Load Balanced Rendezvous Data Collection in Wireless Sensor Networks

Transcription

1 2011 Eghth IEEE Internatonal Conference on Moble Ad-Hoc and ensor ystems Load Balanced endezvous Data Collecton n Wreless ensor Networks Luo Ma 1, Longfe hangguan 1, Chao Lang 1, Junzhao Du 1, Hu Lu 1, Zhenjang L 2,3, and Mo L 3 1 oftware Engneerng Insttute, Xdan Unversty 2 Department of Computer cence and Engneerng, Hong Kong Unversty of cence and echnology 3 chool of Computer Engneerng, Nanyang echnologcal Unversty Emal: {maluo.cn, shanggdlk}@gmal.com, {dujz, luhu}@xdan.edu.cn, lzjang@cse.ust.hk, lmo@ntu.edu.sg Abstract We study the rendezvous data collecton problem for the moble snk n wreless sensor networks. We ntroduce to jontly optmze trajectory plannng for the moble snk and workload balancng for the network. By dong so, the moble snk s able to effcently collect network-wde data wthn a gven delay bound and the network can elmnate the energy bottleneck to dramatcally prolong ts lfetme. uch a jont optmzaton problem s shown to be NP-hard and we propose an approxmaton algorthm, named P-LB, to approach the optmal soluton. In P-LB, accordng to observed propertes of the medan reference structure n the network, a seres of endezvous Ponts (Ps) are selected to construct the trajectory for the moble snk and the derved approxmaton rato of P- LB guarantees that the formed trajectory s comparable wth the optmal soluton. he workload allocated to each P s proven to be balanced mathematcally. We then relax the assumpton that moble snk knows the locaton of each sensor node and present a localzed, fully dstrbuted verson, P-LB-D, whch largely mproves the system applcablty n practce. We verfy the effectveness of our proposals va extensve experments. Keywords-wreless sensor networks, rendezvous data collecton, moble snk, network load balancng I. INODUCION As a promsng technology, Wreless ensor Networks (WNs) spawn a surge of prevously unforeseen applcatons. he dversty of those emergng applcatons nterprets ts great success. One fundamental operaton of such applcatons s data collecton, whch characterzes the transmsson process of n-stu sensory data from sensor nodes to the base staton over the network. A varety of crtcal applcatons and network operatons, such as event detecton [1], localzaton [2], network self dagnoss [3], network reconfguraton [4], robust message delvery [5], and etc., rely on data collecton as a basc component. In most of prevous studes, the statc snk was wldly adopted to conduct data collecton n WNs. Due to the multhop data transmsson style, however, severely unbalanced energy consumpton s caused wth the node-to-snk traffc flow. ensor nodes close to the snk node have to carry much more traffc overhead compared wth dstant sensor nodes. nce sensor nodes are hghly restrcted to the lmted battery power supply, such unbalanced energy consumpton results n the quck power depleton on part of the network, and dramatcally shortens the lfetme of the network as a whole. o reduce the negatve mpact, recent research works ntroduce the moble snk as a potental soluton to the data collecton problem. he moble snk s usually a mnature vehcle or robot wth the moton capablty, whch roams wthn the network, harvests sensory data at a seres of ntermedate endezvous Ponts (Ps),.e., data collecton postons, and carres harvested data back to the base staton. nce the data collecton postons are usually dstrbuted across the entre network, the Ps mplctly average the traffc burden over the network and reduce the energy bottleneck n the network. he lfetme of the network can thus be sgnfcantly prolonged. Compared wth the tradtonal statc data collecton settng, data collecton performed by the moble snk s more complcated n the followng two aspects: moble snk trajectory plannng and network load balancng. Accordng to [6], the typcal movng velocty of a moble snk s around 0.1~2.0 m/s. It wll lead to an extremely long data collecton delay f the moble snk vsts a large porton of the network, whch s normally unable to meet the delay requrement of many practcal applcatons. As a matter of fact, the small movng velocty s the fundamental desgn restrcton, snce ncreasng the movng speed of the moble snk wll lead to a sgnfcantly ncreased manufacturng cost and energy consumpton. For example, a Packbot node consumes about merely 60W when the movng speed s 1 m/s whle the consumed energy ncreases quadratcally wth ts speed as reported by [7]. On the other hand, the moble snk collects only partal sensory data at every P. Dfferent from the scenaro wth the tradtonal statc snk, only a local data routng