{ref174}.
+\item The percentage of wireless sensor nodes that have a route to the sink~\cite{ref170}.
+\item The prediction of the total period of time during which the probability of ensuring the connectivity and k-coverage concurrently is at least $\alpha$~\cite{ref175}.
+\item The time spent by WSN until loosing the connectivity or the coverage~\cite{ref171}.
+\item The time spent by WSN until acceptable event detection ratio is not acceptable in the network~\cite{ref166}.
+\item The time during which the application requirement is satisfied~\cite{ref172}.
+\end{enumerate}
+
+\indent According to the above definitions for network lifetime, there is no universal definition reflects the requirements of each application and the effects of the environment. In real WSN, the network lifetime reflects a set of a particular circumstances of the environment. Accordingly, the current definitions are applicable for the WSNs that meet a particular conditions. However, many more parameters, which are affecting on the network lifetime of WSN such as~\cite{ref92}: heterogeneity, node mobility, topology changes, application characteristics, quality of service, and completeness.
