Life Time Maximization for Connected Target Coverage in Wireless Sensor Networks with Sink

Mobility

Ehsan Saradar Torshizi Computer Engineering Department

Urmia University Urmia, Iran

st_e.saradar@urmia.ac.ir

Saleh Yousefi Computer Engineering Department

Urmia University Urmia, Iran

s.yousefi@urmia.ac.ir

Jamshid Bagherzadeh Computer Engineering Department

Urmia University Urmia, Iran

j.bagherzadeh@urmia.ac.ir

Abstract— In this paper, we study lifetime maximization problem for a CTC (Connected Target Coverage) scenario in which a determined number of targets should be covered continuously. Previous studies mostly aim at prolong the life time by focusing on the energy consumption of sensor nodes. However, in this paper we exploit the impact of sink mobility on the CTC lifetime. We propose new Linear Programming formulations for both full and partial target coverage scenarios. The proposed formulation gives the position of sink nodes in discrete points of time along with an optimum routing path and scheduling policy. Obtained results are used in the extensive simulation study performed by the OMNET++ simulator. For full target coverage cases, simulation results show that using a mobile sink may lead to improve the network lifetime up to 2.6 times. For partial target coverage scenario, simulation results show that a mobile sink can improve the network lifetime up to 2.5 times.

Keywords-wireless sensor networks; lifetime; target coverage; mobility;mobile sink;linear programming;

I. INTRODUCTION Wireless sensor networks (WSNs) are large number of

sensing devices which are deployed over a designated region called the sensor field. Due to a wide-range of potential applications they have attracted significant research efforts. The goals of WSNs include sensing, tracking or monitoring the environmental events [1].

Coverage and connectivity are two important factors in performance evaluation of WSNs. In general coverage is usually interpreted as how well a sensor network will monitor a field of interest. Full coverage and partial coverage are both considered for WSNs applications. In the full coverage, every point in of a given field of interest must be covered by at least one sensor without allowing any uncovered point. However, many applications do not require full coverage. To save energy and prolong network lifetime for such applications, one effective method is to partially cover the field of interest. For example, for environmental monitoring applications, temperature sensing at one point is adequate for a region since it may have the same readings in its surrounding area.

Actually there are many types of coverage based on what is needed to be covered such as area coverage [2], barrier coverage [3] and target coverage [4]. The main objective of the area coverage is to cover (monitor) an area completely, while the goal of the barrier coverage is to detected all intrusion through the barrier of sensor network. Target coverage considers a limited number of discrete points (targets) with known location that need to be monitored. The requirement is that every target must be monitored continuously by at least one sensor. The connectivity issue emphasizes how well sensors connect to the sink node and if the sensed data can be properly delivered to the sink.

Since the sensor nodes are energy constrained and usually not rechargeable, the longevity of WSNs should be addressed. Exploiting mobile sinks, instead of static ones, in WSNs is an interesting concept to enhance the network lifetime by avoiding excessive transmission overhead at nodes that are close to the location that would be occupied by a static sink. Furthermore, mobile sinks may improve the network connectivity by enabling the retrieval from several isolated parts of the WSNs. In the connected target coverage (CTC) problem, there are targets with fixed known locations that are required to be monitored continuously by sensors. In the other words, the CTC problem requires that all of the targets are covered by a subset of sensors (coverage requirement) and all of the targets are connected to the sink node through a subset of sensors (connectivity requirement). If any of the above requirements cannot be satisfied, the deployed WSN reaches the ends of its lifetime.

In this paper, we investigate the problem of lifetime maximization for connected target coverage in WSNs by jointly considering sink mobility, routing and scheduling. We also study on the partial target coverage where sensors are allowed to monitor a subset of the targets (instead of all targets) at any point in time, while connectivity with the base station is retained and the base station is able to move around the sensor field. To the best of our knowledge this is the first study which exploits sink mobility to prolong network lifetime in full and partial target coverage problem.

The rest of this paper is organized as follows. Section II surveys related work. Section III is the problem definition.

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Section IV formulates the problem which introduced in section III. Simulation results are given in section IV. Finally, section V concludes the paper.

