Research ArticleLifetime Optimization Algorithm with Mobile Sink Nodes forWireless Sensor Networks Based on Location Information

Yourong Chen, Zhangquan Wang, Tiaojuan Ren, and Hexin Lv

College of Information Science and Technology, Zhejiang Shuren University, Shuren Street 8, Hangzhou 310015, China

Correspondence should be addressed to Zhangquan Wang; hh75816@sina.com

Received 3 October 2014; Revised 5 February 2015; Accepted 11 February 2015

Academic Editor: Xiaohong Jiang

Copyright © 2015 Yourong Chen et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In order to overcome the energy hole problem in some wireless sensor networks (WSNs), lifetime optimization algorithm withmobile sink nodes for wireless sensor networks (LOA MSN) is proposed. In LOA MSN, hybrid positioning algorithm of satellitepositioning and RSSI positioning is proposed to save energy. Based on location information, movement path constraints, flowconstraint, energy consumption constraint, link transmission constraint, and other constraints are analyzed. Network optimizationmodel is established and decomposed into movement path selection model and lifetime optimization model with known gridmovement paths. Finally, the two models are solved by distributed method. Sink nodes gather data of sensor nodes along thecalculated paths. Sensor nodes select father nodes and transmit data to corresponding sink node according to local information.Simulation results show that LOA MSN makes full use of node energy to prolong network lifetime. LOA MSN with multiplesink nodes also reduces node energy consumption and data gathering latency. Under certain conditions, it outperforms MCP,subgradient algorithm, EASR, and GRAND.

1. Introduction

In most cases all sensor nodes of WSNs are battery-poweredand located in the unattended or harsh environment. Batteryreplacement is difficult or even impossible for battery replace-ment. Once node’s energy exhausts, the node is disabled.It will affect the network operation and even split thenetwork to shorten network lifetime [1, 2]. Therefore, inWSNs, network lifetime is the important indicator of networkperformance.The algorithms ofWSNs should save the energyand maximize the network lifetime.

Some scholars research on lifetime optimization algo-rithm with fixed nodes for WSNs and have got someaccomplishments. For example, [3] proposes an ant colonyoptimization approach for maximizing the lifetime of het-erogeneous wireless sensor networks. In the algorithm, coverconstraint, collection constraint, and routing constraint areconsidered. The objective function is established and antcolony optimization is used to obtain the lifetime optimalscheme. Reference [4] constructs optimal clustering archi-tecture and designs energy-aware cluster-head rotation androuting protocol to maximize network lifetime. Reference

[5] proposes two methods to optimize the lifetime of chain-based protocols using integer linear programming (ILP)formulations. In those algorithms, it is inevitably to causeunbalanced distribution of node energy consumption andenergy hole problem. The problem can be overcome by sinknodes’movement. All nodes have the opportunity to transmitdata near sink nodes and have the same lifetime.

References [6–9] research on the network lifetime max-imization problem, establish the network lifetime optimiza-tion models with mobile sink node, use optimization algo-rithms to solve the models, and obtain optimal scheme. Ref-erence [10] theoretically discusses the relationship betweennetwork lifetime and maximum throughout in the largescale WSNs. However, all references [6–10] assume that themovement path of sink node is already known and do notconsider how to determine the anchors or movement pathof sink node. Reference [11] searches guide agent nodesand intermediate guide nodes, analyzes the TSP (travelingsalesman problem), determines movement path with nodecooperation, and proposes data gathering algorithm whichoptimizes data transmission latency and energy. However,the algorithm does not consider network lifetime. Reference

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2015, Article ID 857673, 11 pageshttp://dx.doi.org/10.1155/2015/857673

2 International Journal of Distributed Sensor Networks

[12] divides network into several grids, and proposes a grid-based clustering algorithm. Reference [13] proposes rangeconstrained clustering (RCC). RCCdivides nodes into severalclusters. Sink node stays at the cluster centers to gather data.The Concorde TSP solver is used to calculate the shortestmovement path of sink node through some cluster centers.References [11–13] determine the locations of mobile sinknode. However, they do not consider the data gathering whensink node is moving. Whether the algorithms can obtainoptimal solution still needs theoretical analysis. Reference[14] proposes energy-aware sink relocation (EASR) algorithmfor mobile sinks. EASR uses maximum capacity path (MCP)protocol for routing, starts to move when two relocationconditions are met, and finds the next moving location whichhas the greatest weight value. But compared with networklifetime, the relocation conditions are met after a long time.The protocol is not good at prolonging network lifetime.

Therefore, lifetime optimization algorithm with mobilesink nodes for wireless sensor networks based on locationinformation (LOA MSN) is proposed. In LOA MSN, energy-saving positioning algorithm of nodes is proposed and themonitoring area is divided into several grids of the samesize. Sink node can move into each grid center to gatherdata.Themovement path constraints, flow constraint, energyconsumption constraint, link transmission constraint, andother constraints are analyzed. The network optimizationmodel is established. Then, the network optimization modelis decomposed into movement path selection model andnetwork lifetime optimization model with knownmovementpaths. The movement path selection model is solved insink nodes by distributed clustering method and graphtheory method. Mobile gathering and static gathering areconsidered and the network lifetime optimization model isapproximately solved by distributed graph theory method.Compared with MCP, subgradient algorithm, EASR andGRAND (for grid random scheme), LOA MSNuses the nodeenergy as much as possible to prolong the network lifetime.

The remaining parts of paper are organized as follows.In Section 2, the energy-saving positioning algorithm ofnodes is proposed. In Section 3, the algorithm assumptionand lifetime optimization model with mobile sink nodes areproposed. In Section 4, the distributed solution of model isproposed. In Section 5, the simulation results are presented.In Section 6, the paper is concluded.

