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\r
13 \title{{\itshape Perimeter-based Coverage Optimization to Improve Lifetime in Wireless Sensor Networks}}
\r
15 \author{Ali Kadhum Idrees$^{a}$, Karine Deschinkel$^{a}$$^{\ast}$\thanks{$^\ast$Corresponding author. Email: karine.deschinkel@univ-fcomte.fr}, Michel Salomon$^{a}$ and Rapha\"el Couturier $^{a}$
\r
16 $^{a}${\em{FEMTO-ST Institute, UMR 6174 CNRS, University of Franche-Comte,
\r
23 The most important problem in a Wireless Sensor Network (WSN) is to optimize the
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24 use of its limited energy provision, so that it can fulfill its monitoring task
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25 as long as possible. Among known available approaches that can be used to
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26 improve power management, lifetime coverage optimization provides activity
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27 scheduling which ensures sensing coverage while minimizing the energy cost. We propose such an approach called Perimeter-based Coverage Optimization
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28 protocol (PeCO). It is a hybrid of centralized and distributed methods: the
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29 region of interest is first subdivided into subregions and our protocol is then
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30 distributed among sensor nodes in each subregion.
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31 The novelty of our approach lies essentially in the formulation of a new
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32 mathematical optimization model based on the perimeter coverage level to schedule
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33 sensors' activities. Extensive simulation experiments demonstrate that PeCO can
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34 offer longer lifetime coverage for WSNs in comparison with some other protocols.
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36 \begin{keywords}Wireless Sensor Networks, Area Coverage, Energy efficiency, Optimization, Scheduling.
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42 \section{Introduction}
\r
43 \label{sec:introduction}
\r
45 \noindent The continuous progress in Micro Electro-Mechanical Systems (MEMS) and
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46 wireless communication hardware has given rise to the opportunity to use large
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47 networks of tiny sensors, called Wireless Sensor Networks
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48 (WSN)~\citep{akyildiz2002wireless,puccinelli2005wireless}, to fulfill monitoring
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49 tasks. A WSN consists of small low-powered sensors working together by
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50 communicating with one another through multi-hop radio communications. Each node
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51 can send the data it collects in its environment, thanks to its sensor, to the
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52 user by means of sink nodes. The features of a WSN made it suitable for a wide
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53 range of application in areas such as business, environment, health, industry,
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54 military, and so on~\citep{yick2008wireless}. Typically, a sensor node contains
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55 three main components~\citep{anastasi2009energy}: a sensing unit able to measure
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56 physical, chemical, or biological phenomena observed in the environment; a
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57 processing unit which will process and store the collected measurements; a radio
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58 communication unit for data transmission and receiving.
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60 The energy needed by an active sensor node to perform sensing, processing, and
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61 communication is supplied by a power supply which is a battery. This battery has
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62 a limited energy provision and it may be unsuitable or impossible to replace or
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63 recharge it in most applications. Therefore it is necessary to deploy WSN with
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64 high density in order to increase reliability and to exploit node redundancy
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65 thanks to energy-efficient activity scheduling approaches. Indeed, the overlap
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66 of sensing areas can be exploited to schedule alternatively some sensors in a
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67 low power sleep mode and thus save energy. Overall, the main question that must
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68 be answered is: how to extend the lifetime coverage of a WSN as long as possible
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69 while ensuring a high level of coverage? These past few years many
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70 energy-efficient mechanisms have been suggested to retain energy and extend the
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71 lifetime of the WSNs~\citep{rault2014energy}.\\\\
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72 This paper makes the following contributions.
\r
74 \item We have devised a framework to schedule nodes to be activated alternatively such
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75 that the network lifetime is prolonged while ensuring that a certain level of
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76 coverage is preserved. A key idea in our framework is to exploit spatial and
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77 temporal subdivision. On the one hand, the area of interest is divided into
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78 several smaller subregions and, on the other hand, the time line is divided into
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79 periods of equal length. In each subregion the sensor nodes will cooperatively
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80 choose a leader which will schedule nodes' activities, and this grouping of
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81 sensors is similar to typical cluster architecture.
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82 \item We have proposed a new mathematical optimization model. Instead of trying to
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83 cover a set of specified points/targets as in most of the methods proposed in
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84 the literature, we formulate an integer program based on perimeter coverage of
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85 each sensor. The model involves integer variables to capture the deviations
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86 between the actual level of coverage and the required level. Hence, an
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87 optimal scheduling will be obtained by minimizing a weighted sum of these
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89 \item We have conducted extensive simulation experiments, using the discrete event
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90 simulator OMNeT++, to demonstrate the efficiency of our protocol. We have compared
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91 our PeCO protocol to two approaches found in the literature:
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92 DESK~\citep{ChinhVu} and GAF~\citep{xu2001geography}, and also to our previous
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93 work published in~\citep{Idrees2} which is based on another optimization model
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94 for sensor scheduling.
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102 The rest of the paper is organized as follows. In the next section we review
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103 some related work in the field. Section~\ref{sec:The PeCO Protocol Description}
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104 is devoted to the PeCO protocol description and Section~\ref{cp} focuses on the
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105 coverage model formulation which is used to schedule the activation of sensor
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106 nodes. Section~\ref{sec:Simulation Results and Analysis} presents simulations
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107 results and discusses the comparison with other approaches. Finally, concluding
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108 remarks are drawn and some suggestions are given for future works in
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109 Section~\ref{sec:Conclusion and Future Works}.