II. RELATED WORK The general target coverage problem is introduced in [5],

where the problem is modeled as finding maximal number of disjoint set covers, such that each cover completely monitors all targets. This problem is extended further in [6], where M. Cardei et al. argued that the network lifetime can be further improved without requirements of operating equal time intervals and sensor sets being disjoint i.e., a sensor may appear in different covers. However, connectivity issue did not consider in [5] and [6]. In [7], M. Lu et al. schedule sensor activity using self-configuring sensing range, in the environment considering discrete target coverage and connectivity. But in their energy consumption model only sensing power is taken into account. Due to the maintaining wide range of connectivity, their proposed heuristic is not efficient because only those sensors along the routes carrying the sensed data are required to be active.

In [8] the CTC problem has been considered as a network lifetime maximization problem which considers coverage as well as connectivity while sensors are omnidirectional. But in their proposed energy consumption model the sensors consume the same amount of energy when sensing and transmitting the data generated from target, regardless to the number of targets i.e., number of targets have not been considered in their energy consumption model. Moreover, they have not considered overlapped targets. Proposed algorithm in [9] is same as [8] but they considered overlapped targets as well as connectivity and coverage.

Partial target coverage and network lifetime in wireless sensor networks has been studied [10] by Yu Gu et al. They proposed a linear programming formulation to find out the optimum solution for partial target coverage. However, they didn’t consider connectivity requirement in their problem. Zorbas et al studied on the partial target coverage with assuming coverage and connectivity in [11]. They showed that monitoring 90% of the targets may yield twice network lifetime provided by a full coverage approach. However, the sink node is static in their proposed model.

Exploiting the sink mobility for maximizing sensor lifetime is addressed in [12-15]. However, none of them consider any coverage requirements. They maximized the network lifetime by using sink mobility while certain connectivity requirements are guaranteed.

III. PROBLEM DEFINITION We consider the following scenario. Targets with fixed

known location should be monitored by the sensors such that the sink node would be aware of the situation of each target continuously. Sensors are energy limited and are not rechargeable. We assume that at the network startup all targets are covered by at least one sensor and there is a way from all sensors to the sink node. We also assume that sensors are aware of their location by using localization mechanism.

A sensor which does sensing task and performs monitoring is called a source sensor and a sensor which doesn’t perform sensing task and does relay task is called relay sensor. Note that a sensor can be both as source and relay node. If a sensor is a source sensor or/and relay sensor, It is an active sensor; otherwise it isn’t an active sensor and it is in the sleep state. Fig.1.a illustrates an example for CTC problem. There are 12 sensors, 4 targets and 1 sink in the sensor field. Consider Fig1.b as solution for Fig.1.a. There are 3 source sensor, 1 source and relay sensor and 4 relay sensors while 4 sensors are in sleep mode.

We assume that all source sensors have the same data generation rate for a target. In the other words, all source sensors use the same sampling frequency, quantization, modulation and coding scheme for each target. Therefore, a fixed amount of bits, denoted by β which is called coverage rate, is generated by each source sensor for a target in a second.

A. Full Target Coverage Problem Definition Given N energy constrained sensors, M targets and a sink

nodes, it is required to schedule the sensor such that:

1- Each target should be covered by at least one source sensor.

2- There should be a route from each source sensor to the sink node which passes through the relay nodes.

Two possible solutions of the CTC problem in Fig.1.a are illustrated in Fig.1.b and Fig.1.c. Communication links are shown by solid arrowed lines while the sensing links are shown by dashed arrowed lines. This figure illustrates that only a subset of deployed sensors is needed to be active during each time interval to cover all targets.

As Fig.1.b shows, the topology of the network will be a tree. Each target is a leaf node, parent of each leaf node is a source or source and relay node, root is a sink node and all other active nodes are relay nodes. Each tree will last for a specific time which is called OTI (Operation Time Interval). We will replace a tree by another one at the end of its OTI. The value of each edge shows the dataflow which passes through that edge. For example if β=10 bps we can use the cover tree in Fig.1.b for 20 sec and then replace it by the cover tree in Fig.1.c and use it for 10 sec. In this case if Fig.1.b and Fig.1.c are the optimum answer for the CTC problem, then the network lifetime would be 30 sec while β=10 bps.