tree s formed, rooted at each P. All the local trees are not overlapped and jontly offer a full coverage of the entre network. hus, the moble snk can be guaranteed to collect the network-wde sensory data by vstng all Ps. In prncple, the work loads of local routng trees rooted at Ps should be balanced. Note that wth the requred delay constrant, badly selected Ps and planned moble snk trajectory may fal n collectng all sensory data across the network; and even worse, a trajectory path whch optmzes the total energy cost over the network does not necessarly lead to balanced local routng trees. As a matter of fact, above two aspects need to be addressed together such that effcent data collecton can be acheved and the network lfetme can be sgnfcantly prolonged at the same tme. However, so far as we know, how to jontly desgn moble snk trajectory plannng and network load balancng s stll not yet thoroughly nvestgated by the /11 $ IEEE DOI /MA

2 communty, and we am to systematcally study such a jont optmzaton problem n ths paper. here have been ntal attempts made to explore the data collecton problem wth moble snks. Most exstng works, however, solely focus on the trajectory plannng aspect. Wthout takng network load balancng nto consderaton, the produced local routng trees may be hghly unbalanced and some of them may run out of energy rapdly, leavng other routng trees excessve resdual energy. he lfetme of the network as a whole wll be severely lmted. In ths paper, we explore the possblty of combnng moble snk trajectory plannng and network load balancng to jontly optmze data collecton for the moble snk n wreless sensor networks. he contrbutons of ths paper can be summarzed as follows. Frst, we formulate such a jont optmzaton problem as the Mnmum-energy endezvous Pont selecton wth Load Balancng (MPLB) Problem and we prove t s NP-hard. hen, based on the observed propertes from the medan reference structure, we propose an approxmaton algorthm, P-LB, talored for the trajectory plannng wth network load balancng consderaton. Next, we mathematcally prove the correctness of the proposed algorthm, analyze the algorthm performance, and derve ts approxmaton rato. o mprove the applcablty of P-LB, we relax the assumpton that the locaton of each sensor node s known by the moble snk and propose a localzed, fully dstrbuted algorthm, named P-LB-D, where the new Ps can be decded based on merely a part of the network knowledge. We verfy the effcency and effectveness of our approaches va large-scale smulatons. he rest of ths paper s organzed as follows. elated work s revewed n ecton II and the problem s formulated n ecton III. We specfy the desgn detal of P-LB and prove ts propertes n ecton IV. In ecton V, the dstrbuted realzaton of P-LB s presented. We evaluate the algorthms n ecton VI and conclude the paper n ecton VII. II. ELAED WOK A surge of recent works explot utlzng the snk moblty to reduce energy consumpton n WNs. [8] gves a survey on the usage of snk moblty for energy-effcent data collecton n delay-tolerant WNs. Chakrabart et al. [9] show that, f actuators move along regular paths, sensors can predct ther arrval after learnng ther movement pattern, whch makes sensors free from detectng actuators arrval by keepng montorng the wreless communcaton channel. everal heurstcs are proposed n [10][11] to schedule the movement of actuators such that source nodes can be vsted accordng to ther buffer lmtaton to avod data loss. Wang et al. [12] show that constranng the moble snk n the neghborhoods of a base staton can maxmze network lfetme. h et al. [13] desgned a provably approxmaton algorthm regardng the locaton of a moble base staton n favor of maxmzng network lfetme. On the other hand, rendezvous-based data collecton draws great attenton recently by tradng off the energy consumpton and the data collecton delay. In [14], sources send ther sensory data to the nodes n the vcnty of actuator trajectores whch are pcked up as the actuators pass by. ao et al. [15] presented a generc data collecton framework wthout locaton nformaton. However, these works do not focus on collectng sensory data wthn bounded tme delay. Xng et al. [17] study rendezvous plannng along a geometrc tree that approxmates the reportng tree of data sources. Furthermore, [16] studes the trade-off between the energy consumpton and the tme delay n the sensor networks. ecently, centralzed technques such as clusterng [18][19] and ntellgent algorthms [20] are also utlzed to mnmze the network energy consumpton of relayng data from sources to several ntermedate ponts. he key lmtaton of ther works s the