sleep scheduling for geographic routing in duty cycled mobile sensor networks

6346 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 11, NOVEMBER 2014

Sleep Scheduling for Geographic Routing inDuty-Cycled Mobile Sensor Networks

Chunsheng Zhu, Student Member, IEEE, Laurence T. Yang, Member, IEEE, Lei Shu, Member, IEEE,Victor C. M. Leung, Fellow, IEEE, Joel J. P. C. Rodrigues, Senior Member, IEEE, and Lei Wang, Member, IEEE

Abstract—Recently, the research focus on geographic routing,a promising routing scheme in wireless sensor networks (WSNs),is shifting toward duty-cycled WSNs in which sensors are sleepscheduled to reduce energy consumption. However, except theconnected-k neighborhood (CKN) sleep scheduling algorithm andthe geographic routing oriented sleep scheduling (GSS) algorithm,nearly all research work about geographic routing in duty-cycledWSNs has focused on the geographic forwarding mechanism;further, most of the existing work has ignored the fact that sensorscan be mobile. In this paper, we focus on sleep scheduling forgeographic routing in duty-cycled WSNs with mobile sensorsand propose two geographic-distance-based connected-k neigh-borhood (GCKN) sleep scheduling algorithms. The first one isthe geographic-distance-based connected-kneighborhood for firstpath (GCKNF) sleep scheduling algorithm. The second one is thegeographic-distance-based connected-kneighborhood for all paths(GCKNA) sleep scheduling algorithm. By theoretical analysis andsimulations, we show that when there are mobile sensors, geo-graphic routing can achieve much shorter average lengths forthe first transmission path explored in WSNs employing GCKNFsleep scheduling and all transmission paths searched in WSNs em-ploying GCKNA sleep scheduling compared with those in WSNsemploying CKN and GSS sleep scheduling.

Manuscript received May 15, 2013; revised August 12, 2013 andNovember 9, 2013; accepted January 14, 2014. Date of publication March 12,2014; date of current version June 6, 2014. This work was based in parton a paper in presented at the 8th Annual IEEE Communications SocietyConference on Sensor, Mesh and Ad Hoc Communications and Networks(IEEE SECON)Utah, USA, June 2011. This work was supported in part bya Four Year Doctoral Fellowship from the University of British Columbia; inpart by funding from the Natural Sciences and Engineering Research Council ofCanada, TELUS, and other industry partners; in part by the Guangdong Univer-sity of Petrochemical Technology’s Internal Project under Grant 2012RC0106;in part by the Instituto de Telecomunicações, Next Generation Networks andApplications Group (NetGNA), Covilhã Delegation, with National Fundingfrom the FCT-Fundação para a Ciência e a Tecnologia through the Pest-OE/EEI/LA0008/2013 Project; and in part by the National Natural ScienceFoundation of China under Grant 61272524.

C. Zhu was with the Department of Computer Science, St. Francis XavierUniversity, Antigonish, NS B2G 2W5, Canada. He is now with the Departmentof Electrical and Computer Engineering, University of British Columbia,Vancouver, BC V6T 1Z4, Canada (e-mail: [email protected]).

L. T. Yang is with the Department of Computer Science, St. Francis XavierUniversity, Antigonish, NS B2G 2W5, Canada (e-mail: [email protected]).

L. Shu is with the Guangdong Provincial Key Laboratory of PetrochemicalEquipment Fault Diagnosis, Guangdong University of Petrochemical Technol-ogy, Maoming 525000, China (e-mail: [email protected]).

V. C. M. Leung is with the Department of Electrical and Computer Engineer-ing, University of British Columbia, Vancouver, BC V6T 1Z4, Canada (e-mail:[email protected]).

J. J. P. C. Rodrigues is with the Instituto de Telecomunicações, University ofBeira Interior, 6201-001 Covilhã, Portugal (e-mail: [email protected]).

L. Wang is with the Department of Network Engineering, Dalian Universityof Technology, Dalian 116620, China (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2014.2311390

Index Terms—Connected-k neighborhood (CKN), duty-cycle,geographic routing, mobility, wireless sensor networks (WSNs).

I. INTRODUCTION

G EOGRAPHIC routing [1]–[4] is one of the most promis-ing routing schemes in wireless sensor networks (WSNs)

[5], due to its simplicity, scalability, and efficiency [6]. In such ascheme, regardless of the network size, the forwarding decisionis determined purely based on the location of each node andit can be done even when there are irregular radio ranges andlocalization errors. Recently, the research focus of geographicrouting is centering on WSNs with duty-cycles, since duty-cycled WSNs have a natural advantage of saving energy bydynamically putting nodes to sleep and waking them accordingto some sleep scheduling algorithms [7]–[10].

However, nearly all these works overlook one importantfact that sensors can actually be mobile to gain better energyefficiency, channel capacity, etc., and enable a lot of new appli-cation scenarios [11]–[14]. For example, because sensors canmove, they can transmit their data from different locations andavoid the problem that sensors near the gateway or sink alwaysexhaust their energy first; thus, energy usage can be more effi-cient [15]. Also, mobile sensors such as mobile phones or carscan become the interface between the information center andthe mobile customers; thus, real-time information (e.g., trafficinformation) transmitted from the information center to thesemobile objects can be provided to nearby customers [16], [17].

