\item \textbf{Asynchronous Schemes:} The time among the wireless sensor nodes does not need synchronization. The wireless sensor node wakes up to send packets without taking into account whether the receiving sensor nodes are waked up and ready to receive. These schemes do not need time synchronization which consumes energy~\cite{ref74}. They do not need to exploit the limited resources (processing, memory, and radio) of the sensor nodes because there are no shared wake up schedules to be exchanged or saved in the memory. Therefore, exchanging the packets among the wireless sensor nodes, which are not aware of each other's wake-up schedules have considered as a major challenge in asynchronous schemes. These schemes can been categorized into three groups~\cite{ref57}:
\begin{enumerate} [(A)]
-\item Transmitter-initiated: a special frame is sent by the transmitting sensor node to inform the receiving sensor node that it has a data frame to send. If the receiving sensor node is hearing the special frame during one of its wake up intervals, it waits for sending the data frame. The major advantage of these schemes is the low requirement of the memory and processing whilst the major disadvantages are low-duty-cycle and the non-deterministic sleep latency.
+\item Transmitter-initiated: a special frame is sent by the transmitting sensor node to inform the receiving sensor node that it has a data frame to send. If the receiving sensor node is hearing the special frame during one of its wake up intervals, the receiving node waits for sending the data frame to receive it. The major advantage of these schemes is the low requirement of the memory and processing whilst the major disadvantages are low-duty-cycle and the non-deterministic sleep latency.
%Examples on these schemes in~\cite{ref75,ref76}.
-\item Receiver-initiated: during each wake-up time interval of receiving wireless sensor node, it sends a special frame to inform the senders, which are waked up and ready to receive the data frames. When the sensor node has a packet to send, it wakes up and wait receiving special frame from neighboring sensor nodes. The waiting sensor node is sending its data frame at the moment of receiving the special frame from the neighbor sensor node. The main advantages are a low processing and storage requirement whilst the disadvantage of these schemes are the low performance during low and high duty cycle, as well as their stochastic sleep latency.
+\item Receiver-initiated: during each wake-up time interval of receiving wireless sensor node, it sends a special frame to inform the senders, which of senders are waked up and ready to receive the data frames. When the sensor node has a packet to send, it wakes up and wait receiving special frame from neighboring sensor nodes. The waiting sensor node is sending its data frame at the moment of receiving the special frame from the neighbor sensor node. The main advantages are a low processing and storage requirement whilst the disadvantage of these schemes are the low performance during low and high duty cycle, as well as their stochastic sleep latency.
%The works that proposed in~\cite{ref77,ref78} represents some instances for these approaches.
\item Combinatorial or random: during the wake-up duration, one or more data packets can be exchanged among the wireless sensor nodes. The exchanged data packets among the wireless sensor nodes are increased as the wake-up time increased. In these schemes, the special frames are removed and the energy consumption is decreased. A common disadvantage of these schemes is the non-deterministic sleep
\begin{enumerate}[(i)]
\item \textbf{Area coverage}~\cite{ref97,ref101} where every point inside an area has to be monitored. The work in this dissertation deals with this type of coverage.
\item \textbf{Target coverage}~\cite{ref98,ref101} where the main objective is to cover only a finite number of discrete points called targets.
-\item \textbf{Barrier coverage}~\cite{ref99,ref100} to prevent intruders from entering into the region of interest.
+\item \textbf{Barrier coverage}~\cite{ref99,ref100} where the main goal is to detect targets as they cross a barrier, which is usually a long belt region such as intrusion detection and border surveillance applications.
\end{enumerate}
\indent The sensing quality and capability can be assessed by a sensing coverage models due to discovering the mathematical relationship between the point and the sensor node in the sensing field. In the real world, there are sometimes obstacles in the environment that affect the sensing range \cite{ref104}. Therefore, several sensing coverage models have been suggested according to application requirements and physical working environment such as~\cite{ref103}: boolean sector coverage, boolean disk coverage, attenuated disk coverage, truncated attenuated disk, detection coverage, and estimation coverage Models. However, two main sensing coverage models have been used for simulating the performance of wireless sensors~\cite{ref104,ref105,ref106}:
\end{enumerate}
-The coverage protocols proposed in this dissertation use the binary disc sensing model as a sensing coverage model for each wireless sensor node in WSN because we consider for each sensor a set of primary points and we assume that the sensing disk defined by a sensor is covered if all the primary points of this sensor are covered.