hgh dependence on the perfect network knowledge, mposng an unrealstc requrement to the moble snk n terms of computaton capacty and the memory sze. However, mnmzng network energy consumpton may not necessarly lead to the maxmum network lfetme, snce the energy consumpton may not be evenly dstrbuted. o the best of our knowledge, there s no exstng work focusng on jontly optmzng both trajectory plannng and work load balancng for data collecton wth the moble snk n WNs. By dong ths, an effcent data collecton can be acheved and the network lfetme can be prolonged at the same tme. III. PELIMINAY In ths secton, we wll formally ntroduce the problem we wll dscuss n ths paper. A. An Illustratve Example In our problem context, a set of source nodes,.e., sensors, that perodcally generate sensory data at an equal rate, are deployed n the target feld. he moble snk roams n the network to collect all those sensory data by vstng a seres of Ps, wth a requred data collecton delay bound D. he delay bound can be measured by the maxmum dstance that the moble snk s allowed to move. More precsely, the maxmum length of the trajectory can be calculated by L vm D, where v M s the average movement speed of the moble snk. In ths paper, our ultmate goal s to determne the locaton of each P and a set of local routng trees rooted at those selected Ps such that (a) all sensory data can be collected wthn the gven delay bound, (b) network load s evenly dstrbuted across the network, and (c) suffcently long lfetme of the network can be acheved. o better llustrate the consdered problem, a smple example s gven n Fgure 1(a) and (b). Fgure 1 (a) rajectory plannng produced by the smple greedy strategy. (b) rajectory plannng wth the workload balancng. (c) Underlyng network topology and the geometrcally approxmated routng tree. he network topology s represented by black lnes and hollow crcles. he routng tree s represented by grey lnes and sold crcles. 283

3 old and hollow crcles n Fgure 1 represent source nodes and the Ps, respectvely. Note that a P can be a relay node as well. uppose a greedy strategy s used,.e., from an arbtrary source node, applyng the depth-frst search along any routng tree embedded n the network to explore a longest trajectory that satsfes the requred delay bound. In Fgure 1(a) the planed trajectory starts from source node 1 and expands followng the depth-frst search path along the longest branch n the routng tree. ubject to the gven delay bound constrant, the fnal trajectory cannot be further expanded after t reaches P 3 as depcted n Fgure 1(a). uch a smple strategy fals to satsfy three desgn requrements mentoned above, e.g., the sze of the local routng tree rooted at P 1 s much larger compared wth routng trees at P 2 and P 3 (he local routng tree rooted at P 3 ncludes source node 3 only). As a result, the routng tree rooted at P 1 needs to relay a much larger volume of sensory data and wll become the energy bottleneck that lmts network lfetme. Although the trajectory gven n Fgure 1(b) comprses the same number of Ps, ts workload s much better balanced among dfferent Ps,.e., each P mantans a local tree structure and relays sensory data for two source nodes. Consequently, there s not explct energy bottleneck exstng n any of the three local routng trees. As the network grows, the problem becomes much more complcated and t s non-trval to fnd the optmal trajectory wth the balanced network load. In ths paper, we refer to such a problem as the Mnmum-energy endezvous Pont selecton wth Load Balancng (MPLB) Problem. We formally defne the MPLB problem n ecton III.C. B. Network Model We assume that a set of sensor nodes V { v1, v2,..., v n } are randomly deployed n an M M feld. Nodes are assumed to know ther physcal locaton nformaton and the data generaton rates across the network are also equal. Locaton nformaton can be obtaned from the equpped GP devces or underlyng localzaton component. et V contans both source nodes and relay nodes. Each source node s V generates a certan amount of data at the begnnng of collecton perod of D and data must be delvered to the moble snk wthn D tme. uch a delvery deadlne s mposed by varous reasons, such as the lmted power supply of the moble snk, the lmted buffer sze of sensors, or smply applcaton requrements for data freshness. As mentoned before, the movement of the moble snk s constraned by a gven delay bound D as well, and ths delay bound can be measured by the maxmum dstance that the moble snk s allowed to move. We assume that a logcal routng tree has been ntally embedded n the network to connect all source nodes. Each