2. Energy-Saving Positioning Algorithm

At present,mostly outdoor positioning uses satellite position-ing module such as GPS or Beidou. But the work current ofthose modules is up to tens of milliamp. In the energy limitedWSNs, they have great energy consumption. RSSI (receivedsignal strength indication) positioning algorithm obtainsthe signal energy through link signal and has low energyconsumption.Therefore, the hybrid positioning algorithm ofsatellite positioning and RSSI positioning is proposed to saveenergy. Assume that each node is equipped with Beidou orGPS positioning module. After network starts, sensor nodesand sink nodes periodically start the positioning module to

obtain their longitude and latitude values. Due to the loca-tions of sensor nodes being fixed, the time interval of sensornodes is much longer than that of sink nodes. When thereare more than 3 sensor nodes in the 1-hop communicationrange of sink node, the sink node shuts down the satellitepositioning module for some time and uses RSSI positioningalgorithm based on latest satellite positioning coordinates.The implementation of hybrid positioning algorithm is asfollows.

Sink nodes transmit positioning query packets to nearbysensor nodes. Sensor nodes in the 1-hop communicationrange of sink nodes transmit their location informationwhich is obtained by satellite positioning module, nodeaddress, and other information back to the correspondingsink node. Sink nodes receive a packet and obtain the RSSIvalue of link signal. If there are historical RSSI data of thesame link, Kalman filtering is used to reduce errors andimprove positioning accuracy [15]. Based on processed RSSIvalues, link distance 𝑑

𝑖from sensor node 𝑖 to sink node is

evaluated as follows:

𝑑𝑖= 10−(RSSI𝑖+𝐴)/(10Loss), (1)

where RSSI𝑖represents the processed signal strength value

of link from sensor node 𝑖 to sink node. A represents thereceived signal strength value when the distance betweentransmitter and receiver is 1m. Its value range is 30–50.Loss represents path loss exponent, namely, attenuationrate of signal energy. Its value range is 1–8. Through datacommunication, sink nodes obtain the location informationof multiple sensor nodes and distances to those senor nodesand use multipoint positioning algorithm to calculate itscoordinates with the following formula:

2

[[[[

[

𝑥𝑁𝑠− 𝑥1

.

.

.

𝑥𝑁𝑠− 𝑥𝑁𝑠−1

𝑦𝑁𝑠− 𝑦1

.

.

.

𝑦𝑁𝑠− 𝑦𝑁𝑠−1

]]]]

]

[𝑥𝑅

𝑠

𝑦𝑅

𝑠

]

=

[[[[

[

(𝑑2

1− 𝑑2

𝑁𝑠) − (𝑥

2

1− 𝑥2

𝑁𝑠) − (𝑦

2

1− 𝑦2

𝑁𝑠)

.

.

.

(𝑑2

𝑁𝑠−1− 𝑑2

𝑁𝑠) − (𝑥

2

𝑁𝑠−1− 𝑥2

𝑁𝑠) − (𝑦

2

𝑁𝑠−1− 𝑦2

𝑁𝑠)

]]]]

]

,

(2)

where (𝑥𝑖, 𝑦𝑖), 𝑖 ∈ (1, 2, . . . , 𝑁

𝑠), represents the 𝑥- and 𝑦-

coordinates of sensor node 𝑖 which are the neighbor nodeof sink node. (𝑥𝑅

𝑠, 𝑦𝑅

𝑠) represents the 𝑥- and 𝑦-coordinates of

sink node with RSSI positioning algorithm.𝑁𝑠represents the

number of neighbor sensor nodes around the sink node.Sink node records the elapsed time after the satellite

positioning module is shut down. According to the satellitepositioning coordinates (𝑥𝑤

𝑠, 𝑦𝑤

𝑠), RSSI positioning coordi-

nates (𝑥𝑅𝑠, 𝑦𝑅

𝑠), the elapsed time 𝑡

𝐿, and themovement speed 𝑢

of sink node, the intersection point between the circle whose

International Journal of Distributed Sensor Networks 3

center is (𝑥𝑤𝑠, 𝑦𝑤

𝑠) and radius is 𝑡

𝐿∗𝑢 and the line from (𝑥

𝑅

𝑠, 𝑦𝑅

𝑠)

to (𝑥𝑤𝑠, 𝑦𝑤

𝑠) is the current coordinates (𝑥

𝑠, 𝑦𝑠) of sink node

𝑥𝑠=

𝑡𝐿𝑢

√(𝑦𝑤𝑠− 𝑦𝑅𝑠)2/ (𝑥𝑤𝑠− 𝑥𝑅𝑠)2+ 1

+ 𝑥𝑤

𝑠,

𝑦𝑠=

𝑡𝐿𝑢 (𝑦𝑤

𝑠− 𝑦𝑅

𝑠)

(𝑥𝑤𝑠− 𝑥𝑅𝑠)√(𝑦𝑤

𝑠− 𝑦𝑅𝑠)2/ (𝑥𝑤𝑠− 𝑥𝑅𝑠)2+ 1

+ 𝑦𝑤

𝑠.

(3)

By the energy-saving positioning algorithm, nodes calcu-late their 𝑥- and 𝑦-coordinates with periodic start of satellitepositioning module. It reduces the energy consumption ofnodes.

3. Establishment of Optimization Model

In the paper, only 2D (two-dimensional) WSNs are consid-ered and all nodes know their own location coordinates. Thealgorithm assumption is as follows. The locations of sensornodes are fixed. Sink nodes can move to any grid centerbased on location information. All sensor nodes continuouslytransmit their sensing data to sink nodes. All sensor nodeshave the same performance (such as sensing rate, maximumcommunication radius, initial energy, and energy consump-tion parameter). Energy of all nodes is limited, but energy ofsink nodes can be renewable.

3.1. Constraints

3.1.1. Movement Path Constraints. Many references considerthat sink node stays at one node location, gathers data, andtakes its responsibilities to sense. It basically limits themobilelocation selection of sink node and does not consider otherlocations where sensor node never distributes. Therefore,their algorithms obtain local optimal solutions. As is shownin Table 1, monitoring area is divided into several grids of thesame size and each grid is numbered. The sink node can stayat each grid center to gather data. The method enlarges theselection range of sojourn locations for sink nodes.