+The coverage protocols proposed in this dissertation use the binary disc sensing model as a sensing coverage model for each wireless sensor node in WSN because it is a widely used in the literatures, as well as it is easy to formulate the linear programs with it. While the probabilistic model is more complex and it is difficult to use it to create integer programs.
+
%The coverage protocols have proposed in this dissertation use the binary disc sensing model as a sensing coverage model for each wireless sensor node in WSN.
\item $\textbf{Activity based Scheduling}$ is to schedule the activation and deactivation of sensor nodes during the network lifetime. The basic objective is to decide which sensors are in what states (active or sleeping mode) and for how long, so that the application coverage requirement can be guaranteed and the network lifetime can be prolonged. Various centralized, distributed, and localized approaches have been proposed for activity scheduling. In distributed algorithms, each node in the network autonomously makes decisions on whether to turn on or turn off itself only using local neighbor information. In centralized algorithms, a central controller (a node or base station) informs every sensor of the time intervals to be activated.
+This dissertation deals with activity based scheduling to ensure the best coverage in WSNs.
\end{enumerate}
\label{RDM}
\end{figure}
-\indent In this model, the radio consumes energy to execute the transmitter and the power amplifier. The receiver circuitry consumes energy to run the radio electronics, as described in figure~\ref{RDM}. The channel model can be either free space ($d^2$ power loss) or multipath fading ($d^4$ power loss), based on the distance between the transmitter and receiver. This power loss can be controlled by setting the power amplifier so that if the distance is less than a threshold, the free space ($\varepsilon_{fs}$) model is used (i.e., $\varepsilon_{amp}$ = $\varepsilon_{fs}$); Otherwise, the multipath ($\varepsilon_{mp}$) model is used (i.e., $\varepsilon_{amp}$ = $\varepsilon_{mp}$). Therefore, to transmit a k-bit packet with a distance d, the radio expends
+\indent In this model, the radio consumes energy to execute the transmitter and the power amplifier. The receiver circuitry consumes energy to run the radio electronics, as described in figure~\ref{RDM}. The channel model can be either free space ($d^2$ power loss) or multipath fading ($d^4$ power loss), based on the distance between the transmitter and receiver. This power loss can be controlled by setting the power amplifier so that if the distance is less than a threshold ($d_0$), the free space ($\varepsilon_{fs}$) model is used (i.e., $\varepsilon_{amp}$ = $\varepsilon_{fs}$); Otherwise, the multipath ($\varepsilon_{mp}$) model is used (i.e., $\varepsilon_{amp}$ = $\varepsilon_{mp}$). Therefore, to transmit a K-bit packet with a distance d, the radio expends
\begin{equation}
-E_{tx}\left(k,d \right) = \left \{
+E_{tx}\left(K,d \right) = \left \{
\begin{array}{l l}
- \emph{ kE_{elec} + k \varepsilon_{fs}d^2} & \mbox{if $d < d_0$} \\
- \emph{ kE_{elec} + k \varepsilon_{mp}d^4} & \mbox{if $d \geqslant d_0$}\\
+ \emph{ KE_{elec} + K \varepsilon_{fs}d^2} & \mbox{if $d < d_0$} \\
+ \emph{ KE_{elec} + K \varepsilon_{mp}d^4} & \mbox{if $d \geqslant d_0$}\\
\end{array} \right.
\label{eq3-ch1}
\end{equation}
-As well as to receive a k-bit packet, the radio expends
+As well as to receive a K-bit packet, the radio expends
\begin{equation}
- E_{rx}\left(k,d \right) = \emph{ kE_{elec} }.
+ E_{rx}\left(k,d \right) = \emph{ KE_{elec} }.
\label{eq4-ch1}
\end{equation}
The typical parameters are set as: $E_{elec}$ = 50 nJ/bit, $\varepsilon_{fs}$ = 10 pJ/bit/$m^2$, $\varepsilon_{mp}$ = 0.0013 pJ/bit/$m^4$. In addition, the energy for data aggregation is set as $E_{DA}$ = 5 nJ/bit.
\indent The radio energy dissipation model considers only the energy consumed by the communication part of the sensor node. However, in order to achieve a more accurate model, it is necessary to take into account the energy consumed by other parts inside the sensor node such as computation unit and sensing unit.
-
+In this dissertation, we developed another energy consumption model that proposed by~\cite{DESK} and based on \cite{ref112}.
%\subsection{Our Energy Consumption Model:}
%\label{ch1:sec9:subsec2}
+
\section{Conclusion}
\label{ch1:sec:10}