Moreover, almost all current works about geographic routingin duty-cycled WSNs [18]–[21] try to change the geographicforwarding mechanism to deal with the dynamic topologycaused by some nodes being cycled off or going to sleep mode.For instance, it is suggested in [18] to wait for the appearanceof the expected forwarding successor first and select a backupnode if the first mechanism fails. In [19], the sensor fieldis sliced into some k-coverage fields, then some always-oncluster heads are selected to collect the data from their nearbysensors and finally transmit all data to the sink. Apart from theconnected-k neighborhood (CKN) sleep scheduling algorithmproposed in [22] and the geographic routing oriented sleepscheduling (GSS) algorithm presented in [23], few researchworks have tackled the node availability uncertainty issue induty-cycled WSNs from the view of sleep scheduling.

This paper addresses the sleep scheduling problem in duty-cycled WSNs with mobile nodes (referred as mobile WSNsin the following) employing geographic routing. We pro-pose two geographic-distance-based connected-k neighbor-hood (GCKN) sleep scheduling algorithms. The first one

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ZHU et al.: SLEEP SCHEDULING FOR GEOGRAPHIC ROUTING IN DUTY-CYCLED MOBILE SENSOR NETWORKS 6347

is the geographic-distance-based connected-kneighborhoodfor first path1 (GCKNF) sleep scheduling algorithm, aim-ing at geographic routing utilizing only the first transmissionpath in duty-cycled mobile WSNs. The second one is thegeographic-distance-based connected-kneighborhood for allpaths2 (GCKNA) sleep scheduling algorithm, for geographicrouting concerning all paths explored in duty-cycled mobileWSNs. By theoretical analysis and performance evaluationsby simulations, we show that when there are mobile sensors,geographic routing can achieve much shorter average lengthsfor the first transmission paths searched in mobile WSNs em-ploying GCKNF sleep scheduling and all transmission pathsexplored in mobile WSNs employing GCKNA sleep schedulingcompared with those in mobile WSNs employing CKN or GSSsleep scheduling.

The main contributions of this paper are summarized asfollows.

1) This paper is a pioneering work proposing and analyzingsleep scheduling algorithms for geographic routing induty-cycled mobile WSNs, which take full advantages ofboth duty cycling and sensor mobility.

2) Specifically, this paper proposes two GCKN algorithms,which effectively extend existing geographic routing al-gorithms designed for static WSNs into duty-cycled mo-bile WSNs by applying sleep scheduling. The GCKNFsleep scheduling algorithm is designed to explore shorterfirst transmission paths for geographic routing in duty-cycled mobile WSNs. The GCKNA sleep schedulingalgorithm aims at shortening all routing paths for mul-tipath transmissions in duty-cycled mobile WSNs. TheseGCKN algorithms incorporate the connected-k neighbor-hood requirement and geographic routing requirement tochange the asleep or awake state of sensor nodes.

For the rest of this paper, Section II reviews the basic idea andrelated work about geographic routing and sleep scheduling.The detailed designs and theoretical analysis of the GCKNalgorithms are presented in Section III. Section IV evaluatesthe performance of the GCKN algorithms. Section V concludesthe paper.

II. RELATED WORK

A. Geographic Routing

The basic idea of geographic routing is greedy routing.Specifically, each packet is tagged with the coordinates of itsdestination, all nodes know their own coordinates, and a nodeforward the packet to its neighbor that is geographically closestto the destination.

The earliest proposal for geographic routing is in [24], whichhas a local minimum problem in that a node may have no closerneighbor to the destination. For this reason, face routing [1]and its variants are proposed to use geometric rules (e.g., righthand rule) to route around voids near the local minimum incase it happens. However, these algorithms require convertingthe network into a planar graph (e.g., [25]) or removing the

1This is the first path searched by geographic routing.2These include all the paths found by geographic routing.

problematic cross links from the network (e.g., [3]), which arenot very applicable in realistic conditions [26]. Moreover, thereis also a hole problem in geographic routing, in that a hole canbe formed by a set of dead sensor nodes running out of energyor being damaged. To solve this problem, some research work(e.g., [27]) try to identify the hole boundary nodes first andthen use these boundary nodes to avoid the hole. Others (e.g.,[28]) try to use geometric modeling to find an optimized hole-bypassing routing path. Recently, by using a step back and markstrategy when it cannot find the next-hop node, a two-phasegeographic forwarding (TPGF), which does not have the localminimum or the hole problem, is shown in [29]. With a label-based optimization method, TPGF can optimize the routingpaths by finding one with the least number of hops. However,all these works only consider WSNs with static nodes.

