\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 (UBFC), Belfort, France}} \\
+ University Bourgogne Franche-Comt\'e, Belfort, France}} \\
$^{b}${\em{Department of Computer Science, University of Babylon, Babylon, Iraq}}
}
A WSN consisting of $J$ stationary sensor nodes randomly and uniformly
distributed in a bounded sensor field is considered. The wireless sensors are
deployed in high density to ensure initially a high coverage ratio of the area
-of interest. We assume that all the sensor nodes are homogeneous in terms of
+of interest. All the sensor nodes are supposed to be homogeneous in terms of
communication, sensing, and processing capabilities and heterogeneous from the
energy provision point of view. The location information is available to a
sensor node either through hardware such as embedded GPS or location discovery
-algorithms. We consider a Boolean disk coverage model, which is the most widely
-used sensor coverage model in the literature, and all sensor nodes have a
+algorithms. A Boolean disk coverage model, which is the most widely used sensor
+coverage model in the literature, is considered and all sensor nodes have a
constant sensing range $R_s$. Thus, all the space points within a disk centered
at a sensor with a radius equal to the sensing range are said to be covered by
-this sensor. We also assume that the communication range $R_c$ satisfies $R_c
-\geq 2 \cdot R_s$. In fact, \citet{Zhang05} proved that if the transmission
+this sensor. We also assume that the communication range $R_c$ satisfies $R_c
+\geq 2 \cdot R_s$. In fact, \citet{Zhang05} proved that if the transmission
range fulfills the previous hypothesis, the complete coverage of a convex area
implies connectivity among active nodes.
sensor~$j$.
\end{itemize}
$I_j$ refers to the set of coverage intervals which have been defined according
-to the method introduced in subsection~\ref{CI}. For a coverage interval $i$,
+to the method introduced in Subsection~\ref{CI}. For a coverage interval $i$,
let $a^j_{ik}$ denote the indicator function of whether sensor~$k$ is involved
in coverage interval~$i$ of sensor~$j$, that is:
\begin{equation}
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}
+consumption values, in milliWatt per second, given in Table~\ref{tab:EC}.
based on the energy model proposed in \citep{ChinhVu}.
\begin{table}[h]
\label{tab:EC}
\begin{tabular}{|l||cccc|}
\hline
- {\bf Sensor status} & MCU & Radio & Sensor & {\it Power (mW)} \\
+ {\bf Sensor status} & MCU & Radio & Sensing & {\it Power (mW)} \\
\hline
LISTENING & On & On & On & 20.05 \\
ACTIVE & On & Off & On & 9.72 \\
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 LiCO and PeCO protocols put to sleep status more redundant sensors
-(which slightly decreases the coverage ratio), while the three 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 allows later a
-substantial increase of the coverage performance.
+the beginning DiLCO and PeCO protocols put to sleep status more redundant
+sensors (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
+allows later a substantial increase of the coverage performance.
\parskip 0pt
\begin{figure}[h!]
sensor-testbed to evaluate it in real world applications.
-\subsection{Acknowledgements}
+\subsection*{Acknowledgements}
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