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111 \section{Related Literature}
\r
112 \label{sec:Literature Review}
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114 \noindent In this section, we summarize some related works regarding the
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115 coverage problem and distinguish our PeCO protocol from the works presented in
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118 The most discussed coverage problems in literature can be classified in three
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119 categories~\citep{li2013survey} according to their respective monitoring
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120 objective. Hence, area coverage \citep{Misra} means that every point inside a
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121 fixed area must be monitored, while target coverage~\citep{yang2014novel} refers
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122 to the objective of coverage for a finite number of discrete points called
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123 targets, and barrier coverage~\citep{HeShibo,kim2013maximum} focuses on
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124 preventing intruders from entering into the region of interest. In
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125 \citep{Deng2012} authors transform the area coverage problem into the target
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126 coverage one taking into account the intersection points among disks of sensors
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127 nodes or between disk of sensor nodes and boundaries. In
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128 \citep{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of
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129 sensors are sufficiently covered it will be the case for the whole area. They
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130 provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of
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131 each sensor, where $d$ denotes the maximum number of sensors that are
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132 neighbors to a sensor and $n$ is the total number of sensors in the
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133 network. {\it In PeCO protocol, instead of determining the level of coverage of
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134 a set of discrete points, our optimization model is based on checking the
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135 perimeter-coverage of each sensor to activate a minimal number of sensors.}
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137 The major approach to extend network lifetime while preserving coverage is to
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138 divide/organize the sensors into a suitable number of set covers (disjoint or
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139 non-disjoint)\citep{wang2011coverage}, where each set completely covers a region of interest, and to
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140 activate these set covers successively. The network activity can be planned in
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141 advance and scheduled for the entire network lifetime or organized in periods,
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142 and the set of active sensor nodes is decided at the beginning of each period
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143 \citep{ling2009energy}. Active node selection is determined based on the problem
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144 requirements (e.g. area monitoring, connectivity, or power efficiency). For
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145 instance, \citet{jaggi2006} address the problem of maximizing
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146 the lifetime by dividing sensors into the maximum number of disjoint subsets
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147 such that each subset can ensure both coverage and connectivity. A greedy
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148 algorithm is applied once to solve this problem and the computed sets are
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149 activated in succession to achieve the desired network lifetime.
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150 \citet{chin2007}, \citet{yan2008design}, \citet{pc10}, propose algorithms
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151 working in a periodic fashion where a cover set is computed at the beginning of
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152 each period. {\it Motivated by these works, PeCO protocol works in periods,
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153 where each period contains a preliminary phase for information exchange and
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154 decisions, followed by a sensing phase where one cover set is in charge of the
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157 Various centralized and distributed approaches, or even a mixing of these two
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158 concepts, have been proposed to extend the network lifetime \citep{zhou2009variable}. In distributed algorithms~\citep{Tian02,yangnovel,ChinhVu,qu2013distributed} each sensor decides of its
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159 own activity scheduling after an information exchange with its neighbors. The
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160 main interest of such an approach is to avoid long range communications and thus
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161 to reduce the energy dedicated to the communications. Unfortunately, since each
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162 node has only information on its immediate neighbors (usually the one-hop ones)
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163 it may make a bad decision leading to a global suboptimal solution. Conversely,
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165 algorithms~\citep{cardei2005improving,zorbas2010solving,pujari2011high} always
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166 provide nearly or close to optimal solution since the algorithm has a global
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167 view of the whole network. The disadvantage of a centralized method is obviously
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168 its high cost in communications needed to transmit to a single node, the base
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169 station which will globally schedule nodes' activities, data from all the other
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170 sensor nodes in the area. The price in communications can be huge since
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171 long range communications will be needed. In fact the larger the WNS is, the
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172 higher the communication and thus the energy cost are. {\it In order to be
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173 suitable for large-scale networks, in the PeCO protocol, the area of interest
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174 is divided into several smaller subregions, and in each one, a node called the
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175 leader is in charge of selecting the active sensors for the current
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176 period. Thus our protocol is scalable and is a globally distributed method,
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177 whereas it is centralized in each subregion.}
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179 Various coverage scheduling algorithms have been developed these past few years.
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180 Many of them, dealing with the maximization of the number of cover sets, are
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181 heuristics. These heuristics involve the construction of a cover set by
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182 including in priority the sensor nodes which cover critical targets, that is to
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183 say targets that are covered by the smallest number of sensors
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184 \citep{berman04,zorbas2010solving}. Other approaches are based on mathematical
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185 programming formulations~\citep{cardei2005energy,5714480,pujari2011high,Yang2014}
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186 and dedicated techniques (solving with a branch-and-bound algorithm available in
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187 optimization solver). The problem is formulated as an optimization problem
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188 (maximization of the lifetime or number of cover sets) under target coverage and
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189 energy constraints. Column generation techniques, well-known and widely
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190 practiced techniques for solving linear programs with too many variables, have
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192 used~\citep{castano2013column,doi:10.1080/0305215X.2012.687732,deschinkel2012column}. {\it In the PeCO
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193 protocol, each leader, in charge of a subregion, solves an integer program
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194 which has a twofold objective: minimize the overcoverage and the undercoverage
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195 of the perimeter of each sensor.}
\r
199 \section{ The P{\scshape e}CO Protocol Description}
\r
200 \label{sec:The PeCO Protocol Description}
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202 \noindent In this section, we describe in details our Perimeter-based Coverage
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203 Optimization protocol. First we present the assumptions we made and the models
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204 we considered (in particular the perimeter coverage one), second we describe the
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205 background idea of our protocol, and third we give the outline of the algorithm
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206 executed by each node.