edge on represents a mult-hop path (va relay nodes). In most prevous works [15][18], fndng the optmal moble snk trajectory always requres perfect network knowledge such as the topology of the entre routng tree and the locatons of all source nodes and relay nodes; however, such nformaton s expensve to be obtaned n practce. herefore, the global routng tree s a logcal approxmated tree that representng the geometrcal features of actual network topology. uch concept s llustrated n Fgure 1(c). he use of approxmated tree allows us to determne the locaton of Ps wthout the global network nformaton. Our algorthms can yeld a better soluton f the completed network topology s avalable. o quantfy the energy consumpton of the proposed protocol, we assume that the total energy consumpton of delverng a data packet along a path s proportonal to the Eucldean dstance between the source node and destnaton node. uch an assumpton s usually vald when sensor nodes are densely deployed n the network. Nodes can approxmately estmate ther energy consumpton durng the data transmsson based on the geographc relatonshp between any par of source and destnaton nodes. Our work can also be extended to utlze the expected transmsson count (EX) as the lnk qualty metrc and ts detals can be found n our earler work [24]. Plenty of exstng data dssemnaton protocols, e.g. [16], also adopt such an energy model. In addton, we assume that the storage capacty of the moble snk and sensor nodes s large enough to buffer the total volume of sensory data generated from source nodes wthn tme D. everal recent sensor network platforms [21] can ntegrate 10~100 MB NAND flash memory wth ultra-low power consumpton. C. Problem tatement Now, we formally defne the MPLB problem as follows: Defnton 1: Gven an ntal routng tree (, E) that connects a set of source nodes { s } V by edges E n the network, determne 1) a set of Ps { r } and ther sequence formng a trajectory U of the moble snk that s no longer than L vmd and 2) a set of workload balanced routng trees coverng all source nodes n, such that mn d( s, r), U s where d( s, r) s the length of the path from s to ts nearest r on tree. he energy consumpton of each P comes from recevng and transmttng sensory data wthn a perod of D. In our network model, source nodes generate the same amount of sensory data wthn tme D. he energy consumpton of a specfc P r s therefore proportonal to the number of ts assocated source nodes, whch s defned as the workload of r. We focus on achevng workload balancng among Ps,.e., every P should be allocated almost the same number of source nodes. he optmzaton objectve s to mnmze the total energy consumpton durng the entre data collecton process. Equvalently, t s to mnmze the average energy consumpton of each sensor node to prolong network lfetme. he MPLB problem n Defnton 1 can be proven NPhard by the reducton from the Geometrc ravelng alesman Problem (G-P) [16]. he problem optmzes the locatons of a set of Ps such that the network energy consumpton ncurred by data delvery can be mnmzed. In partcular, a specal-case decson verson of MPLB s to ask f there exsts a set of Ps resultng n zero network energy consumpton. Clearly, only when all source nodes are servng as the Ps, the network energy consumpton can be zero,.e., the moble snk must vst every source va a tour wthn the lmted length. It s exactly a decson verson of the G-P problem, n whch a salesman needs to vst a set of stes along a tour no longer than a gven dstance bound. 284

4 IV. POOCOL DEIGN AND ANALYI A. Overvew he ntal dea of our protocol s nspred by the followng two observatons that serve as the basc gudelnes n desgnng algorthms n ths secton. Extng state-of-the-art rendezvousbased data collecton protocols, such as [18][19][20], attempt to provde a one-tme soluton for addressng the routng structure formaton problem wth a set of networkng constrants, whch usually ncurs hgh computaton and communcaton costs, suffers a relatvely longer delay, and may rely on perfect network knowledge. Dfferent from exstng solutons, we plan to determne the optmal locaton of each P through an ncremental process. In partcular, we start from selectng a sensor node as the reference node that can balance the current workload of the network. We ncrementally expand the Ps set whle keepng the moble snk trajectory wthn the requred delay bound. Durng the entre ncremental trajectory plannng process, the balanced workload structure should be mantaned n our proposed soluton. he balanced workload at the reference node ndcates the beneft to deploy the frst P close to the reference node. Durng the