B. Partial Target Coverage Problem Definition Given N energy constrained sensors, M targets, a sink

nodes and known ρ value it is required to schedule the sensor such that:

1- At any point of time, at least ρ% of all targets should be monitored by at least one source sensor.

2- There should be a route from each source sensor to the sink node which passes through the relay nodes.

Due to spatial redundancy of sensor nodes, switching among different coverage trees subject to energy constraints can maximize the network lifetime. However, not all targets have the same impact on network lifetime.

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C. Connected Target Coverage with Mobile Definition Without loss of generality, we assume

with N energy constrained sensors, M targetThe sink node can move and change its locthe network lifetime. Actually there are unconstrained and constrained mobility, fomobility to improve network lifetime. mobility scenarios, the sink node can be mothe field. Since there is no limitation on the number of possible locations for sink mobilitincreasing the number of possible locatiocomplexity increases too. But the optimal sincould be found by using this approach. Conode can just move between a finite numlocations in constrained mobility scenarios. handful of points are possible locations, thcannot be always achievable. On the other hhas less complexity than the previous one. Ifare good representatives for all locations, theclose to the optimum answer.

Optimizing an objective in a high-dimenleads to a result no worse than what can subspace of reduced dimension. Thus sink munconstrained or constrained mobility, cnetwork lifetime because mobility increases the degree of freedom of the problem.

In this paper we focus on constrained mThe sink is constrained to where the sensor nosensor nodes are scattered randomly in tlocation can be a good handful of all possibfield. Accordingly in target coverage probsink, no matter full or partial target covescheduling of the sensors and the sink sojopossible locations should be determined suchlifetime is maximized.

Sink Target

a. Illustration of the CTC problem.

F

Sink Problem

the CTC problem ts and a sink node. ation to maximize

two approaches, or exploiting sink In unconstrained

ove to any point in sink mobility, the

ty is too many. By ons, the problem nk mobility pattern onversely, the sink mbers of possible Given that only a

he optimal answer hand, this approach f the possible ones e answer would be

nsion space always be achieved in a

mobility, no matter can increase the the dimension and

mobility approach. odes are. Since the the field, sensors

ble locations in the blem with mobile erage, routing and ourn time at each h that the network

IV. PROBLEM

Let S= { , , ,..., } (( | | =M) and R denote the stargets and the sink node, respethe set of sensors which areSuppose that the cover trees optimum answers of Fig.1.a these two cover trees, we willedge cost is the amount of data network. Obviously, we can dFig.1.c from the graph in FigCTCG (Connected Target Covfinding the optimum edge coptimum solution for the CTCBeside, in the case of mobile possible location should be dete

A. Sensor’s Energy ConsumptLet denotes the energy co

from node i to node j. Then it w

=

Where and are constdistance between node i and j.takes value between [2,4]. Let for receiving a bit of data. Sintransmission power level, thconstant amount of energy fordenotes the energy consumed data. Suppose that denotsensor s monitors them for τ sethen the energy consumed in a sum of sensing and transmconsumed in a source sensor i wsecond to and transmits the mwould be:

Sensor in sleep mode Source node Source

b. Solution 1

Figure 1. An example of CTC problem and it's solutions

M FORMULATION (| |=N) , P={ , , ,..., } set of deployed sensor nodes , ectively and Let and indicate e in source and relay modes. in Fig.1.b and Fig.1.c are the CTC problem. If we combine l have a graph like Fig.2. Each which passes throw that edge in erive cover trees in Fig.1.b and

g.2. We call this kind of graph verage Graph). Consequently, by ost for the CTCG graph, the C problem could be found too. sink, sink sojourn time at each

ermined too.

ion Model onsumed to transmit a bit of data

would be:

(1)

tants and is the Euclidean α is path loss parameter which

denotes the energy consumed nce the sender node controls its he receiver node consumes a r receiving a bit of data. Let for sensing a target for a bit of

tes the number of targets which econds. If the coverage rate is β source sensor for τ second is the

mitting energy. So the energy which monitors targets for τ

monitored information to node j

e-and-relay node Relay node

c. Solution 2

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, . . . . A relay node receives data from its

transmits them to its parent. For a given rdenotes the number of targets which node i rτ second. The energy consumed in relay sensreceiving and transmitting energy. So the enegiven relay sensor i which transmits its trafsecond would be: , . . . .