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209 \subsection{Assumptions and Models}
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212 \noindent A WSN consisting of $J$ stationary sensor nodes randomly and uniformly
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213 distributed in a bounded sensor field is considered. The wireless sensors are
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214 deployed in high density to ensure initially a high coverage ratio of the area
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215 of interest. We assume that all the sensor nodes are homogeneous in terms of
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216 communication, sensing, and processing capabilities and heterogeneous from
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217 the energy provision point of view. The location information is available to a
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218 sensor node either through hardware such as embedded GPS or location discovery
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219 algorithms. We assume that each sensor node can directly transmit its
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220 measurements to a mobile sink node. For example, a sink can be an unmanned
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221 aerial vehicle (UAV) flying regularly over the sensor field to collect
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222 measurements from sensor nodes. A mobile sink node collects the measurements and
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223 transmits them to the base station. We consider a Boolean disk coverage model,
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224 which is the most widely used sensor coverage model in the literature, and all
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225 sensor nodes have a constant sensing range $R_s$. Thus, all the space points
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226 within a disk centered at a sensor with a radius equal to the sensing range are
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227 said to be covered by this sensor. We also assume that the communication range
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228 $R_c$ satisfies $R_c \geq 2 \cdot R_s$. In fact, \citet{Zhang05}
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229 proved that if the transmission range fulfills the previous hypothesis, the
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230 complete coverage of a convex area implies connectivity among active nodes.
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232 The PeCO protocol uses the same perimeter-coverage model as \citet{huang2005coverage}. It can be expressed as follows: a sensor is
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233 said to be perimeter covered if all the points on its perimeter are covered by
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234 at least one sensor other than itself. They proved that a network area is
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235 $k$-covered if and only if each sensor in the network is $k$-perimeter-covered (perimeter covered by at least $k$ sensors).
\r
237 Figure~\ref{figure1}(a) shows the coverage of sensor node~$0$. On this
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238 figure, we can see that sensor~$0$ has nine neighbors and we have reported on
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239 its perimeter (the perimeter of the disk covered by the sensor) for each
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240 neighbor the two points resulting from the intersection of the two sensing
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241 areas. These points are denoted for neighbor~$i$ by $iL$ and $iR$, respectively
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242 for left and right from a neighboing point of view. The resulting couples of
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243 intersection points subdivide the perimeter of sensor~$0$ into portions called
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246 \begin{figure}[ht!]
\r
248 \begin{tabular}{@{}cr@{}}
\r
249 \includegraphics[width=75mm]{figure1a.eps} & \raisebox{3.25cm}{(a)} \\
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250 \includegraphics[width=75mm]{figure1b.eps} & \raisebox{2.75cm}{(b)}
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252 \caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of
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253 $u$'s perimeter covered by $v$.}
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257 Figure~\ref{figure1}(b) describes the geometric information used to find the
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258 locations of the left and right points of an arc on the perimeter of a sensor
\r
259 node~$u$ covered by a sensor node~$v$. Node~$v$ is supposed to be located on the
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260 west side of sensor~$u$, with the following respective coordinates in the
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261 sensing area~: $(v_x,v_y)$ and $(u_x,u_y)$. From the previous coordinates we can
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262 compute the euclidean distance between nodes~$u$ and $v$: $Dist(u,v)=\sqrt{\vert
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263 u_x - v_x \vert^2 + \vert u_y-v_y \vert^2}$, while the angle~$\alpha$ is
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264 obtained through the formula:
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266 \alpha = \arccos \left(\frac{Dist(u,v)}{2R_s}
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269 The arc on the perimeter of~$u$ defined by the angular interval $[\pi
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270 - \alpha,\pi + \alpha]$ is said to be perimeter-covered by sensor~$v$.
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272 Every couple of intersection points is placed on the angular interval $[0,2\pi]$
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273 in a counterclockwise manner, leading to a partitioning of the interval.
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274 Figure~\ref{figure1}(a) illustrates the arcs for the nine neighbors of
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275 sensor $0$ and figure~\ref{figure2} gives the position of the corresponding arcs
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276 in the interval $[0,2\pi]$. More precisely, we can see that the points are
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277 ordered according to the measures of the angles defined by their respective
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278 positions. The intersection points are then visited one after another, starting
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279 from the first intersection point after point~zero, and the maximum level of
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280 coverage is determined for each interval defined by two successive points. The
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281 maximum level of coverage is equal to the number of overlapping arcs. For
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283 between~$5L$ and~$6L$ the maximum level of coverage is equal to $3$
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284 (the value is highlighted in yellow at the bottom of figure~\ref{figure2}), which
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285 means that at most 2~neighbors can cover the perimeter in addition to node $0$.
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286 Table~\ref{my-label} summarizes for each coverage interval the maximum level of
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287 coverage and the sensor nodes covering the perimeter. The example discussed
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288 above is thus given by the sixth line of the table.
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291 \begin{figure*}[t!]