Recently, many opportunistic routing protocols [18], [19],[30], [31]) have been proposed to extend geographic routingto duty-cycled WSNs. They all try to achieve this goal bydynamically choosing the forwarding node based on the bestpotential node that can transmit packets. Specially, these proto-cols typically take into account such factors as link uncertaintyto adapt routing accordingly. However, few of these worksaddress the local minimum or hole problem, and nearly all theseworks do not consider the situation that sensor nodes can bemobile.

B. Sleep Scheduling

The basic mechanism for sleep scheduling is to select a sub-set of nodes to be awake in a given epoch while the remainingnodes are in the sleep state that minimizes power consumption,so that the overall energy consumption can be reduced.

Existing works on sleep scheduling in WSNs mainly focuson two targets: point coverage and node coverage. For pointcoverage (also known as spatial coverage), the awake nodes ineach epoch are chosen to cover every point of the deployedfield. Existing point coverage oriented algorithms differ intheir sleep scheduling goals: minimizing energy consumption[7], or minimizing average event detection latency [8]. Fornode coverage (also called network coverage), awake nodes areselected to construct a globally connected network such thateach asleep node is an immediate neighbor of at least one awakenode [32], [33]. However, all these works generally focused onthe medium access layer of static WSNs with static nodes.

The only recent works addressing sleep scheduling in duty-cycled WSNs employing geographic routing are the CKNscheme proposed in [22] and the GSS method presented in [23].CKN is a sleep scheduling method providing node coverageand a probabilistic point coverage, which tunes the number ofawake nodes in the network by changing the value of k in CKN.GSS is based on CKN and differs from CKN only by makingthe potential nearest neighbor nodes to the sink to be awake.However, both CKN and GSS do not consider the scenarios inwhich sensor nodes can be mobile, and both CKN and GSSdetermine the awake or asleep state of each node based onlyon a random rank, which may keep awake many nodes faraway from the destination and thus degrade the performanceof geographic routing.


III. GCKN ALGORITHMS

A. Network Model

We consider a multihop WSN with N sensor nodes, whichcan be modeled by a communication graph G = (U,L), whereU = {u1, u2, . . . , uN} is the set of normal sensor nodes ex-cluding the source and the sink node and L is the set of links.The default transmission radius of each sensor is tr and themaximum transmission radius of each sensor is trm. The sourceand sink are always-on and both assumed to have unlimitedenergy supplies. The sink or a normal sensor can move toa randomly chosen position with a randomly selected speedwithin the WSN boundary and it will pause for a time periodafter it reaches the selected position, according to the randomwaypoint model in [34], [35]. Normal sensors can dynamicallychange states between asleep and awake. Two sensors areneighbors if they are within the transmission range of eachother and a link l(u,v) ∈ L if nodes u and v can communicatewith each other directly without relaying. Two sensors are two-hop neighbors if l(u,v) �∈ L and there exists another node wsatisfying l(u,w) ∈ L, l(w,v) ∈ L, or l(v,w) ∈ L, l(w,u) ∈ L.

B. Assumptions

We assume that each node knows its own location by usinga Global Position System (GPS) receiver or some mobility-based localization algorithm [36]. We further assume that eachnode also knows the locations of the source and sink nodesby flooding or opportunistic flooding [37]. Specifically, as eachsensor knows its own location, if the sink is static and normalsensor nodes are mobile, the sink location information onlyneeds to be flooded once. If the sink is mobile and normalsensor nodes are static, the sink location information needs tobe flooded when it moves to a new location.

C. Design Factors

For both GCKNF and GCKNA, we incorporate theconnected-k neighborhood3 requirement and geographic rout-ing requirement in their designs.

Specifically, we consider the following six factors for bothGCKNF and GCKNA.

1) A node should go to sleep assuming that at least k of itsneighbors will remain awake so as to save energy as wellas keep it k-connected.

2) The asleep or awake state of nodes should be allowedto change between epochs so that all nodes can have theopportunity to sleep and avoid staying awake all the time,thus distributing the sensing, processing, and routingtasks across the network to prolong the network lifetime.

3) Although each node decides to sleep or wake up locally,the whole network should be globally connected so thatdata transmissions can be performed.

4) Each node should have enough initial neighbors [38],in order to make it easier for the node to satisfy the

3Given a constant k and an undirected graph G = (U,L), a connected-kneighborhood is a subsect C ⊆ U with the following two characteristics:1) each node u ∈ U has at least m = min(k, du) neighbors from C, wheredu is the degree of u in G; 2) the nodes in C are connected.

connected-k neighborhood requirement; thus, it is morelikely to be asleep after sleep scheduling. For GCKNF,which emphasizes the first transmission path of geo-graphic routing, we further take the following factor intoaccount.

5) The neighbor of each node, which is closest to sink,should be awake so that geographic routing can utilizethese nearest neighbor nodes to make the first transmis-sion path as short as possible. For GCKNA, which consid-ers all transmission paths, we further take the followingfactor into consideration.

6) For each node, as many as possible of its neighbor nodesthat are closer to the sink should be awake so that geo-graphic routing can make all transmission paths as shortas possible.