As mentioned before, a sensor can operatand relay mode. In this situation the energsecond would be the summation of equatiosensor which is neither in source nor in relaymode and does not consume energy.

B. Full Target Coverage with Mobile Sink FAssume that the initial energy of each

denotes the network lifetime. For each targtotal information flow from node i to node jtarget l (i.e. monitored information of target

as the time span for the kth epoch. A nwhen the sink node changes its location. formulation by assuming that the sink is colloduring the kth epoch. Therefore, shows ththe sink node at sensor k in second. Hformulation of the problem is as follows:

Max Z = T

s.t 0 0

Figure 2. CTCG model

(2)

child nodes and relay node i, relay their data for or is the sum of its

ergy consumed in a ffic to node j for τ

(3)

te at both of source gy consumed for τ on (2) and (3). A y mode is in sleep

Formulation sensor is .Let T

get l, shows the j which belongs to l). We also define

new epoch begins We simplify the

ocated with node k he sojourn time of Hence, the linear

(4)

∊ (5)

∊ ,∊ (6)

∑ , + ∑ ,∑

The objective function (4lifetime. Constraints (5) are written for each target l and insrate of β for T second. Constconstraints written for each seinput and output flow of each Since the sink will be co-locaand receivesβ bit per second ftotal output flow of the sensor ∑ shows the total itarget.

We assumed that sink nodtarget and can just receive datathat, the total input flow to eacheach target should be greater insure that the sink node will rewhile the sink is co-located to sstay at the location of sensor i instead of the sensor i, the seenergy for receiving bitsbits per second).Constraints (8energy for receiving, transmittinot greater that its initial energytotal sojourn time of the sinklifetime.

We call this model, mobiTarget Coverage). The output network lifetime, sink sojournand dataflow matrix which shsolution.

C. Partial Target Coverage wiWe assumed that the value

any point of time ρ% of all tcontrast with full target covermonitored for T seconds (i.e. tshould be Tβ), in partial targemonitored less than T seconds. shows the amount of data whwhile the sink node is co-locatlinear formulation of the proble

Max Z= T S.T 0

,

(7)

+ i∊S (8)

(9)

4) tries to maximize network the flow balance constraints

sure that target l is monitored by traints (6) are the flow balance ensor i and guarantee that total sensor for each target is equal.

ated with sensor i for seconds from each of the m targets, the i will be∑ while nput flow for sensor i for each

de is not capable of sensing a a from other sensors. Because of h sensor i from other sensors for or equal to . Constraints (7)

eceive its data from other sensors sensor i. Since the sink node will for seconds and receives data

ensor node would not consume s (i.e. the sink node receive mβ ) insure that the sum consumed

ing and sensing in each sensor is y. Constraints (9) insure that the

k node is equal to the network

ile sink-FCTC (Full Connected of this formulation will be the

n time at each possible location hows the routing in the optimal

ith Mobile Sink Formulation of ρ is given by the user and in

targets should be monitored. In rage that each target should be total output flow of each target et coverage each target can be Let be a dummy flow which

hich is not covered for target l ted with sensor i. Therefore, the em is as follows:

(10) ∊ (11)

0 ∊ ,∊ (12)

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∑ 1 ∑ , + ∑ , +∑

Constraints (11) insure that the total ouflow for each target is equal to Tβ. Constrsame as constraints (6). Constraint (13) innode will receive for each targesensors while it is co-located with sensocoverage rate β, the total amount of monicoverage for m target in seconds is mβcoverage for a given ρ , the total amount would be greater than or equal ρmβ. In thamount of dummy flow would be less than orρ) (i.e. (1-ρ)+ρ=1→ mβ= ρmβ+ mβ(1-ρ))by constraints(14). Constraints (15) are the s(8) but the sink node receives ρmβ insteasecond. Constraint (16) is the same as constra