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293 \includegraphics[width=127.5mm]{figure2.eps}
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294 \caption{Maximum coverage levels for perimeter of sensor node $0$.}
\r
302 \tbl{Coverage intervals and contributing sensors for sensor node 0 \label{my-label}}
\r
303 {\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\r
305 \begin{tabular}[c]{@{}c@{}}Left \\ point \\ angle~$\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ left \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ right \\ point\end{tabular} & \begin{tabular}[c]{@{}c@{}}Maximum \\ coverage\\ level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}Set of sensors\\ involved \\ in coverage interval\end{tabular}} \\ \hline
\r
306 0.0291 & 1L & 2L & 4 & 0 & 1 & 3 & 4 & \\ \hline
\r
307 0.104 & 2L & 3R & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline
\r
308 0.3168 & 3R & 4R & 4 & 0 & 1 & 4 & 2 & \\ \hline
\r
309 0.6752 & 4R & 1R & 3 & 0 & 1 & 2 & & \\ \hline
\r
310 1.8127 & 1R & 5L & 2 & 0 & 2 & & & \\ \hline
\r
311 1.9228 & 5L & 6L & 3 & 0 & 2 & 5 & & \\ \hline
\r
312 2.3959 & 6L & 2R & 4 & 0 & 2 & 5 & 6 & \\ \hline
\r
313 2.4258 & 2R & 7L & 3 & 0 & 5 & 6 & & \\ \hline
\r
314 2.7868 & 7L & 8L & 4 & 0 & 5 & 6 & 7 & \\ \hline
\r
315 2.8358 & 8L & 5R & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline
\r
316 2.9184 & 5R & 7R & 4 & 0 & 6 & 7 & 8 & \\ \hline
\r
317 3.3301 & 7R & 9R & 3 & 0 & 6 & 8 & & \\ \hline
\r
318 3.9464 & 9R & 6R & 4 & 0 & 6 & 8 & 9 & \\ \hline
\r
319 4.767 & 6R & 3L & 3 & 0 & 8 & 9 & & \\ \hline
\r
320 4.8425 & 3L & 8R & 4 & 0 & 3 & 8 & 9 & \\ \hline
\r
321 4.9072 & 8R & 4L & 3 & 0 & 3 & 9 & & \\ \hline
\r
322 5.3804 & 4L & 9R & 4 & 0 & 3 & 4 & 9 & \\ \hline
\r
323 5.9157 & 9R & 1L & 3 & 0 & 3 & 4 & & \\ \hline
\r
332 In the PeCO protocol, the scheduling of the sensor nodes' activities is formulated with an
\r
333 integer program based on coverage intervals. The formulation of the coverage
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334 optimization problem is detailed in~section~\ref{cp}. Note that when a sensor
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335 node has a part of its sensing range outside the WSN sensing field, as in
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336 figure~\ref{figure3}, the maximum coverage level for this arc is set to $\infty$
\r
337 and the corresponding interval will not be taken into account by the
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338 optimization algorithm.
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343 \includegraphics[width=62.5mm]{figure3.eps}
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344 \caption{Sensing range outside the WSN's area of interest.}
\r
349 \subsection{The Main Idea}
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351 \noindent The WSN area of interest is, in a first step, divided into regular
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352 homogeneous subregions using a divide-and-conquer algorithm. In a second step
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353 our protocol will be executed in a distributed way in each subregion
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354 simultaneously to schedule nodes' activities for one sensing period.
\r
356 As shown in figure~\ref{figure4}, node activity scheduling is produced by our
\r
357 protocol in a periodic manner. Each period is divided into 4 stages: Information
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358 (INFO) Exchange, Leader Election, Decision (the result of an optimization
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359 problem), and Sensing. For each period there is exactly one set cover
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360 responsible for the sensing task. Protocols based on a periodic scheme, like
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361 PeCO, are more robust against an unexpected node failure. On the one hand, if
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362 a node failure is discovered before taking the decision, the corresponding sensor
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363 node will not be considered by the optimization algorithm. On the other
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364 hand, if the sensor failure happens after the decision, the sensing task of the
\r
365 network will be temporarily affected: only during the period of sensing until a
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366 new period starts, since a new set cover will take charge of the sensing task in
\r
367 the next period. The energy consumption and some other constraints can easily be
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368 taken into account since the sensors can update and then exchange their
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369 information (including their residual energy) at the beginning of each period.
\r
370 However, the pre-sensing phases (INFO Exchange, Leader Election, and Decision)
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371 are energy consuming, even for nodes that will not join the set cover to monitor
\r
376 \includegraphics[width=80mm]{figure4.eps}
\r
377 \caption{PeCO protocol.}
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381 We define two types of packets to be used by PeCO protocol:
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384 \item INFO packet: sent by each sensor node to all the nodes inside a same
\r
385 subregion for information exchange.
\r
386 \item ActiveSleep packet: sent by the leader to all the nodes in its subregion
\r
387 to transmit to them their respective status (stay Active or go Sleep) during
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392 Five status are possible for a sensor node in the network:
\r
395 \item LISTENING: waits for a decision (to be active or not);
\r
396 \item COMPUTATION: executes the optimization algorithm as leader to
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397 determine the activities scheduling;
\r
398 \item ACTIVE: node is sensing;
\r
399 \item SLEEP: node is turned off;
\r
400 \item COMMUNICATION: transmits or receives packets.
\r
404 \subsection{PeCO Protocol Algorithm}
\r
406 \noindent The pseudocode implementing the protocol on a node is given below.
\r
407 More precisely, Algorithm~\ref{alg:PeCO} gives a brief description of the
\r
408 protocol applied by a sensor node $s_k$ where $k$ is the node index in the WSN.