The mth sink node starts at initial location and finallymoves back to the initial location. The initial location con-straints ofmth sink node are as follows:

∑

𝑤∈𝐺𝑑

𝑝𝑚

𝑠,𝑤= 1, ∀𝑚,

∑

𝑤∈𝐺𝑑

𝑝𝑚

𝑤,𝑠= 1, ∀𝑚,

(4)

where s represents grid𝑠and initial location of mth sink

node, gridV represents the center of grid v, and Gd representsthe set of all grid centers. 𝑝𝑚V,𝑤 is the state indicator, whichrepresents whether 𝐿(gridV, grid𝑤) appears in the movementpath ofmth sink node. 𝐿(gridV, grid𝑤) represents the directedline segment from gridV to grid

𝑤. 𝑝𝑚V,𝑤 = 1 represents

𝐿(gridV, grid𝑤) is in the movement path ofmth sink node. Asis shown in Table 1, the grids (1, 𝑛, (𝑛 − 1)𝑛 + 1, 𝑛2) have only2 neighbor grids and 2 line segments to neighbor grids. The

Table 1: Grids in the monitoring area.

1 2 ⋅ ⋅ ⋅ 𝑛 − 1 𝑛

𝑛 + 1 𝑛 + 2 ⋅ ⋅ ⋅ 2𝑛 − 1 2𝑛

.

.

....

.

.

....

.

.

.

(𝑛 − 2) 𝑛 + 1 (𝑛 − 2) 𝑛 + 2 ⋅ ⋅ ⋅ 𝑛2− 𝑛 − 1 𝑛

2− 𝑛

(𝑛 − 1) 𝑛 + 1 (𝑛 − 1) 𝑛 + 2 ⋅ ⋅ ⋅ 𝑛2− 1 𝑛

2

other boundary grids have 3 neighbor grids. Others (such as𝑛 + 1, 2𝑛 − 1) have 4 neighbor grids.

Because each sink node cyclically moves along the path,the sum of state indicators which represent from gridV to allits neighbor grid centers is equal to the sum of state indicatorswhich represent from all neighbor grid centers to gridV. Thestate indicator balance constraint is

∑

𝑤∈𝐺𝑑,𝐿(gridV ,grid𝑤)∈𝐿𝑑𝑝𝑚

V,𝑤

= ∑

𝑤∈𝐺𝑑,𝐿(gridV ,grid𝑤)∈𝐿𝑑

𝑝𝑚

𝑤,V, ∀V ∈ 𝐺𝑑, ∀𝑚,(5)

where Ld represents the set of all possible line segments.To avoid two mutually movable grids and eliminate the

subtours, the state indicator limitation constraint is

𝑝𝑚

V,𝑤 + 𝑝𝑚

𝑤,V ≤ 1, ∀𝑤, V ∈ 𝐺𝑑, ∀𝑚. (6)

3.1.2. Flow Constraint. The transmission data are composedof the sensing data and received data from neighbor nodes.The flow constraint is

∑

𝑗∈𝑁(𝑖)

𝑓𝑚

𝑖𝑗= 𝑆𝑖+ ∑

𝑗∈𝑁(𝑖)

𝑓𝑚

𝑗𝑖, ∀𝑖 ∈ 𝑉

𝑚, ∀𝑚, (7)

where 𝑆𝑖represents the data sensing rate of node i and 𝑓𝑚

𝑖𝑗

represents the data transmission rate from node 𝑖 to node𝑗 when the data of node 𝑖 aggregate to mth sink node. 𝑉

𝑚

represents a nonempty set of sensor nodes which are inthe gathering range of mth sink node. 𝑁(𝑖) represents theneighbor node set of node 𝑖 in 𝑉

𝑚.

3.1.3. Energy Consumption Constraint. During the gatheringtime 𝑇

𝑚 of mth sink node, the energy consumption ofreceiving data fromneighbor nodes is𝑇𝑚∑

𝑚∑𝑗∈𝑁(𝑖)

𝑓𝑚

𝑗𝑖𝐸elec,

where 𝐸elec represents electric energy consumption of receiv-ing or transmitting unit data. The energy consumption oftransmitting data is 𝑇𝑚∑

𝑚∑𝑗∈𝑁(𝑖)

𝑓𝑚

𝑖𝑗(𝐸elec + 𝜀

𝑓𝑠𝑑2

𝑖𝑗), where

𝜀𝑓𝑠

represents electronic energy consumption of amplifyingunit signal. The total energy consumption is not larger thaninitial energy. The energy consumption constraint is

𝑇𝑚∑

𝑚

( ∑

𝑗∈𝑁(𝑖)

𝑓𝑚

𝑗𝑖𝐸elec + ∑

𝑗∈𝑁(𝑖)

𝑓𝑚

𝑖𝑗(𝐸elec + 𝜀𝑓𝑠𝑑

2

𝑖𝑗))

≤ 𝐸initial, ∀𝑖 ∈ 𝑉𝑚, ∀𝑚,

(8)

where 𝐸initial represents the initial energy of sensor nodes.

4 International Journal of Distributed Sensor Networks

3.1.4. Link Transmission Constraint. Because link bandwidthresource is limited, the total amount of link transmission datais limited. Then the link transmission constraint is

𝑓𝑚

𝑖𝑗+ 𝑓𝑚

𝑗𝑖≤ 𝑅max, 𝐿 (𝑖, 𝑗) ∈ 𝐿

𝑚, 𝑗 > 𝑖, ∀𝑚, (9)

where 𝑅max represents the maximum transmission rates ofnodes, 𝐿(𝑖, 𝑗) represents the link from node 𝑖 to node 𝑗, and𝐿𝑚represents the set of all wireless links in all sensor nodes

of 𝑉𝑚.

3.2. Network OptimizationModel. When network starts, sinknode leaves from initial location to next grid center andfinally moves back to initial location. The data gatheringsof sink node are mobile gathering and static gathering. Themobile gathering of sink node is that, during its movement,sink node dynamically gathers data. The static gathering ofsink node is that it stays at some grid centers for some sojourntime and statically gathers data.