ncremental trajectory plannng, the beneft needs to be updated once a new P s added, whch requres mantanng a reference structure to gude the deployment of subsequent Ps. Wth such a reference structure, the overall energy consumpton of the network could be reduced. At the same tme, workload balancng among dfferent local routng trees at Ps should be acheved as well. In addton, the reference structure needs to guarantee that the length of the trajectory formed by all deployed Ps s bounded by the maxmum movng dstance L, mposed by the delay bound D. B. Medan earchng Algorthm Desgn Essentally, the reference structure resdes at the medan of the global routng tree and locatons of all Ps can be determned f the medan s founded. he medan s a node on the tree. It not only mnmzes the total energy consumpton of gatherng sensory data at tself, but balances the current network load n an optmal manner as well. hus, the frst step n our protocol s to effcently locate the medan on a routng tree n the network. Peng et al. propose an algorthm to fnd the medan of a tree n [22]; however, the length of each edge n [22] s requred to be dentcal. nce each edge n our geometrcally approxmated routng tree may represent a multhop path, whose length s proportonal to ts Eucldean dstance. As a result, such an exstng algorthm cannot be appled to our scenaro drectly. MedanearchngAlgorthm Input:routng tree Output:medan m Arbtrarly select a node r as the root of the nputted routng tree and orent t nto a rooted drected tree r. For any node v on r, we compute the v. raverse the tree r n a bottom-up manner (from leaves to the root) to compute the D r () r va the formula n Lemma 1. Compute the D r ( v) for any node v on r n breadth-frst fashon usng the formula n Lemma 2. he medan m s the node wth the mnmum D r (.). Algorthm 1 he pseudo code of the medan searchng algorthm. o ths end, we desgn a medan searchng algorthm to locate the medan n O( ) tme. he effcent searchng process depends on two lemmas as follows, whch enable us to decde the medan by smply traversng sensor nodes n the routng tree n a bottom-up, breadth-frst search manner. Lemma 1: Gven a drected mnmum spannng tree 1 r rooted at any source node r, we can compute the sum of dstances from all other source nodes n r to node r n a bottom-up manner va the formula: D ( r ) d v, par v, r v desc( r) v r where desc(v) denotes the descendent of node v, par(v) denotes the parent of node v, and v denotes the number of nodes n the local routng tree rooted at v. Lemma 2: Gven a drected mnmum spannng tree r rooted at any node r, we can compute the sum of dstances from all other nodes n r to an arbtrary node v n breadth-frst fashon va the formula: D () v D () ( ) (,) (,) r par v r r v d r v r v d r v. r he pseudo code of the Medan earchng algorthm s gven n Algorthm 1 and we also provde a smple example n Fgure 2 to llustrate the algorthm. he algorthm contans four major steps. At step (1), we randomly select a node, e.g., node E n Fgure 2, as the root node. Accordng to the formula gven n Lemma 1, we get that D E ( E ) s 37. hen at step (3), D E (.) for each source node can be calculated n breadth-frst fashon usng the formula gven n Lemma 2. For nstance, we can frst obtan the values of D E ( D) 52, D E ( G) 57, D E ( C) 34. Next, D E ( B ) and D E ( F ) can be calculated. In the end, D E ( A) s determned to be 71. Clearly, D E ( C ) s the one wth the mnmum D E (.) value compared wth all other nodes. hus node C s selected as the medan n ths example. C. P-LB Algorthm Desgn Based on the obtaned medan, we ntroduce the desgn detal of endezvous Ponts electon wth Load Balancng (P-LB) algorthm n ths subsecton. Notce that after the Fgure 2 Executon of Algorthm 1. he number close to each edge ndcates ts length n Eucldean dstance. (a) Orent the routng tree nto a drected rooted tree. (b) Determne the medan. 1 Note that the reference structure can be formed based on the Mnmum pannng ree (M) rooted at any source node n the network. M can be effcently bult up by the well-known Kruskal algorthm. For the presentaton smplcty, we assume that there exsts a global M embedded n the network ntally and our protocol wll run on top of ths global routng tree. 285