\r
413 % \KwIn{all the parameters related to information exchange}
\r
414 % \KwOut{$winer-node$ (: the id of the winner sensor node, which is the leader of current round)}
\r
416 %\emph{Initialize the sensor node and determine it's position and subregion} \;
\r
418 \noindent{\bf If} $RE_k \geq E_{th}$ {\bf then}\\
\r
419 \hspace*{0.6cm} \emph{$s_k.status$ = COMMUNICATION;}\\
\r
420 \hspace*{0.6cm} \emph{Send $INFO()$ packet to other nodes in subregion;}\\
\r
421 \hspace*{0.6cm} \emph{Wait $INFO()$ packet from other nodes in subregion;}\\
\r
422 \hspace*{0.6cm} \emph{Update K.CurrentSize;}\\
\r
423 \hspace*{0.6cm} \emph{LeaderID = Leader election;}\\
\r
424 \hspace*{0.6cm} {\bf If} $ s_k.ID = LeaderID $ {\bf then}\\
\r
425 \hspace*{1.2cm} \emph{$s_k.status$ = COMPUTATION;}\\
\r
426 \hspace*{1.2cm}{\bf If} \emph{$ s_k.ID $ is Not previously selected as a Leader} {\bf then}\\
\r
427 \hspace*{1.8cm} \emph{ Execute the perimeter coverage model;}\\
\r
428 \hspace*{1.2cm} {\bf end}\\
\r
429 \hspace*{1.2cm}{\bf If} \emph{($s_k.ID $ is the same Previous Leader)~And~(K.CurrentSize = K.PreviousSize)}\\
\r
430 \hspace*{1.8cm} \emph{ Use the same previous cover set for current sensing stage;}\\
\r
431 \hspace*{1.2cm} {\bf end}\\
\r
432 \hspace*{1.2cm} {\bf else}\\
\r
433 \hspace*{1.8cm}\emph{Update $a^j_{ik}$; prepare data for IP~Algorithm;}\\
\r
434 \hspace*{1.8cm} \emph{$\left\{\left(X_{1},\dots,X_{l},\dots,X_{K}\right)\right\}$ = Execute Integer Program Algorithm($K$);}\\
\r
435 \hspace*{1.8cm} \emph{K.PreviousSize = K.CurrentSize;}\\
\r
436 \hspace*{1.2cm} {\bf end}\\
\r
437 \hspace*{1.2cm}\emph{$s_k.status$ = COMMUNICATION;}\\
\r
438 \hspace*{1.2cm}\emph{Send $ActiveSleep()$ to each node $l$ in subregion;}\\
\r
439 \hspace*{1.2cm}\emph{Update $RE_k $;}\\
\r
440 \hspace*{0.6cm} {\bf end}\\
\r
441 \hspace*{0.6cm} {\bf else}\\
\r
442 \hspace*{1.2cm}\emph{$s_k.status$ = LISTENING;}\\
\r
443 \hspace*{1.2cm}\emph{Wait $ActiveSleep()$ packet from the Leader;}\\
\r
444 \hspace*{1.2cm}\emph{Update $RE_k $;}\\
\r
445 \hspace*{0.6cm} {\bf end}\\
\r
448 \hspace*{0.6cm} \emph{Exclude $s_k$ from entering in the current sensing stage;}\\
\r
455 In this algorithm, K.CurrentSize and K.PreviousSize respectively represent the
\r
456 current number and the previous number of living nodes in the subnetwork of the
\r
457 subregion. Initially, the sensor node checks its remaining energy $RE_k$, which
\r
458 must be greater than a threshold $E_{th}$ in order to participate in the current
\r
459 period. Each sensor node determines its position and its subregion using an
\r
460 embedded GPS or a location discovery algorithm. After that, all the sensors
\r
461 collect position coordinates, remaining energy, sensor node ID, and the number
\r
462 of their one-hop live neighbors during the information exchange. The sensors
\r
463 inside a same region cooperate to elect a leader. The selection criteria for the
\r
464 leader, in order of priority, are: larger numbers of neighbors, larger remaining
\r
465 energy, and then in case of equality, larger index. Once chosen, the leader
\r
466 collects information to formulate and solve the integer program which allows to
\r
467 construct the set of active sensors in the sensing stage.
\r
470 \section{Perimeter-based Coverage Problem Formulation}
\r
473 \noindent In this section, the coverage model is mathematically formulated. We
\r
474 start with a description of the notations that will be used throughout the
\r
476 First, we have the following sets:
\r
478 \item $S$ represents the set of WSN sensor nodes;
\r
479 \item $A \subseteq S $ is the subset of alive sensors;
\r
480 \item $I_j$ designates the set of coverage intervals (CI) obtained for
\r
483 $I_j$ refers to the set of coverage intervals which have been defined according
\r
484 to the method introduced in subsection~\ref{CI}. For a coverage interval $i$,
\r
485 let $a^j_{ik}$ denotes the indicator function of whether sensor~$k$ is involved
\r
486 in coverage interval~$i$ of sensor~$j$, that is:
\r
488 a^j_{ik} = \left \{
\r
490 1 & \mbox{if sensor $k$ is involved in the } \\
\r
491 & \mbox{coverage interval $i$ of sensor $j$}, \\
\r
492 0 & \mbox{otherwise.}\\
\r
493 \end{array} \right.
\r
495 Note that $a^k_{ik}=1$ by definition of the interval.
\r
497 Second, we define several binary and integer variables. Hence, each binary
\r
498 variable $X_{k}$ determines the activation of sensor $k$ in the sensing phase
\r
499 ($X_k=1$ if the sensor $k$ is active or 0 otherwise). $M^j_i$ is an integer
\r
500 variable which measures the undercoverage for the coverage interval $i$
\r
501 corresponding to sensor~$j$. In the same way, the overcoverage for the same
\r
502 coverage interval is given by the variable $V^j_i$.
\r
504 If we decide to sustain a level of coverage equal to $l$ all along the perimeter
\r
505 of sensor $j$, we have to ensure that at least $l$ sensors involved in each
\r
506 coverage interval $i \in I_j$ of sensor $j$ are active. According to the
\r
507 previous notations, the number of active sensors in the coverage interval $i$ of
\r
508 sensor $j$ is given by $\sum_{k \in A} a^j_{ik} X_k$. To extend the network
\r
509 lifetime, the objective is to activate a minimal number of sensors in each
\r
510 period to ensure the desired coverage level. As the number of alive sensors
\r
511 decreases, it becomes impossible to reach the desired level of coverage for all
\r
512 coverage intervals. Therefore we use variables $M^j_i$ and $V^j_i$ as a measure
\r
513 of the deviation between the desired number of active sensors in a coverage
\r
514 interval and the effective number. And we try to minimize these deviations,
\r
515 first to force the activation of a minimal number of sensors to ensure the
\r
516 desired coverage level, and if the desired level cannot be completely satisfied,
\r
517 to reach a coverage level as close as possible to the desired one.