In contrast with CKN and GSS, the fourth design factorof both GCKNF and GCKNA is the extra considerationthat makes it easier for each node to satisfy the connected-kneighborhood requirement during sleep scheduling. In addition,the fifth design factors for both GCKNF and GCKNA to meetthe geographic routing requirement in case they encountermobile sensor nodes or mobile sinks are ignored by the CKNand GSS schemes.

D. GCKN Algorithms

The pseudocode of GCKNF and GCKNA is shown below.Specifically, in GCKNF, each node sends probe packets to itsneighbor nodes and receives the ACK packet from its neighbornodes (Step 1 of the first part of GCKNF). With that, eachnode calculates whether it currently satisfies the connected-kneighborhood requirement or not (Step 2 of the first part ofGCKNF). If it already belongs to a connected-k neighborhoodor its transmission radius is the maximum, the node maintainsits transmission radius. Otherwise, the node increases its trans-mission radius until the connected-k neighborhood appears(Step 3 of the first part of GCKNF) [38]. In the second partof GCKNF, the geographic locations (e.g., gu) of each node uand the sink are obtained (Step 1 of the second part of GCKNF)and the each node’s neighbor that is nearest to sink is identified(Step 3 of the second part of GCKNF). In the third part ofGCKNF, a random rank ranku4 of each node u is picked (Step 1of the third part of GCKNF) and the subset Cu of u’s currentlyawake neighbors having rank > ranku is computed (Step 5 ofthe third part of GCKNF). Before u can go to sleep, it needsto ensure that 1) all nodes in Cu are connected by nodes withrank < ranku, 2) each of its neighbors has at least k neighborsfrom Cu, and 3) it is not the neighbor node closest to the sinkfor any other node (Step 6 of the third part of GCKNF).

In GCKNA, each node u also sends a probe packet to eachneighbor node and receives the corresponding ACK packet(Step 1 of the first part of GCKNA). Then, whether it currentlybelongs to a connected-k neighborhood is also checked (Step 2of the first part of GCKNA). The transmission radius of thenode is increased if the connected-k neighborhood requirement

4The ranku here is the same as the ranku in CKN. The value of bothranku are random in each epoch and they are without real meaning.


is not satisfied and the transmission radius is maintained if thenodes form a connected-k neighborhood or the transmissionradius is already the maximum (Step 3 of the first part ofGCKNA) [38]. In the second part of GCKNA, the geographicdistance between itself and the sink granku

5 is picked (Step 1of the second part of GCKNA) and the subset Cu of u’s cur-rently awake neighbors having grank< granku is computed(Step 5 of the second part of GCKNA). Before u can go to sleep,it needs to ensure that 1) all nodes in Cu are connected by nodeswith grank < granku and 2) each of its neighbors has at leastk neighbors from Cu (Step 6 of the second part of GCKNA).

Pseudocode of GCKNF algorithm

First: Run the following at each node u.1) Send probe packet pu to neighbors and receive the ack

packet.2) Compute whether u’s current neighbors CNu ≥

min(k, du).3) Maintain its transmission radius if the above condition

holds or its current transmission radius is the maximum.Otherwise, increase its transmission radius until CNu ≥min(k, du).

Second: Run the following at each node u.1) Get its geographic location gu and sink location gs.2) Broadcast gu and receive the geographic locations of its

all neighbors Au. Let Gu be the set of these geographiclocations.

3) Unicast a flag to w, w ∈ Au and gw is the closest to sinkin Gu.

Third: Run the following at each node u.1) Pick a random rank ranku.2) Broadcast ranku and receive the ranks of its currently

awake neighbors Nu. Let Ru be the set of these ranks.3) Broadcast Ru and receive Rv from each v ∈ Nu.4) If |Nu| < k or |Nv| < k for any v ∈ Nu, remain awake.

Return.5) Compute Cu = {v|v ∈ Nu and rankv < ranku}.6) Go to sleep if the following three conditions hold. Remain

awake otherwise.• Any two nodes in Cu are connected either directly

themselves or indirectly through nodes within u’stwo-hop neighborhood that have rank less thanranku.

• Any node in Nu has at least k neighbors from Cu.• It does not receive a flag.

7) Return.

Pseudocode of GCKNA algorithm

First: Run the following at each node u.1) Send probe packet pu to neighbors and receive the ack

packet.

5This granku here is a little different from the ranku in CKN. grankurepresents the geographic distance between node u and the sink, while rankuis a random value without real meaning.

2) Compute whether u’s current neighbors CNu ≥min(k, du).

3) Maintain its transmission radius if the above conditionholds or its current transmission radius is the maximum.Otherwise, increase its transmission radius until CNu ≥min(k, du).

Second: Run the following at each node u.1) Get its geographic location gu and sink location gs.

Further get the geographic distance between itself andsink granku.

2) Broadcast granku and receive the geographic distanceranks of its currently awake neighbors Nu. Let Ru be theset of these ranks.

3) Broadcast Ru and receive Rv from each v ∈ Nu.4) If |Nu| < k or |Nv| < k for any v ∈ Nu, remain awake.