5 medan s determned, the medan becomes the ntal poston to form and update the reference structure n the network and we name such a structure as the medan reference structure n the rest of ths paper. uch structure s a subtree on the routng tree n actual. It not only mnmzes the total dstances from all sources to tself, but mnmzes the largest branch t ncurs. Implctly, such structure can be exploted to gude us n fndng the optmal locaton for each P. he medan reference structure has several mportant propertes related to our desgn as follows: (a) he total energy consumpton of transmttng sensory data from sources nodes to the medan reference structure s monotoncally decreasng when ts sze ncreases; (b) he number of nodes n the largest local routng tree monotoncally decreases when ts sze ncreases; and (c) he sze of the medan reference structure can mplctly ndcate the length of the resultng trajectory planned for the moble snk. uch propertes nspre us that deployng Ps at the ntersectons between the medan reference structure and the approxmated routng tree may yeld a good soluton for trajectory plannng wth the workload balancng. We wll later show that the argument turns out to be true. P-LB operates teratvely. In each teraton, the current trajectory of the moble snk s expanded by addng a new P to share the load of the P wth the heavest workload. In addton, to satsfy the maxmum movng dstance requrement, the quantty of the medan reference structure expanson n each teraton should be restrcted as well. uch a process allows P-LB to dynamcally mgrate the workload of source nodes wth heavy traffc burden to those wth lght traffc burden, and thus acheves well planned trajectory wth balanced workload. Algorthm 2 shows the pseudo code of P-LB, n whch s a parameter set by the system operator accordng to the desrable trade-off between the soluton qualty and the computatonal complexty. When s small, P-LB operates wth more teratons yet provdes more P canddates. Note that the sze of a tree n ths subsecton s defned as ts total edge length along the tree. Fgure 3 llustrates how the P-LB algorthm works. For smplcty, we omt the detals of the branches B 1, B 2, B 3, and B 4, where the numbers of nodes belongng to B 1, B 2, B 3, and B 4 are assumed to be equal. At step (1) of Algorthm 2 the medan reference structure m (represented by the black dotted lne segments) only contans the medans. From step (2) to step (3), P-LB expands m toward the largest branch(s) wth an equal rate (We set the rate as a constant value,.e., 1 m per unt tme). he ntermedate result s shown n Fgure 3(a), where = {s 2, s 5, s 6, s 3 } and they are all the ntersectons between m and the paths from source nodes to medans. For example, the P r 4 s the ntersecton node between m and the path s4 m1. hen, at step (5) and step (6), P-LB checks whether m can be further expanded due to the delay bound D. If L -P() >, heorem 3 guarantees that the answer s postve and we wll prove t soon. P() s a P solver that returns the length of a snk tour that vst all the Ps n. After the frst teraton, P-LB fnds that m can be further expanded. hus, the algorthm executes back to step (2) and further grows m towards the current largest branches {s 1, B 1 }, {s 4, B 2 }, {s 7, B 3 }, {s 8, B 4 }, as shown n Fgure 3(b). After the second teraton, P-LB fnds that the sze of m reaches Y. In other words, L -P() < and P-LB returns. Fgure 3 An example of the P-LB algorthm s executon. (a) m after the frst teraton. (b) he fnal m s of sze Y. (c) he fnal soluton. PLBAlgorthm Input:routng tree E (, ), medan m, snk tour length L, and Output:he Ps set Let Y = L / 2, m = {m}. // m s the medan reference structure Count the number of nodes n each branch n the set { m }. Denote the branches wth the maxmum nodes as B max. m grows nto each branch n B max at an equal rate (constant value) untl the sze of m reaches Y or any node not n m s ncluded. = {r r s the ntersecton node between m and the path s m and s }. f X = L P() > Y Y X /2; goto step ; else return. Algorthm 2 he pseudo code of the P-LB algorthm. o construct a fnal soluton, the nodes resdng n the nteror of medan reference structure are assgned to ther nearest Ps respectvely, and the fnal result s shown n Fgure 3(c). Ps found by the P-LB algorthm are represented by the physcal locatons. It s possble that there s no sensor nodes resdng exactly at those locatons to serve as Ps. We address ths ssue as follows: the moble snk sends out an Anycast message [23] when arrvng at the desred poston. ensor nodes around the moble snk wll receve such a message and respond. he moble snk wll select the frst respondng sensor node as the P. D. heoretcal Analyss In the followng, we frst prove the correctness of our proposed P-LB algorthm, and then derve ts approxmaton rato to show ts effectveness. In ths subsecton, for a gven graph G, we defne the sze of G, denoted by s(g), as the total lengths of the edges on t. heorem 1: Among all possble subtrees of sze Y, the total of dstances from all source nodes n the routng tree to the medan subtree 2 s always mnmzed. Proof:We omt the proof due to the page lmtaton. 2 From the example gven n Fgure 3 we can see that the medan reference structure s essentally a tree structure. Actually, t s true n general. We omt the proof of ths fact due to the page lmtaton and use medan reference structure and medan subtree nterchangeably n the rest of ths paper. 286