\r
522 Our coverage optimization problem can then be mathematically expressed as follows:
\r
527 \min \sum_{j \in S} \sum_{i \in I_j} (\alpha^j_i ~ M^j_i + \beta^j_i ~ V^j_i )&\\
\r
528 \textrm{subject to :}&\\
\r
529 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) + M^j_i \geq l \quad \forall i \in I_j, \forall j \in S\\
\r
530 \sum_{k \in A} ( a^j_{ik} ~ X_{k}) - V^j_i \leq l \quad \forall i \in I_j, \forall j \in S\\
\r
531 X_{k} \in \{0,1\}, \forall k \in A
\r
536 $\alpha^j_i$ and $\beta^j_i$ are nonnegative weights selected according to the
\r
537 relative importance of satisfying the associated level of coverage. For example,
\r
538 weights associated with coverage intervals of a specified part of a region may
\r
539 be given by a relatively larger magnitude than weights associated with another
\r
540 region. This kind of integer program is inspired from the model developed for
\r
541 brachytherapy treatment planning for optimizing dose distribution
\r
542 \citep{0031-9155-44-1-012}. The integer program must be solved by the leader in
\r
543 each subregion at the beginning of each sensing phase, whenever the environment
\r
544 has changed (new leader, death of some sensors). Note that the number of
\r
545 constraints in the model is constant (constraints of coverage expressed for all
\r
546 sensors), whereas the number of variables $X_k$ decreases over periods, since we
\r
547 consider only alive sensors (sensors with enough energy to be alive during one
\r
548 sensing phase) in the model.
\r
550 \section{Performance Evaluation and Analysis}
\r
551 \label{sec:Simulation Results and Analysis}
\r
554 \subsection{Simulation Settings}
\r
557 The WSN area of interest is supposed to be divided into 16~regular subregions
\r
558 and we use the same energy consumption than in our previous work~\citep{Idrees2}.
\r
559 Table~\ref{table3} gives the chosen parameters settings.
\r
562 \tbl{Relevant parameters for network initialization \label{table3}}{
\r
566 \begin{tabular}{c|c}
\r
569 Parameter & Value \\ [0.5ex]
\r
572 % inserts single horizontal line
\r
573 Sensing field & $(50 \times 25)~m^2 $ \\
\r
575 WSN size & 100, 150, 200, 250, and 300~nodes \\
\r
577 Initial energy & in range 500-700~Joules \\
\r
579 Sensing period & duration of 60 minutes \\
\r
580 $E_{th}$ & 36~Joules\\
\r
583 $\alpha^j_i$ & 0.6 \\
\r
591 To obtain experimental results which are relevant, simulations with five
\r
592 different node densities going from 100 to 300~nodes were performed considering
\r
593 each time 25~randomly generated networks. The nodes are deployed on a field of
\r
594 interest of $(50 \times 25)~m^2 $ in such a way that they cover the field with a
\r
595 high coverage ratio. Each node has an initial energy level, in Joules, which is
\r
596 randomly drawn in the interval $[500-700]$. If its energy provision reaches a
\r
597 value below the threshold $E_{th}=36$~Joules, the minimum energy needed for a
\r
598 node to stay active during one period, it will no more participate in the
\r
599 coverage task. This value corresponds to the energy needed by the sensing phase,
\r
600 obtained by multiplying the energy consumed in active state (9.72 mW) with the
\r
601 time in seconds for one period (3600 seconds), and adding the energy for the
\r
602 pre-sensing phases. According to the interval of initial energy, a sensor may
\r
603 be active during at most 20 periods.
\r
605 The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen to ensure a good
\r
606 network coverage and a longer WSN lifetime. We have given a higher priority to
\r
607 the undercoverage (by setting the $\alpha^j_i$ with a larger value than
\r
608 $\beta^j_i$) so as to prevent the non-coverage for the interval~$i$ of the
\r
609 sensor~$j$. On the other hand, we have assigned to
\r
610 $\beta^j_i$ a value which is slightly lower so as to minimize the number of active sensor nodes which contribute
\r
611 in covering the interval.
\r
613 We introduce the following performance metrics to evaluate the efficiency of our
\r
618 \item {\bf Network Lifetime}: the lifetime is defined as the time elapsed until
\r
619 the coverage ratio falls below a fixed threshold. $Lifetime_{95}$ and
\r
620 $Lifetime_{50}$ denote, respectively, the amount of time during which is
\r
621 guaranteed a level of coverage greater than $95\%$ and $50\%$. The WSN can
\r
622 fulfill the expected monitoring task until all its nodes have depleted their
\r
623 energy or if the network is no more connected. This last condition is crucial
\r
624 because without network connectivity a sensor may not be able to send to a
\r
625 base station an event it has sensed.
\r
626 \item {\bf Coverage Ratio (CR)} : it measures how well the WSN is able to
\r
627 observe the area of interest. In our case, we discretized the sensor field as
\r
628 a regular grid, which yields the following equation:
\r
633 \mbox{CR}(\%) = \frac{\mbox{$n$}}{\mbox{$N$}} \times 100
\r
637 where $n$ is the number of covered grid points by active sensors of every
\r
638 subregions during the current sensing phase and $N$ is total number of grid
\r
639 points in the sensing field. In our simulations we have set a layout of
\r
640 $N~=~51~\times~26~=~1326$~grid points.