Return.5) Compute Cu = {v|v ∈ Nu and grankv < granku}.6) Go to sleep if both the following conditions hold. Remain

awake otherwise.• Any two nodes in Cu are connected either directly

themselves or indirectly through nodes within u’stwo-hop neighborhood that have grank less thangranku.

• Any node in Nu has at least k neighbors from Cu.7) Return.

E. Analysis of GCKN Algorithms

Theorem: Node u will have at least min (k, ou) awake neigh-bors after running GCKN algorithms, if it has ou neighbors inthe original network.

Proof: If ou < k, all of u’s neighbors should keep awake(Step 4 of the third part of GCKNF or Step 4 of the second partof GCKNA) and the node will have ou awake neighbors.

Otherwise, when ou ≥ k, we prove the theorem by contra-diction [22], [23]. Suppose that node u will not have at least kawake neighbors after running GCKN algorithms, i.e., we canassume that the i’th lowest ranked (for GCKNF) or granked (forGCKNA) neighbor v of u, i ≤ k, decides to sleep. Then Cu

will have at most i− 1 nodes that are neighbors of u. But sincei− 1 < k, v cannot go to sleep according to the Step 6 of thirdpart of GCKNF or Step 6 of second part of GCKNA. This is acontradiction. In other words, the k lowest granked neighbors ofu will all remain awake after running the algorithm, and hence,u will have at least k awake neighbors. �

Theorem 2: Running GCKN algorithms produces aconnected-network if the original network is connected.

Proof: We prove this theorem by contradiction [22], [23].Assuming that the output network after running GCKN algo-rithms is not connected. Then, we put the deleted nodes (asleepnodes decided by GCKN algorithms) back in the network inascending order of their ranks (for GCKNF) or granks (forGCKNA), and let u be the first node that makes the networkconnected again. Note that by the time we put u back, all themembers of Cu are already present and nodes in Cu are alreadyconnected since they are connected by nodes with rank <ranku (for GCKNF) or grank < granku (for GCKNA). Let


v be a node that was disconnected from Cu but now getsconnected to Cu by u. But this contradicts the fact that u cansleep only if all its neighbors (including v) are connected to ≥ knodes in Cu (Step 6 of third part of GCKNF or Step 6 of secondpart of GCKNA). �

Theorem: GCKN sleep scheduling-based WSN can provideas short as possible transmission path explored by geographicrouting when there are mobile sensor nodes.

Proof: We prove this by analyzing the resultant topologyafter running GCKNF or GCKNA. Concerning GCKNF, giventhat there is a network Ngcknf resulting from GCKNF, basedon the algorithm presentation of GCKNF, we can deduce thatthe neighbor node that is closest to the sink for any node,will be among the awake nodes of the Ngcknf (Step 6 ofthe third part of GCKNF). In other words, no matter whichnode the geographic routing chooses to be the first forwardingnode, all successor nodes closest to sink can be utilized bythe geographic routing. Thus, the length of the first transmis-sion path explored by geographic routing can be as short aspossible.

Regarding GCKNA, assume that there is a network Ngckna

created by GCKNA. From the algorithm description ofGCKNA, we can determine that for any node, say u, if itdetermines to be asleep, it must make sure that either 1) itsall awake 1-hop neighbor nodes are connected by themselveswith grank < granku or connected by their two-hop neighbornodes with grank < granku; 2) any of its awake one-hopneighbor nodes should have at least k neighbor nodes from thesubset of the one-hop neighbor nodes with grank < granku(Step 6 of the second part of GCKNA). This means thatcompared with the asleep nodes, the awake nodes generallyhave closer geographic distance to the sink. In other words,geographic routing can have access to as many as possiblecloser neighbor nodes to the sink under the priority of networkconnectivity after sleep scheduling. Thus, the length of alltransmission paths searched by geographic routing can also beas short as possible. �

IV. PERFORMANCE EVALUATIONS

A. Evaluation Setup

To evaluate the performance of the proposed GCKN al-gorithms when applying geographic routing into duty-cycledmobile WSNs, we conduct extensive simulations in NetTopo6

[39]. We use TPGF [29] as our geographic routing due to theunique desirable characters of TPGF in dealing with the localminimum or hole problem as well as the shortest and multi-path transmission prosperities of TPGF, which are introducedin Section II. We compare the performance of the proposedGCKN algorithms with CKN and GSS, since CKN and GSSare the only other sleep scheduling algorithms focusing ongeographic routing in duty-cycled WSNs, which is also illus-trated in Section II. The performance metric is the lengthsof the transmission paths searched by TPGF in duty-cycledWSNs employing GCKN, CKN, and GSS, as the length of

6NetTopo (available online at http://sourceforge.net/projects/nettopo/) is anopen source software on SourceForge for simulating and visualizing WSNs.

TABLE IEVALUATION PARAMETERS

geographic routing transmission path is widely used to estimatethe transmission time, transmission delay, etc. [40]. In addition,the network lifetime7 of WSNs employing GCKN, CKN, andGSS based are also observed to check whether GCKN degradesthe network lifetime.