The total time of𝑚th sink node movement is

𝑇𝑚= ∑

𝑛

∑

𝑝

𝑡𝑛,𝑚

𝑝+∑𝑛∑V∈𝐺𝑑∑𝑤∈𝐺𝑑 𝑑V𝑤𝑝

𝑚

V,𝑤

𝑢, (10)

where 𝑇𝑚 represents total time ofmth sink node movement.𝑡𝑛,𝑚

𝑝represents the sojourn time in whichmth sink node stays

at grid𝑝in its 𝑛th movement. 𝑑V𝑤 represents the distance

between gridV and grid𝑤. 𝑢 represents the movement speed

of sink nodes.If there is one sink node in the network, formula (10)

represents the network lifetime 𝑇net. If there are severalsink nodes, sink nodes broadcast their location informationbefore gathering data. Sensor nodes select the nearest sinknode to transmit data. Then the network is divided intomultiple clusters. The network lifetime 𝑇net is defined as theaverage value of all 𝑇𝑚; namely, 𝑇net = ∑

𝑚𝑇𝑚/𝑀, where

𝑀 represents the number of sink nodes. The optimizationproblem of multiple sink nodes is transformed into multipleoptimization problems of single sink node. The lifetimeoptimization model of𝑚th sink node is

max(𝑇𝑚 = ∑𝑛

∑

𝑝

𝑡𝑛,𝑚

𝑝+∑𝑛∑V∈𝐺𝑑∑𝑤∈𝐺𝑑 𝑑V𝑤𝑝

𝑚

V,𝑤

𝑢) (11a)

s.t. Constraints (4)–(6)

∑

𝑗∈𝑁(𝑖)

𝑓𝑚

𝑖𝑗= 𝑆𝑖+ ∑

𝑗∈𝑁(𝑖)

𝑓𝑚

𝑗𝑖, ∀𝑖 ∈ 𝑉

𝑚, (11b)

𝑇𝑚∑

𝑚

( ∑

𝑗∈𝑁(𝑖)

𝑓𝑚

𝑗𝑖𝐸elec + ∑

𝑗∈𝑁(𝑖)

𝑓𝑚

𝑖𝑗(𝐸elec + 𝜀𝑓𝑠𝑑

2

𝑖𝑗))

≤ 𝐸initial, ∀𝑖 ∈ 𝑉𝑚,

(11c)

𝑓𝑚

𝑖𝑗+ 𝑓𝑚

𝑗𝑖≤ 𝑅max, 𝐿 (𝑖, 𝑗) ∈ 𝐿

𝑚, 𝑗 > 𝑖, (11d)

𝑡𝑛,𝑚

𝑝≥ 0, ∀V, 𝑚, 𝑛, (11e)

𝑓𝑚

𝑖𝑗≥ 0, ∀𝑖, 𝑗 ∈ 𝑉

𝑚, (11f)

𝑝𝑚

V,𝑤 ∈ {0, 1} , ∀V, 𝑤 ∈ 𝐺𝑑. (11g)

4. Solution Method

Network optimization model (11a) considers movementpath selection of sink node and data routing. The modelhas too many parameters and its solution is complicated.In the model, movement path constraints mainly limit∑𝑛∑V∈𝐺𝑑∑𝑤∈𝐺𝑑 𝑑V𝑤𝑝

𝑚

V,𝑤/𝑢 in target function. It means find-ing a relatively optimal path. The flow constraint, energyconsumption constraint, and link transmission constraintmainly limit∑

𝑛∑𝑝𝑡𝑛,𝑚

𝑝in target function. It means searching

optimal lifetime and routing solution. In order to reducesolving complication, the network optimization model (11a)is divided into movement path selection model and lifetimeoptimization model with known movement paths.

4.1. Movement Path Selection Model. The movement pathconstraints are too loose for path selection. It does notconsider the node density and node energy. It needs a lot oftime to calculate the solution of themodel.Therefore, the pathselection of sink nodes needs to consider the node locationinformation and energy and determines some anchors forsink nodes. The anchors are some locations around wherenode density is high and residual energy of nodes is large.The clusteringmethods can be used to determine the anchorsat which sink nodes stay to gather data of sensor nodes. Inthe paper, modified subtractive clustering algorithm is usedto calculate the anchors [16]. The number and the set ofanchors which mth sink node needs to stay at are obtained.The implementation steps ofmth sink node are as follows.

Step 1. The number of anchors is𝑁𝑚= 1. The potential value

of each grid is initialized as follows:

𝑃 (V) = 𝑥1 ∑𝑗∈𝑁(V)

exp(−𝛼1𝑑V𝑗

𝑑max)

+ 𝑥2∑

𝑗∈𝑁(V)exp(−

𝛼2𝐸initial

Re (𝑗)) ,

(12)

where 𝑃(V) represents potential value of gridv. 𝑑V𝑗 representsthe distance from sensor node 𝑗 to grid center gridv. 𝑁(V)represents the set of sensor nodes from which the distanceto grid center is no longer than maximum communicationdistance 𝑑max. Re(𝑗) represents the residual energy of node j.𝛼1represents distance potential factor. 𝛼

2represents residual

energy potential factor. 𝑥1represents distance weight factor.

𝑥2represents residual energy weight factor, and 𝑥

1+ 𝑥2= 1.

Step 2. Thegrid ofmaximumpotential value is found. Its gridcenter as anchor point is selected. 𝑃∗

𝑁𝑚represents its potential

value.

International Journal of Distributed Sensor Networks 5

Step 3. The grid center is aggregation point. Potential valuesof the grids are subtracted by formula

𝑃 (V) = 𝑃 (V) − 𝑃∗𝑁𝑚

(exp(−𝛽𝑑V𝑎

𝑑max)) , ∀V, (13)

where 𝛽 represents attenuation factor. 𝑑V𝑎 represents thedistance from grid center gridv to the aggregation point.

Step 4. If the following inequality holds, end the algorithm;otherwise𝑁

𝑚= 𝑁𝑚+ 1 and go to Step 2:

maxV

𝑃 (V) ≤ 𝜀𝑃∗1, (14)

where 𝜀 represents judgment factor.