\r
641 \item {\bf Active Sensors Ratio (ASR)}: a major objective of our protocol is to
\r
642 activate as few nodes as possible, in order to minimize the communication
\r
643 overhead and maximize the WSN lifetime. The active sensors ratio is defined as
\r
648 \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R \mbox{$|A_r^p|$}}{\mbox{$|S|$}} \times 100
\r
651 where $|A_r^p|$ is the number of active sensors in the subregion $r$ in the
\r
652 current sensing period~$p$, $|S|$ is the number of sensors in the network, and
\r
653 $R$ is the number of subregions.
\r
654 \item {\bf Energy Consumption (EC)}: energy consumption can be seen as the total
\r
655 energy consumed by the sensors during $Lifetime_{95}$ or $Lifetime_{50}$,
\r
656 divided by the number of periods. The value of EC is computed according to
\r
661 \mbox{EC} = \frac{\sum\limits_{p=1}^{P} \left( E^{\mbox{com}}_p+E^{\mbox{list}}_p+E^{\mbox{comp}}_p
\r
662 + E^{a}_p+E^{s}_p \right)}{P},
\r
665 where $P$ corresponds to the number of periods. The total energy consumed by
\r
666 the sensors comes through taking into consideration four main energy
\r
667 factors. The first one, denoted $E^{\scriptsize \mbox{com}}_p$, represents the
\r
668 energy consumption spent by all the nodes for wireless communications during
\r
669 period $p$. $E^{\scriptsize \mbox{list}}_p$, the next factor, corresponds to
\r
670 the energy consumed by the sensors in LISTENING status before receiving the
\r
671 decision to go active or sleep in period $p$. $E^{\scriptsize \mbox{comp}}_p$
\r
672 refers to the energy needed by all the leader nodes to solve the integer
\r
673 program during a period. Finally, $E^a_{p}$ and $E^s_{p}$ indicate the energy
\r
674 consumed by the WSN during the sensing phase (active and sleeping nodes).
\r
678 \subsection{Simulation Results}
\r
680 In order to assess and analyze the performance of our protocol we have
\r
681 implemented PeCO protocol in OMNeT++~\citep{varga} simulator. Besides PeCO, two
\r
682 other protocols, described in the next paragraph, will be evaluated for
\r
683 comparison purposes. The simulations were run on a DELL laptop with an Intel
\r
684 Core~i3~2370~M (1.8~GHz) processor (2 cores) whose MIPS (Million Instructions
\r
685 Per Second) rate is equal to 35330. To be consistent with the use of a sensor
\r
686 node based on Atmels AVR ATmega103L microcontroller (6~MHz) having a MIPS rate
\r
687 equal to 6, the original execution time on the laptop is multiplied by 2944.2
\r
688 $\left(\frac{35330}{2} \times \frac{1}{6} \right)$. The modeling language for
\r
689 Mathematical Programming (AMPL)~\citep{AMPL} is employed to generate the integer
\r
690 program instance in a standard format, which is then read and solved by the
\r
691 optimization solver GLPK (GNU linear Programming Kit available in the public
\r
692 domain) \citep{glpk} through a Branch-and-Bound method.
\r
694 As said previously, the PeCO is compared to three other approaches. The first
\r
695 one, called DESK, is a fully distributed coverage algorithm proposed by
\r
696 \citep{ChinhVu}. The second one, called GAF~\citep{xu2001geography}, consists in
\r
697 dividing the monitoring area into fixed squares. Then, during the decision
\r
698 phase, in each square, one sensor is chosen to remain active during the sensing
\r
699 phase. The last one, the DiLCO protocol~\citep{Idrees2}, is an improved version
\r
700 of a research work we presented in~\citep{idrees2014coverage}. Let us notice that
\r
701 PeCO and DiLCO protocols are based on the same framework. In particular, the
\r
702 choice for the simulations of a partitioning in 16~subregions was made because
\r
703 it corresponds to the configuration producing the best results for DiLCO. The
\r
704 protocols are distinguished from one another by the formulation of the integer
\r
705 program providing the set of sensors which have to be activated in each sensing
\r
706 phase. DiLCO protocol tries to satisfy the coverage of a set of primary points,
\r
707 whereas the PeCO protocol objective is to reach a desired level of coverage for each
\r
708 sensor perimeter. In our experimentations, we chose a level of coverage equal to
\r
711 \subsubsection{\bf Coverage Ratio}
\r
713 Figure~\ref{figure5} shows the average coverage ratio for 200 deployed nodes
\r
714 obtained with the four protocols. DESK, GAF, and DiLCO provide a slightly better
\r
715 coverage ratio with respectively 99.99\%, 99.91\%, and 99.02\%, compared to the 98.76\%
\r
716 produced by PeCO for the first periods. This is due to the fact that at the
\r
717 beginning the DiLCO protocol puts to sleep status more redundant sensors (which
\r
718 slightly decreases the coverage ratio), while the three other protocols activate
\r
719 more sensor nodes. Later, when the number of periods is beyond~70, it clearly
\r
720 appears that PeCO provides a better coverage ratio and keeps a coverage ratio
\r
721 greater than 50\% for longer periods (15 more compared to DiLCO, 40 more
\r
722 compared to DESK). The energy saved by PeCO in the early periods allows later a
\r
723 substantial increase of the coverage performance.
\r
728 \includegraphics[scale=0.5] {figure5.eps}
\r
729 \caption{Coverage ratio for 200 deployed nodes.}
\r
736 \subsubsection{\bf Active Sensors Ratio}
\r
738 Having the less active sensor nodes in each period is essential to minimize the
\r
739 energy consumption and thus to maximize the network lifetime. Figure~\ref{figure6}
\r
740 shows the average active nodes ratio for 200 deployed nodes. We observe that
\r
741 DESK and GAF have 30.36 \% and 34.96 \% active nodes for the first fourteen
\r
742 rounds and DiLCO and PeCO protocols compete perfectly with only 17.92~\% and
\r
743 20.16~\% active nodes during the same time interval. As the number of periods
\r
744 increases, PeCO protocol has a lower number of active nodes in comparison with
\r
745 the three other approaches, while keeping a greater coverage ratio as shown in
\r
746 figure \ref{figure5}.