For both GCKNF and GCKNA, the detailed simulationparameters are shown in Table I. The network size is 800×600 m2. The number of deployed sensor nodes ranges from 100to 1000 (each time increased by 100) and the value of k in CKNis changed from 1 to 10 (each time increased by 1). The defaulttransmission radius of each node is 60 m, and the maximumtransmission radius of each node is 120 m. There is one constantsource node deployed at location (50, 50) and we consider twomobility cases: 1) the sink is still at location (750, 550) and allnormal sensor nodes randomly move a random number between100 to 1000 times; 2) all normal sensor nodes are static andthe sink moves a random number between 10 and 100 times in100 different network topologies. The mobility model in bothcases is the random waypoint model illustrated in Section III. Inaddition, the initial energy of each normal node is 100 000 mJ.The energy consumption of a sensor by transmitting, receivingone byte and transmitting amplifier are 0.0144 mJ, 0.00576 mJ,and 0.0288 nJ/m2, respectively [23], [41]. Each packet is12 bytes long, and each node transmits 1000 packets for eachtime epoch which is 1 min.

B. Evaluation Results

A snapshot of the first transmission path from the sourcenode to the sink node explored by TPGF in a GCKNF-basedWSN when the sink is at different locations is shown in Fig. 1.An example of all transmission paths from the source node tothe sink node explored by TPGF in a GCKNA-based WSNwhen the sink is at different locations is presented in Fig. 2.

1) GCKNF Versus CKN Versus GSS—Static Sink With Mo-bile Sensor Nodes: From Fig. 3(a)–(c), we can clearly seethat the average length of the first explored transmission pathof TPGF in GCKNF-based WSNs with mobile sensor nodesis nearly always shorter than that in CKN-based WSNs with

7The network lifetime is the instant from the network deployment to theinstant when the first sensor node runs out of energy.


Fig. 1. Snapshot of the first transmission path from source node (red color) tothe sink node (green color) explored by TPGF in a GCKNF-based WSN. Thesource node is at location (50, 50) and the sink node is at locations (400, 300),(50, 550), (400, 550), and (750, 550) in (a), (b), (c), and (d), respectively. Thereare 500 sensor nodes and the k in CKN is 1. The black nodes are asleep and theblue nodes are awake.

Fig. 2. Example of all transmission paths from source node (red color) tothe sink node (green color) explored by TPGF in a GCKNA-based WSN. Thesource node is at location (50, 50) and the sink node is at locations (400, 300),(50, 550), (400, 550), and (750, 550) in (a), (b), (c), and (d), respectively. Thereare 500 sensor nodes and the k in CKN is 1. The black nodes are asleep and theblue nodes are awake.

mobile sensor nodes and almost the same as that in GSS-based WSNs with mobile sensor nodes. It is because of theawake nodes that are closest to the sink in GCKNF-basedWSNs, whereas such nodes do not usually appear in CKN-based WSNs. And the potential awake nodes closest to sink inGCKNF-based WSNs and that in GSS-based WSNs are almostthe same. In addition, the average network lifetime in GCKNF-based WSNs with mobile sensor nodes is almost the same asthat in CKN-based WSNs with mobile sensor nodes and muchbetter than that in GSS-based WSNs with mobile sensor nodes,which are shown in Fig. 3(d)–(f), respectively.

2) GCKNF Versus CKN Versus GSS—Mobile Sink WithStatic Sensor Nodes: From Fig. 4(a)–(c), we can also see that

the average length of the first transmission path explored byTPGF in GCKNF-based WSNs with a mobile sink is alsoalmost always shorter than that in CKN-based WSNs with amobile sink and almost the same as that in GSS-based WSNswith a mobile sink. That is also due to that there are much moreawake nodes closest to sink in GCKNF-based WSNs, comparedwith that in CKN-based WSNs. And GCKNF-based WSNs andGSS-based WSNs share the same criteria to choose the awakenodes closest to sink. Furthermore, the average network lifetimein GCKNF-based WSNs with a mobile sink shown in Fig. 4(d)is nearly the same as that in CKN-based WSNs with a mobilesink shown in Fig. 4(e) and much higher than that in GSS-basedWSNs presented in Fig. 4(f).

3) GCKNA Versus CKN Versus GSS—Static Sink With Mo-bile Sensor Nodes: Fig. 5(a)–(c) describe the average length ofall transmission paths explored by TPGF in GCKNA and CKNas well as GSS-based WSNs with mobile sensor nodes. Fromthese three figures, we can clearly see that the average lengthsof all transmission paths explored by TPGF in GCKNA-basedWSNs with mobile sensor nodes are mostly much shorter thanthat in CKN and GSS-based WSNs with mobile sensor nodes.It is because more nodes closer to the sink are kept awakein GCKNA-based WSNs than that in CKN and GSS-basedWSNs. Moreover, there is not too much difference regardingthe average network lifetime in GCKNA-based WSNs withmobile sensor nodes and the average network lifetime in CKN-based WSNs with mobile sensor nodes, which are shown inFig. 5(d) and (e), respectively. In addition, both the averagenetwork lifetimes in GCKNA and CKN-based WSNs withmobile sensor nodes are greatly higher than that in GSS-basedWSNs presented in Fig. 5(f).