Network environment is complicated.Themobile gather-ing efficiency of sink nodes is far lower than static gatheringefficiency. Therefore the movement time of sink nodes is asshort as possible. Movement distance of mth sink node inone data gathering period is∑V∈𝐺𝑑∑𝑤∈𝐺𝑑(𝑑V𝑤𝑝

𝑚

V,𝑤)/𝑢. Size ofeach grid is the same.Therefore, themovement path selectionmodel of all sink nodes can be represented as follows whenanchors are determined:

min ∑

V∈𝐺𝑑∑

𝑤∈𝐺𝑑

𝑝𝑚

V,𝑤 (15a)

s.t.: ∑𝑤∈𝐺𝑑

𝑝𝑚

V,𝑤 = 1 ∑

𝑤∈𝐺𝑑

𝑝𝑚

𝑤,V = 1, ∀V ∈ {𝑃𝑚, 𝑠} , ∀𝑚,

Constraints (4)–(6), (11g),(15b)

where 𝑃𝑚 represents the set of anchors which is obtained bythe modified subtractive clustering algorithm.

Model (15a) shows that the movement path selection ofsink nodes is essentially TSP problem. It can be solved bygenetic method, graph theory, and other methods. Becausethe number of anchors is not large, nearest neighbor inter-polation algorithm is used to find the approximate solutionof shortest path [17]. The implementation steps of mth sinknode are as follows.

Step 1. The location of sink node is initialized and 𝑖 = 0. Theanchor V

0is the starting point.The initial closed path is V

0V0.

Step 2. In {𝑃𝑚, 𝑠} − {V0, V1, . . . , V

𝑖}, anchor V

𝑖+1is found which

has the nearest distance to any anchor in {V0, V1, . . . , V

𝑖} set.

Step 3. The anchor V𝑖+1

is inserted into the closedpath V

0V1⋅ ⋅ ⋅ V𝑖V0. The paths V

0V𝑖+1

V1⋅ ⋅ ⋅ V𝑖V0

andV0V1V𝑖+1

⋅ ⋅ ⋅ V𝑖V0, . . . , V

0V1⋅ ⋅ ⋅ V𝑖V𝑖+1

V0are obtained. The

shortest path is selected as the new shortest closed path.

Step 4. If 𝑖 < (𝑁𝑚+1), then go to Step 2; otherwise obtain the

approximate solution, and go to Step 5.

Step 5. According to the approximate solution, namely theobtained close path, sink node moves along the directed linesegment from one anchor to its next anchor periodically. If

sink node stays at the end anchor in the path, it moves back toinitial anchor. Then all possible grids which sink node passesthrough are founded in turn. The selected anchors and gridcenters constitute the solution of movement path selectionmodel (15a). The grid centers that the sink node stays at,namely, the gridmovement paths of sink nodes, are obtained.

4.2. Lifetime Optimization Model. When the grid movementpaths of sink nodes are determined, according to the def-inition of network lifetime, network lifetime optimizationmodel can be transformed to the models of single sinknode. Their target is to obtain the lifetime 𝑇

𝑚 and nodetransmission rates 𝑓𝑚

𝑖𝑗

max 𝑇𝑚= ∑

𝑛

∑

𝑝

𝑡𝑛,𝑚

𝑝+∑𝑛∑V∈𝐺𝑑∑𝑤∈𝐺𝑑 𝑑V𝑤𝑝

𝑚

V,𝑤

𝑢

s.t.: Constraints (11b)–(11f).

(16)

The mobile gathering process of sink nodes is consideredas sink nodes stay at the grid centers which are in theirgrid movement paths for some sojourn time to gather data.Therefore, the mobile gathering problem is converted intodiscrete multiple static gathering problems whose sojourntime is 𝑑V𝑤/𝑢. The lifetime is composed of sojourn times forwhich sink nodes stay at the anchors and passing grid centers.

Therefore, the model is simplified.The lifetime optimiza-tion problem is transformed to several lifetime optimizationmodels in which sink node stays at different grid centers.When mth sink node stays at location 𝑃

𝑘, the lifetime

optimization model is

max 𝑇V (17a)

s.t.: ∑𝑗∈𝑉𝑃𝑘

𝑓𝑃𝑘,𝑚

𝑖𝑗= 𝑆𝑖+ ∑

𝑗∈𝑉𝑃𝑘

𝑓𝑃𝑘,𝑚

𝑗𝑖, ∀𝑖 ∈ 𝑉

𝑃𝑘 (17b)

( ∑

𝑗∈𝑉𝑃𝑘

𝑓𝑃𝑘,𝑚

𝑗𝑖𝐸elec + ∑

𝑗∈𝑉𝑃𝑘

𝑓𝑃𝑘,𝑚

𝑖𝑗(𝐸elec + 𝜀𝑓𝑠𝑑

2

𝑖𝑗))

≤𝐸initial𝑇V

, ∀𝑖 ∈ 𝑉𝑃𝑘

(17c)

𝑓𝑃𝑘,𝑚

𝑖𝑗+ 𝑓𝑃𝑘,𝑚

𝑗𝑖≤ 𝑅max, 𝐿 (𝑖, 𝑗) ∈ 𝐿

𝑚, 𝑗 > 𝑖 (17d)

𝑓𝑃𝑘,𝑚

𝑗𝑖≥ 0, ∀𝑖, 𝑗 ∈ 𝑉

𝑃𝑘, (17e)

where𝑇V represents the network lifetimewhenmth sink nodestays at location 𝑃

𝑘, 𝑓𝑃𝑘,𝑚𝑖𝑗

represents the data transmissionrate from node 𝑖 to node 𝑗 when the data of node 𝑖 aggregateto mth sink node andmth sink node stays at location 𝑃

𝑘. 𝑉𝑃𝑘

represents the set of sensor nodes whose data aggregate tomth sink node. If node 𝑗 is not the neighbor node of nodei, 𝑓𝑃𝑘,𝑚𝑖𝑗

= 0. The lifetime optimization model (17a) can besolved by optimization methods such as distributed subgra-dient method [18] and approximately solved by distributedgraph methods [19].