\r
750 \includegraphics[scale=0.5]{figure6.eps}
\r
751 \caption{Active sensors ratio for 200 deployed nodes.}
\r
755 \subsubsection{\bf Energy Consumption}
\r
757 We studied the effect of the energy consumed by the WSN during the communication,
\r
758 computation, listening, active, and sleep status for different network densities
\r
759 and compared it for the four approaches. Figures~\ref{figure7}(a) and (b)
\r
760 illustrate the energy consumption for different network sizes and for
\r
761 $Lifetime95$ and $Lifetime50$. The results show that our PeCO protocol is the
\r
762 most competitive from the energy consumption point of view. As shown in both
\r
763 figures, PeCO consumes much less energy than the three other methods. One might
\r
764 think that the resolution of the integer program is too costly in energy, but
\r
765 the results show that it is very beneficial to lose a bit of time in the
\r
766 selection of sensors to activate. Indeed the optimization program allows to
\r
767 reduce significantly the number of active sensors and so the energy consumption
\r
768 while keeping a good coverage level.
\r
772 \begin{tabular}{@{}cr@{}}
\r
773 \includegraphics[scale=0.475]{figure7a.eps} & \raisebox{2.75cm}{(a)} \\
\r
774 \includegraphics[scale=0.475]{figure7b.eps} & \raisebox{2.75cm}{(b)}
\r
776 \caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
\r
782 \subsubsection{\bf Network Lifetime}
\r
784 We observe the superiority of PeCO and DiLCO protocols in comparison with the
\r
785 two other approaches in prolonging the network lifetime. In
\r
786 Figures~\ref{figure8}(a) and (b), $Lifetime95$ and $Lifetime50$ are shown for
\r
787 different network sizes. As highlighted by these figures, the lifetime
\r
788 increases with the size of the network, and it is clearly largest for DiLCO
\r
789 and PeCO protocols. For instance, for a network of 300~sensors and coverage
\r
790 ratio greater than 50\%, we can see on figure~\ref{figure8}(b) that the lifetime
\r
791 is about twice longer with PeCO compared to DESK protocol. The performance
\r
792 difference is more obvious in figure~\ref{figure8}(b) than in
\r
793 figure~\ref{figure8}(a) because the gain induced by our protocols increases with
\r
794 time, and the lifetime with a coverage of 50\% is far longer than with
\r
799 \begin{tabular}{@{}cr@{}}
\r
800 \includegraphics[scale=0.475]{figure8a.eps} & \raisebox{2.75cm}{(a)} \\
\r
801 \includegraphics[scale=0.475]{figure8b.eps} & \raisebox{2.75cm}{(b)}
\r
803 \caption{Network Lifetime for (a)~$Lifetime_{95}$ \\
\r
804 and (b)~$Lifetime_{50}$.}
\r
810 Figure~\ref{figure9} compares the lifetime coverage of our protocols for
\r
811 different coverage ratios. We denote by Protocol/50, Protocol/80, Protocol/85,
\r
812 Protocol/90, and Protocol/95 the amount of time during which the network can
\r
813 satisfy an area coverage greater than $50\%$, $80\%$, $85\%$, $90\%$, and $95\%$
\r
814 respectively, where the term Protocol refers to DiLCO or PeCO. Indeed there are applications
\r
815 that do not require a 100\% coverage of the area to be monitored. PeCO might be
\r
816 an interesting method since it achieves a good balance between a high level
\r
817 coverage ratio and network lifetime. PeCO always outperforms DiLCO for the three
\r
818 lower coverage ratios, moreover the improvements grow with the network
\r
819 size. DiLCO is better for coverage ratios near 100\%, but in that case PeCO is
\r
820 not ineffective for the smallest network sizes.
\r
823 \centering \includegraphics[scale=0.5]{figure9.eps}
\r
824 \caption{Network lifetime for different coverage ratios.}
\r
831 \section{Conclusion and Future Works}
\r
832 \label{sec:Conclusion and Future Works}
\r
834 In this paper we have studied the problem of Perimeter-based Coverage Optimization in
\r
835 WSNs. We have designed a new protocol, called Perimeter-based Coverage Optimization, which
\r
836 schedules nodes' activities (wake up and sleep stages) with the objective of
\r
837 maintaining a good coverage ratio while maximizing the network lifetime. This
\r
838 protocol is applied in a distributed way in regular subregions obtained after
\r
839 partitioning the area of interest in a preliminary step. It works in periods and
\r
840 is based on the resolution of an integer program to select the subset of sensors
\r
841 operating in active status for each period. Our work is original in so far as it
\r
842 proposes for the first time an integer program scheduling the activation of
\r
843 sensors based on their perimeter coverage level, instead of using a set of
\r
844 targets/points to be covered.
\r
847 We have carried out several simulations to evaluate the proposed protocol. The
\r
848 simulation results show that PeCO is more energy-efficient than other
\r
849 approaches, with respect to lifetime, coverage ratio, active sensors ratio, and
\r
850 energy consumption.
\r
852 We plan to extend our framework so that the schedules are planned for multiple
\r
855 We also want to improve our integer program to take into account heterogeneous
\r
856 sensors from both energy and node characteristics point of views.
\r
858 Finally, it would be interesting to implement our protocol using a
\r
859 sensor-testbed to evaluate it in real world applications.
\r
861 \bibliographystyle{gENO}
\r
862 \bibliography{biblio}
\r