4) GCKNA Versus CKN Versus GSS—Mobile Sink WithStatic Sensor Nodes: Fig. 6(a)–(c) presents the average lengthsof all transmission paths explored by TPGF in GCKNA andCKN as well as GSS-based WSNs with a mobile sink. Fromthese three figures, we can also clearly see that the averagelength of all transmission paths explored by TPGF in GCKNA-based WSNs with a mobile sink is almost always much shorterthan that in CKN and GSS-based WSNs with a mobile sink.That also results from the more awake closer nodes to sink inGCKNA-based WSNs than that in CKN and GSS-based WSNs.Apart from that, it is hard to distinguish the average networklifetime in GCKNA-based WSNs with a mobile sink from thatin CKN-based WSNs with a mobile sink, which are shown inFig. 6(d) and (e). And the average network lifetime in GSS-based WSNs with a mobile sink presented in Fig. 6(f) is quitelower than that in GCKNA and CKN-based WSNs.

C. Application Scenarios

Regarding both case 1) and case 3) evaluated above (i.e.,static sink with mobile sensor nodes), they can particularlybe applied to enhance the data transmission scenarios such asinformation center (i.e., source node) needs the robots (i.e.,sensor nodes with mobility) randomly move to monitor andgather the environment data and then transmit these data alongthe path between the information center and a remote basestation (i.e., static sink node).


Fig. 3. (a) Average length of the first transmission path explored by TPGF in GCKNF-based WSNs with mobile sensor nodes, (b) in CKN-based WSNs withmobile sensor nodes, (c) in GSS-based WSNs with mobile sensor nodes, (d) average network lifetime in GCKNF-based WSNs with mobile sensor nodes, (e) inCKN-based WSNs with mobile sensor nodes, and (f) in GSS-based WSNs with mobile sensor nodes.

Fig. 4. (a) Average length of the first transmission path explored by TPGF in GCKNF-based WSNs with a mobile sink, (b) in CKN-based WSNs with a mobilesink, (c) in GSS-based WSNs with a mobile sin, (d) average network lifetime in GCKNF-based WSNs with a mobile sink, (e) in CKN-based WSNs with a mobilesink, and (f) in GSS-based WSNs with a mobile sink.

With respect to case 2) and case 4) in the previous sub-section (i.e., mobile sink with static sensor nodes), they canspecifically be employed to speed up services in some in-formation providing applications. For example, a customerwith a mobile phone (i.e., mobile sink node) can randomly

move and the information center (i.e., source node) needsto provide the traffic information or house monitoring in-formation gathered by various location predetermined envi-ronment monitoring sensors (i.e., static sensors) as fast aspossible.


Fig. 5. (a) Average length of all transmission paths explored by TPGF in GCKNA-based WSNs with mobile sensor nodes, (b) in CKN-based WSNs withmobile sensor nodes, (c) in GSS-based WSNs with mobile sensor nodes, (d) average network lifetime in GCKNA-based WSNs with mobile sensor nodes, (e) inCKN-based WSNs with mobile sensor nodes, and (f) in GSS-based WSNs with mobile sensor nodes.

Fig. 6. (a) Average length of all transmission paths explored by TPGF in GCKNA-based WSNs with a mobile sink, (b) in CKN-based WSNs with a mobile sink,(c) in GSS-based WSNs with a mobile sink, (d) average network lifetime in GCKNA-based WSNs with a mobile sink, (e) in CKN-based WSNs with a mobilesink, and (f) in GSS-based WSNs with a mobile sink.

For all the above four cases, we can further observe that whenthere are more number of sensor nodes, the advantage of GCKNalgorithms will become more obvious. That is because highernetwork density will enable GCKN algorithms to create morefavorable nodes for TPGF to utilize.

V. CONCLUSION

In this paper, we have explored geographic routing in duty-cycled mobile WSNs and proposed two geographic-distance-based connected-k neighborhood (GCKN) sleep schedulingalgorithms for geographic routing schemes to be applied into


duty-cycled mobile WSNs which can incorporate the advantageof sleep scheduling and mobility. The first geographic-distance-based connected-kneighborhood for first path (GCKNF) sleepscheduling algorithm minimizes the length of first transmissionpath explored by geographic routing in duty-cycled mobileWSNs. The second geographic-distance based connected-kneighborhood for all paths (GCKNA) sleep schedulingalgorithm reduces the length of all paths searched by geo-graphic routing in duty-cycled mobile WSNs. In duty-cycledmobile WSNs, from the view of sleep scheduling, GCKNFand GCKNA do not require the geographic routing to changeits original geographic forwarding mechanism, and they bothconsider the connected-k neighborhood requirement and ge-ographic routing requirement to change the asleep or awakestate of sensor nodes. Detailed design of both GCKNF andGCKNA as well as further theoretical analysis and evaluationwith respect to GCKNF and GCKNA has been shown in thispaper. They demonstrate that GCKNF and GCKNA are veryeffective in shortening the length of the transmission pathexplored by geographic routing in duty-cycled mobile WSNscompared with the CKN sleep scheduling algorithm and theGSS algorithm. Our work has shown that sleep scheduling isa worthy research direction to adapt geographic forwardingmethods into duty-cycled mobile WSNs.