6 International Journal of Distributed Sensor Networks

In the paper, in order to reduce the time complexity ofthe algorithm, the model (17a) is approximately solved by thedistributed asynchronous Bellman-Ford algorithm. Namely,when sink node starts to gather data, it transmits data querypackets from time to time.Then, the implementation steps ofsensor node 𝑖 are as follows.

Step 1. If sensor node 𝑖 receives the routing informationpacket of its sink node, the address and shortest path weight𝐷𝑠(𝑡) = 0 of sink node are added to the information table of

neighbor nodes. The link weight 𝑤𝑖𝑠from sensor node 𝑖 to its

sink node is calculated as follows:

𝑤𝑖𝑠= (𝑔𝑖𝑠𝐸elec + 𝑔𝑖𝑠𝜀𝑓𝑠 (𝑑

𝑠

𝑖)2)𝑦1

(1

Re (𝑗))

𝑦2

, (18)

where 𝑠 represents sink node. 𝑑𝑠𝑖represents the distance from

sensor node 𝑖 to its sink node. 𝑔𝑖𝑠represents the amount

of data which sensor node 𝑖 needs to transmit. 𝑦1is energy

consumption factor. 𝑦2is residual energy factor of neighbor

node.

Step 2. If the shortest path weight 𝐷𝑖(𝑡) of sensor node 𝑖 is

not infinite, it broadcasts routing information packet fromtime to time. The packet includes the address of sensor node𝑖, 𝐷𝑖(𝑡), and data transmission hop to sink node. If sensor

node 𝑖 doesn’t receive any routing information packet before,it lets 𝐷

𝑖(𝑡) = ∞, caches its data, broadcasts routing failure

packet and waits until the routing information packets ofother nodes are received. If sensor node 𝑖 receives the routinginformation packet of neighbor node 𝑗, it obtains the𝐷

𝑗(𝑡) of

neighbor node 𝑗. Then go to Step 3.

Step 3. The link weight 𝑤𝑖𝑗from sensor node 𝑖 to sensor

node 𝑗 is calculated.The information table of neighbor nodesupdates

𝑤𝑖𝑗= (2𝑔

𝑖𝑗𝐸elec + 𝑔𝑖𝑗𝜀𝑓𝑠 (𝑑

𝑗

𝑖)2

)

𝑦1

(1

Re (𝑗))

𝑦2

, (19)

where 𝑑𝑗𝑖represents the distance from sensor node 𝑖 to sensor

node j. 𝑔𝑖𝑗represents the amount of data which sensor node 𝑖

transmits to sensor node j.

Step 4. According to the information table of neighbor nodes,the father node is selected through the following formula:

𝐷𝑖 (𝑡) = min

𝑗

(𝑤𝑖𝑗+ 𝐷𝑗 (𝑡)) . (20)

Step 5. Sensor node 𝑖 transmits the date through its fathernode to sink node.

In the data gathering process of sink node, if sensor nodedoes not receive the latest routing information packet orfeedback packet of neighbor node, it considers that the linkis failure and deletes the information of the neighbor node inthe information table.

Network starts

Broadcasts positioningquery packets

Receives and processesRSSI values

Broadcasts informationquery packets

Receives information ofcoverage nodes

Determines the anchors

Selects the gridmovement path and

moves along the path

Broadcasts routinginformation packet

Gathers the data ofsensor nodes

Calculates the x- and y-coordinates

Figure 1: The work flowchart of sink nodes.

4.3. Distributed Realization. LOA MSN is a distributed algo-rithm. Sensor nodes and sink nodes separately implementtheir own program.

As shown in Figure 1, when network starts, the specificsteps of sink nodes are as follows.

Step 1. Each sink node broadcasts information query packetsto sensor nodes in flooding way. The packets include itslocation information and node address. It gets information ofcoverage sensor nodes and establishes the information table.

Step 2. When the satellite positioning module is shut down,the sink node broadcasts positioning query packets andreceives and processes RSSI values. Then it calculates the 𝑥-and 𝑦-coordinates of its own through formulae (1)–(3).

Step 3. Sink node determines some anchors based on nodelocation information and energy with clustering method,solves the TSP problem to find the solution of optimalmovement paths, and obtains the grid movement scheme.Sink node moves along the grid movement path; namely, itrepeatedly stays at one anchor for some sojourn time or onepassing grid center for 𝑑V𝑤/𝑢 time and moves to next gridcenter. It broadcasts routing information packet and gathersthe data of sensor nodes.

As shown in Figure 2, when network starts, each sensornode is in listening state. If sensor node receives the informa-tion query packets of sink nodes, it analyzes the content ofthe packets. If it has not received the packet before, it addsthe information (location coordinates, node address, etc.) ofpacket to the information table of sink nodes and forwardsthe packet, else it discards the packet. According to theinformation table of sink nodes, each sensor node selects thenearest sink node as its aggregation node. Then it transmitsthe information of its own back to its aggregation node in

International Journal of Distributed Sensor Networks 7

Network starts

Receives informationquery packets

Selects the nearest sinknode as its aggregation

node

Transmits theinformation to sink node

Receives positioningquery packet

Transmits theinformation to sink node

Receives routinginformation packet

Calculates the linkweight and shortest path

weight

Selects the father node

Senses the data

Transmits the datato father node

Broadcasts the routinginformation packet if

necessary

Figure 2: The work flowchart of sensor nodes.

the same path. If the sensor node receives the positioningquery packet, it transmits its node address, coordinates, andother information back to the corresponding sink node. Ifthe sensor node receives the routing information packet, itcalculates the link weight and shortest path weight, selectsthe father node, transmits sensing data to correspondingsink node, and consumes energy. If the routing informationof sensor node changes or it is already after a period oftime, it broadcasts the routing information packet to informother nodes. If the sensor node needs to transmit the data, ittransmits the data to sink node through father node.