We call this model, mobile sink-PCTC (Target Coverage). The output of this formulathe previous one. Besides, it results the amois not covered by the sink node at location i, f

V. SIMULATION RESULT

In this section, we evaluate the performmodels by solving them using the programming formulations. Furthermore, tosuperiority of our algorithm, we compare(Communication Weighted Greedy Cover) and SPT-Greedy [9] for different scenariostationary network which its sensors and tarrandomly in a 100 m×100 m area. Data senseis generated by rate 10Kbps(β=10Kbps).Theeach sensor is 20 J and the values of other pabe =50 ⁄ , =150 ⁄ , =150⁄⁄ and =3.Each sensor covers aitself with a fixed sensing range equal to the dall sensors sensing range is equal to 20 m(have the same maximum communication ranto 40 m( =40m). In static sink scenarioslocated at the center of the field.

Each scenario plotted on the figure is thnetworks which are generated randomly. LINfor solving the proposed linear programmThereafter, OMNET++ [17] is used to simusolve by LINGO (i.e. sink sojourn time location and dataflow matrix which shows the

In Fig.3, for full coverage, we study thedensity on the performance of our algorithmwith CWGC and SPT-Greedy. The numbevaries between 50 and 100 while there scattered targets (M=20) in each scenario. I

,

(13)

(14)

+ ∊S (15)

(16)

utput and dummy raints (12) are the

nsure that the sink et form the other or i. For a given itored data in full β while in partial of monitored data

he same way, total r equal to ρmβ(1-) which is insured same as constraints ad of mβ bits per aint (9).

(Partial Connected ation is the same as ount of data which for each target.

TS mance of proposed

proposed linear o demonstrate the e it with CWGC introduced by [8]

os. We simulate a rgets are deployed ed from each target e initial energy of

arameters are set to 0 ⁄ , b=100

a disk centered at disk radius and for ( =20m)and they nge which is equal s the sink node is

he average of 100 NGO [16] is used

ming formulations. ulate the solutions

at each possible e routing).

e impact of sensor m and compare it er of sensors (N) are 20 randomly

It can be seen that

the lifetime achieved by SPT-and the lifetime achieved by three times of CWGC and abou

In Fig.4, for full coverage, different number of targets vcompare it with CWGC anApparently network lifetime deincrease. More targets resultsnetwork. Since CWGC doesnmore redundant data traffic wothe number of targets. Thus decreasing faster than SPT-Grefigure also shows that the netwsink-CTC is always higher thaGreedy algorithms.

In Fig.5, for partial target csensor density on the perforcompare it with PCH [11].The

Figure 4. Impact of target dnetwork

Figure 3. Impact of sensonetwo

-Greedy is about 1.2 of CWGC our mobile sink-CTC is about

ut 2.62 of SPT-Greedy.

we evaluate our algorithm with varying between10 to 45 and nd SPT-Greedy while N=80. ecreases as the number of targets s in more data traffic in the ’t consider overlapping targets, ould be produced by increasing

CWGC’s network lifetime is eedy and mobile sink-CTC. The

work lifetime achieved by mobile an the one by CWGC or SPT-

overage, we study the impact of rmance of our algorithm and e number of sensors (N) varies

density on full target coverage k lifetime

or density on full target coverage ork lifetime

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between 50 and 100 while M=20 and ρ=90that the mobility increase the lifetime of partin about 2.5 times.

In addition we study the impact of partianetwork lifetime. Fig.6 shows the impact owith different ρ values. Obviously by ρ decresame time network lifetime increases whdecreases. Deciding a good value for ρ canbetween network lifetime and precisiondependent to the application.

VI. CONCLUSION In this paper we study impact of sink

network lifetime in CTC problem in WSNmodel called CTCG. Each CTC problem mmodel. New Linear Programming formulaobtain the optimum routing and sojourn timeach location. Simulation results shows that improve the network lifetime to 2.6 timerespectively for full and partial CTC, in cstatic sink. Moreover, we compared the partcoverage lifetime. Simulation results show tabout 90% of all targets and using a moblifetime can improve about 1.8 times in ctarget coverage with mobile sink.

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