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Chunsheng Zhu (S’12) received the B.E. degreein network engineering from Dalian University ofTechnology, Dalian, China, in 2010, and the M.Sc.degree in computer science from St. Francis XavierUniversity, Antigonish, NS, Canada, in 2012. He iscurrently working toward the Ph.D. in the Depart-ment of Electrical and Computer Engineering, Uni-versity of British Columbia, Vancouver, BC, Canada.

His research interests include wireless sensor net-works and cloud computing.

Laurence T. Yang (M’97) received the B.E. degreein computer science and technology from TsinghuaUniversity, Beijing, China, in 1992, and the Ph.D.degree in computer science from the University ofVictoria, Victoria, BC, Canada, in 2006.

Currently, he is a Professor in the Departmentof Computer Science, St. Francis Xavier Univer-sity, Antigonish, NS, Canada. His research inter-ests include parallel and distributed computing, andembedded and ubiquitous/pervasive computing. Hisresearch is supported by the National Sciences and

Engineering Research Council, Canada, and the Canada Foundation forInnovation.

Lei Shu (M’07) received the B.Sc. degree in com-puter science from South Central University for Na-tionalities, Wuhan, China, in 2002, the M.Sc. degreein computer engineering from Kyung Hee Univer-sity, Seoul, Korea, in 2005, and the Ph.D. degreein computer engineering from the Digital EnterpriseResearch Institute, National University of Ireland,Galway, Ireland, in 2010.

Currently, he is a Full Professor at the Collegeof Electronic Information and Computer, GuangdongUniversity of Petrochemical Technology, Maoming,

China, and also the Vice-Director of the Guangdong Petrochemical EquipmentFault Diagnosis (PEFD) Key Laboratory. He was a Specially Assigned Re-search Fellow in the Department of Multimedia Engineering, Graduate Schoolof Information Science and Technology, Osaka University, Osaka, Japan. Hisresearch interests include wireless sensor network, sensor network middleware,multimedia communication, and security.

Dr. Shu is a member of the Association for Computing Machinery.

Victor C. M. Leung (S’75–M’89–SM’97–F’03) re-ceived the B.A.Sc. (Hons.) and Ph.D. degrees inelectrical engineering from the University of BritishColumbia (UBC), Vancouver, BC, Canada, in 1977and 1981, respectively.

Currently, he is a Professor and TELUS MobilityResearch Chair in Advanced TelecommunicationsEngineering in the Department of Electrical andComputer Engineering, UBC. His research interestsinclude wireless networks and mobile systems.

Dr. Leung is a Registered Professional Engineer inthe Province of British Columbia, Canada. He is a Fellow of the Royal Societyof Canada, a Fellow of the Engineering Institute of Canada, and a Fellow of theCanadian Academy of Engineering.

Joel J. P. C. Rodrigues (S’01–M’06–SM’06) re-ceived the B.Sc. degree (licentiate) in informat-ics engineering from the University of Coimbra,Coimbra, Portugal, in 1995, the M.Sc. degree inknowledge management from the University of BeiraInterior, Covilhã, Portugal, in 2002, and the Ph.D.degree in informatics engineering from University ofBeira Interior, Covilhã, Portugal, in 2006.

Currently, he is a Professor in the Departmentof Informatics, University of Beira Interior, and aResearcher at the Instituto de Telecomunicações,

Covilhã, Portugal. His research interests include sensor networks, e-health,e-learning, vehicular delay-tolerant networks, and mobile and ubiquitouscomputing.

Dr. Rodrigues is a Licensed Professional Engineer (as a Senior Member),a member of the Internet Society, an International Academy, Research andIndustry Association Fellow, and a Senior Member of the Association forComputing Machinery.

Lei Wang (M’01) received the B.S., M.S., andPh.D. degrees in computer science from TianjinUniversity, Tianjin, China, in 1995, 1998, and 2001,respectively.

Currently, he is a Full Professor in the Depart-ment of Network Engineering, Dalian University ofTechnology, Dalian, China. He was a member ofthe Technical Staff with Bell Labs Research China,Beijing, China (2001–2004); a Senior Researcherat Samsung, Seoul, Korea (2004–2006); a Re-search Scientist at Seoul National University, Seoul

(2006–2007); and a Research Associate at Washington State University,Pullman, WA, USA (2007–2008). His research interests include wireless adhoc networks, sensor networks, and embedded systems.

Dr. Wang is a member of the Association for Computing Machinery and aSenior Member of the China Computer Federation (CCF).

sleep scheduling for geographic routing in duty cycled mobile sensor networks

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