5. Simulation Realization and Analysis

5.1. Simulation Parameters. In the simulation, only energyconsumption of data wireless communication is consid-ered. Number of grids is 30 ∗ 30. 𝐸elec is 50 nJ/bit. 𝜀

𝑓𝑠is

100 pJ/bit/m2. 𝑑max is 200m. Edge length of simulation areais 1000m. 𝐸initial is 1000 J. Sensing rate of sensor node 𝑆

𝑖is

1Mbit/h. Link maximum transmission rate 𝑅max is 5Mbit/h.Movement speed of sink nodes 𝑢 is 5.5m/s. Distance weight-ing factor 𝑥

1is 0.5. Residual energy weighting factor 𝑥

2is 0.5.

Distance potential factor 𝛼1is 2. Residual energy potential

factor 𝛼2is 2. Attenuation factor 𝛽 is 1. Judgment factor 𝜀

is 0.3. Energy consumption factor 𝑦1is 0.7. Residual energy

factor 𝑦2of neighbor node is 1. Simulation and comparison

of the two MCP [14] and subgradient [18] algorithms whensink node are fixed in the center of simulation area, and thethree EASR [14], GRAND (for grid random scheme), andLOA MSN algorithms when sink node is mobile are realized.In GRAND, sink node randomly periodically selects the nextmovement location among neighbor grid centers and usesMCP protocol to gather data when sink node stays at one gridcenter. Then the algorithm performance indicators are givenas follows.

One data gathering cycle (DGC) is the working time(does not include the sleep time) that all sensor nodes suc-cessfully transmit 1Mbit data to sink node. The networklifetime is defined as the average numbers of DGC in whichsink nodes complete in the time when network starts to rununtil one node runs out of energy.

Average node energy consumption = total energy con-sumption of all sensor nodes/(number of senor nodes ∗network lifetime).

0 200 400 600 800 10000

200

400

600

800

1000

1

2

3

4

5

6

X-coordinate (m)

Y-c

oord

inat

e (m

)

Figure 3: Grid movement path of single sink node in the WSNs ofuniformly distributed nodes.

Average node residual energy = total residual energy ofall sensor nodes/number of senor nodes.

Data gathering latency = total number of hops for datatransmission of sensor nodes/(number of senor nodes ∗network lifetime).

5.2. Simulation Result Analysis

5.2.1. WSNs of Uniformly Distributed Nodes. Firstly, themovement paths of single sink node and two sink nodesare analyzed when sensor nodes are uniformly distributed.As is shown in Figure 3, the locations of 100 sensor nodes(open circles) are generated randomly and uniformly. The1000m ∗ 1000m simulation area is divided into 900 numberof grids. Sink node gathers the location information of sensornodes and uses modified subtractive clustering algorithm toobtain six anchors (five-pointed stars). Sink node staticallyand dynamically gathers data of sensor nodes along thegrid movement path. As is shown in Figure 4, there aretwo clusters. Each cluster has three anchors. Each sink nodestatically and dynamically gathers data along its grid move-ment path.

8 International Journal of Distributed Sensor Networks

0 200 400 600 800 10000

200

400

600

800

1000

2

3

1

X-coordinate (m)

Y-c

oord

inat

e (m

)

1

2

3

Figure 4: Grid movement paths of two sink nodes in the WSNs ofuniformly distributed nodes.

80 100 120 140 160 180 200

20

40

60

80

100

Number of nodes

Net

wor

k lif

etim

e (D

GC)

SubgradientMCPEASR

GRANDLOA MSN (SST)LOA MSN (TSN)

Figure 5: Network lifetime comparison in the WSNs of uniformlydistributed nodes.

In summary, LOA MSM finds the paths which areapproximate solution of movement path selection model(15a).

Secondly, in order to verify the effectiveness, MCP, sub-gradient algorithm, EASR, GRAND, LOA MSN with singlesink node (SSN), and two sink nodes (TSN) are compared.The location coordinates of 80, 100, 120, 140, 160, 180, and200 sensor nodes are uniformly generated in the area. Foreach fixed number of sensor nodes, 10 different networktopologies are generated. The network lifetime, average nodeenergy consumption, average node residual energy, and datagathering latency are calculated. The mean values are thesimulation result to evaluate the algorithm’s performance.

Figure 5 compares the network lifetime when sensornodes distribute uniformly. LOA MSN (TSN) uses two sinknodes to gather data. Each sink node only moves to gatherdata of some sensor nodes. And LOA MSN comprehensively

80 100 120 140 160 180 200

6

8

10

12

14

16

Number of nodes

Aver

age n

ode e

nerg

y co

nsum

ptio

n (J

)

SubgradientMCPEASR

GRANDLOA MSN (SST)LOA MSN (TSN)

Figure 6: Average node energy consumption comparison.

uses modified subtractive clustering algorithm to obtainthe anchors and uses distributed synchronous Bellman-Ford algorithm to prolong network lifetime and obtain datatransmission scheme. EASR and GRAND are not suitable forthe WSNs of uniformly distributed nodes, but they considermobile sink nodes. MCP and subgradient algorithm whosesink node is fixed have energy hole problem. Therefore, as isshown in Figure 5, network lifetime of LOA MSN (TSN) islongest and network lifetime of LOA MSN (SSN) is second.Network lifetime of EASR and GRAND is lower than thatof LOA MSN but longer than that of MCP and subgradientalgorithms. Network lifetime of MCP is shortest.

Figure 6 compares the average node energy consumption.LOA MSN (TSN) divides sensor nodes into two clustersaccording to location information. Each sink node onlymoves to some grid centers around which sensor nodesdensely distribute. It reduces communication distance andthe node energy consumption and has the lowest averagenode energy consumption. LOA MSN (SSN) only has onesink node. In order to prolong network lifetime, sink nodemoves to some anchors distributed around the simulationarea. It increases communication distances of some nodesand the energy consumption of relay nodes.Then LOA MSN(SSN) has a little larger average node energy consumption.Therefore, as is shown in Figure 6, LOA MSN (TSN) hasthe lowest average node energy consumption. subgradientalgorithm has the largest. Average node energy consumptionin MCP, EASR, GRAND, and LOA MSN (SSN) has a littledifference.