6 emarks: As Ps are deployed at the ntersecton between the medan subtree and the routng tree, heorem 1, mnmzng the dstance-sum of the medan subtree, ensures that the network operated by P-LB experences the mnmum energy consumpton of relayng sensory data from source nodes to the Ps compared wth other protocols. heorem 2: Among all possble subtrees of sze Y, the number of nodes n the largest branch nduced by the medan subtree s always mnmzed. Proof:We omt the proof due to the page lmtaton. emarks: he Ps collect sensory data from the sources n ther local routng trees,.e. ther assocated branches. It s clear that the workload wll be balanced f the sze of the largest branch s small n the network. heorem 3 shows that our proposed P-LB can acheve such a goal. Consequently, heorems 1 and 2 jontly demonstrate the workload can be well balanced among the Ps durng trajectory plannng based on our proposed algorthm. Next, we prove that there always exsts a P tour no longer than L that allows the moble snk to vst all the Ps n (determned by Algorthm 2) wthn the delay bound. heorem 3: P( ) L,.e., step (5) n P-LB, always holds before P-LB s termnaton, where s the Ps set found n the -tme teraton. Proof:We omt the proof due to the page lmtaton. emarks: heorem 3 shows that there always exsts a trajectory no longer than L to vst all selected Ps. hs enables the output soluton to satsfy the delay constrant n our network model. Now we focus on dervng the approxmaton rato of the P-LB algorthm to deeply understand how close the proposed algorthm can perform compared to the optmal soluton, whch characterzes the performance qualty of the trajectory planned by P-LB. uppose M s the mnmum spannng tree connectng source nodes set. Let be the rato of L to the total edge length of M,.e., = L sm. We assume that 1, because f L s too long, the data collecton delay becomes extremely large due to the moble snk s low movement speed. In addton, the power supply of the moble snk may not support such a long-dstance traversal n many real applcatons. We defne the e-dstance between node u and v, denoted by e ( u, v ), as the length of the path ur' v on tree, where r ' s the nearest P to u. uch dstance metrc can be paraphrased as the length of data delvery path, where source nodes should frst send ther sensory data to the respectve nearest Ps and then proceed to the destnaton node. For nstance, n Fgure 3(b), e ( s6, s5) s equal to the length of path s6 r3 s6 s5. Let E (, u ) represent the e- dstance-sum from all source nodes to node u,.e., E (, u ) e ( v, u ). he use of e-dstance facltates our v expresson of the network energy consumpton ncurred by the soluton from P-LB. Besdes, we also defne cluster(s) of the P node r, denoted by c(r), as the set of branches all rooted at r. For nstance, n Fgure 3(c), c(r 2 ) = {{s 5 },{s 8, B 2 } }. heorem 4: he approxmaton rato of P-LB s no greater than 1, where and 2, L s ( M ) and 1. Proof: uppose represents the set of the Ps n the optmal soluton. represents the set of the local routng trees rooted at the. We frst derve the energy consumpton of the optmal soluton to be the lower bound of our proposal. As the energy cost of transmttng a data packet s proportonal to the Eucldean dstance between the sender and recever, the total consumpton of transmttng data s proportonal to the total of dstances from every source s to ts r followng the correspondng t. hs cost can be represented by Copt D, (5-1) where D, = d ( s, r ) s, r, d ( s, ) r represents the dstance of routng path from source s to ts P r on the tree t, and the constant denotes the energy cost that s requred to transmt a packet ahead on ts way per meter. Let M denote the mnmum spannng tree wth the termnal nodes set as. Note that M s a subtree resde n the nteror of the abovementoned M. Accordng to the defnton of mnmum spannng tree, the total edge length of the unon of and M s no shorter than the total edge length of M. Hence, s s M s M (5-2) As the paths connectng sources and the Ps are overlapped wth each other, D, would never be smaller than the total edge length of. hus, the equaton (5-2) can be transformed to: D, s M s M (5-3) Let denote a subtree nduced by removng an edge