Figure 7 compares average node residual energy whenone sensor node runs out of energy. In LOA MSN, all sensornodes have the opportunity to transmit data near and far fromthe corresponding sink node. Itmakes full use of node energy.But, in other algorithms, only hub sensor nodes consumea lot of energy. Other sensor nodes have much residualenergy. Therefore, as shown in Figure 7, LOA MSN (TSN)

International Journal of Distributed Sensor Networks 9

80 100 120 140 160 180 200400

500

600

700

800

900

Number of nodes

Aver

age n

ode r

esid

ual e

nerg

y (J

)

SubgradientMCPEASR

GRANDLOA MSN (SST)LOA MSN (TSN)

Figure 7: Average node residual energy comparison.

80 100 120 140 160 180 2002

2.5

3

3.5

Number of nodes

Dat

a gat

herin

g lat

ency

MCPEASRGRAND

LOA MSN (SST)LOA MSN (TSN)

Figure 8: Data gathering latency comparison.

and LOA MSN (SSN) have the lower average node residualenergy than other algorithms. MCP has the largest averagenode residual energy.

Subgradient algorithm uses the optimization algorithmto solve the model (17a) and obtain data routing scheme. Itcannot calculate the number of hops of each sensor node.Therefore, Figure 8 compares the data gathering latency ofMCP, EASR, GRAND, LOA MSN (SSN), and LOA MSN(TSN). LOA MSN (TSN) reduces the communication dis-tance with two mobile sink nodes. LOA MSN (SSN) stays atsome anchors surrounding the simulation area and increasesthe number of hops of sensor nodes which are far from sinknode. In MCP, fixed sink node gathers data in the centerof simulation area. In EASR and GRAND, sink node movesaround the center of simulation area and uses MCP to gatherdata when sink node stays at one grid center. Therefore,

0 200 400 600 800 10000

200

400

600

800

1000

1 2

3

X-coordinate (m)

Y-c

oord

inat

e (m

)

1

2

Figure 9: Grid movement paths of two sink nodes when sensornodes distribute nonuniformly.

LOA MSN (TSN) has the lowest data gathering latency. Datagathering latency in MCP, EASR, and GRAND has littledifference. LOA MSN (SSN) has the largest data gatheringlatency.

In summary, in theWSNs of uniformly distributed nodes,and LOA MSN makes full use of node energy to prolongnetwork lifetime.When LOA MSN uses multiple sink nodes,it also reduces node energy consumption and data gatheringlatency.

5.2.2. WSNs of Nonuniformly Distributed Nodes. In thesimulation, 3–5 numbers of points around the center ofsimulation area are generated as the mean parameters ofPoisson distribution. The locations of 100 sensor nodes arePoisson randomly generated around the mean parameters.As is shown in Figure 9, in the 1000m ∗ 1000m simulationarea there are four mean points. 100 sensor nodes Poissondistribute around the four points. Namely, the nodes denselydistribute around the four points. They sparsely distribute,even no node distributes in the regions which are far awayfrom the four points. According to the node location infor-mation, LOA MSNfinds the centers of dense subregions, andobtains the five anchors (five-pointed stars).When sink nodesstay at those anchors, all sensor nodes have the opportunityto transmit data near their corresponding sink node.

Figure 10 compares the network lifetime when sensornodes distribute nonuniformly. In the network of nonuni-form node distribution, sensor nodes concentrate in severalsubregions. LOA MSN successfully finds the center of eachdense subregion and uses distributed synchronous Bellman-Ford algorithm to obtain the data transmission schemewhich prolongs network lifetime. Network lifetime of otheralgorithms is affected by the network topology.Thehubnodesin dense subregions forward a lot of data and are disablequickly. Therefore, as shown in Figure 10, LOA MSN (TSN)has the longest network lifetime. LOA MSN (SSN) has thesecond. Network lifetime of LOA MSN has not been affected

10 International Journal of Distributed Sensor Networks

80 100 120 140 160 180 2000

50

100

150

200

250

300

350

Number of nodes

Net

wor

k lif

etim

e (D

GC)

SubgradientMCPEASR

GRANDLOA MSN (SST)LOA MSN (TSN)

Figure 10: Network lifetime comparison in the WSNs of nonuni-formly distributed nodes.

by the node locations and even increases compared with thenetwork lifetime in theWSNs of uniformly distributed nodes.Other algorithms have low network lifetime.

In the WSNs of nonuniformly distributed nodes, thesimulation results of average node energy consumption,average residual energy, and data gathering latency are similarto the simulation results in theWSNs of uniformly distributednodes. Therefore, the results are not elaborated.

In summary, in the WSNs of nonuniformly distributednodes, LOA MSN makes full use of node energy to prolongnetwork lifetime.

6. Conclusion

In the paper, lifetime optimization algorithm with mobilesink nodes for wireless sensor networks based on loca-tion information (LOA MSN) is proposed. In the proposedscheme, satellite positioning and RSSI positioning algorithmsare used to obtain the location information of all nodes.Then,the constraints are analyzed and movement path selectionmodel and lifetime optimization model with known move-ment paths are established. Sink nodes gather the locationinformation of sensor nodes and use the clustering methodand graph theory method to find the movement paths. Theystay at the grid centers which are in the movement path forsome time, and gather data of sensor nodes with distributedmethod. Finally, the performances of MCP, subgradientalgorithm, EASR, GRAND, and LOA MSN are compared. Ithas been shown through various experiments that sink nodesfind the appropriate paths. LOA MSNmakes full use of nodeenergy to prolong network lifetime. When LOA MSN usesmultiple sink nodes, it also reduces node energy consumptionand data gathering latency.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgments

This research was supported by Zhejiang Provincial NaturalScience Foundation of China under Grants LY14F030006,Y15F030007, and LY13F010013 andZhejiang Provincial PublicWelfare Technology Application and Research Project ofChina under Grant 2014C33108.

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