from the P tour P( ) that vsts each node n. It s obvous that s( ) P( ). hen, we have D, s M s M s M L (5-4) Accordng to the defnton of e-dstance, only n the case that the destnaton sets are the same Ps set, the e-dstancesum and dstance-sum both dervng from the same sources set can be equal,.e., D, = E,. Hence, (5-4) can be further transformed nto:, E s M L (5-5) where EM m, represents the e-dstance-sum from all source nodes n to the medan node m through the tree M. Accordng to the defnton of medan, any path startng from a P and endng at the m s no longer than L 2, where r denotes the th node n the optmal Ps set,.e., em ( r ) ( ) 2 m dm r m L. Hence, EM, m E, ( ) ( ) c r em r M r EM, ( ) c r L r (5-6) 2 EM, L 2 If, we further have: 2 E, m E, L (5-7) M M In the followng, we proceed to dscuss the energy consumpton of data transmsson ncurred by the P-LB 287

7 algorthm. For smplcty, we frst analyze the energy cost ncurred by a P solely. uch cost, denoted by C r, can be represented as follows: Cr E ( ), ( ), M c r m c r EM r m (5-8) hrough summng up the equaton (5-8), we can obtan the total energy consumpton CP LB : CP LB C r r EM c( r), ( ), r m c r EM r m (5-9) E c( r), m c( r) E r, m r M r M E (, m) c( r) E r, M M r M Accordng to the defnton of the Ps n the P-LB algorthm, there s at least one source assocated wth each P. Based on ths observaton, we can know cr ( ) 1. Besdes, the executon of P-LB can always guarantee that E ( r, m ) s M ( ) L 2 r m, where m s the medan subtree. In short, we have cr ( ) EM ( r, ) m r (5-10) EM ( r, ) L r m 2 In addton, let L sm ( ) to be ntegrated wth (5-5), we have L EM (, ) (5-11) 1 Further ntegratng the equaton (5-10) and (5-11) wth (5-7), then EM, E, M m L E, 1 M m L 2 2 L (5-12) EM, m c( r) (, ) r EM r M 1 2 L Multplyng the constant wth both sdes of (5-12), and smultaneously ntegratng wth the equaton (5-1) and (5-9), we can fnally establsh the relatonshp of energy cost between the optmal soluton and the P-LB algorthm, E, m c( r) E r, m, C M r M E L M C C C 1 2 CP LB opt P LB opt opt (5-13) emarks: If the delay bound s extremely small or the energy supply of the moble snk s hghly lmted, the coeffcent becomes very small and the derved approxmaton rato ndcates that the performance of P-LB s close to the optmal soluton. V. LOCALIZED POOCOL DEIGN As mentoned before, the proposed P-LB reles on the locaton nformaton of each source node. uch global nformaton, however, usually lmts the scalablty of the system and hnders the applcablty of the proposed protocol. o enhance the applcablty of P-LB n practce, we release the requrement about the perfect locaton nformaton at the moble snk sde and propose a localzed, fully dstrbuted verson of the protocol named as P-LB-D n ths secton. In Algorthm 2, P-LB explores a new P only dependng on the current workload of each P already deployed, whch nspres us that f such a decson can be made based on merely local nformaton, the global network knowledge (such as the topology of the approxmated routng tree) requred n P-LB can be avoded. Based on our study, we fnd that such a goal can be acheved n practce. In the network, the moble snk always knows the sze of the local routng tree rooted at each P, based on whch the moble snk s aware where the current energy bottleneck s. uch local nformaton s enough for the moble snk to decde how to expand ts current trajectory n local. We mplement such an dea nto P-LB-D and descrbe t n detal n the rest of ths secton. A. Network Intalzaton he P-LB-D algorthm starts wth a two-phase network ntalzaton, durng whch the moble snk can construct ts local vew of the entre network effcently. It s also essentally to buld the global network topology n a dstrbuted manner. Phase 1: the sensor node closest to the moble snk s ntal poston wll be chosen as the center node. he center node broadcasts a beacon to ts neghbors wth ts own physcal locaton, nvtng neghborng nodes to act as ts chld nodes. After a neghbor node receves such an nvtaton, t may face two dfferent choces. If ths node already has a parent, a message sayng NO wll be sent back to the center node. Otherwse, t sends out a messages sayng YE wth ts own locaton and broadcasts a new beacon to search ts own chld nodes. uch a process advances at each sensor node sde teratvely, untl phase 2 begns. Phase 2: If a sensor node does not receve any YE message, t wll nform the sze of ts subtree to update the local vew for the topology of ts parent. Once a sensor node receves updatng messages from all chld nodes, t mmedately updates the topology nformaton stored locally and sends the updated result to ts parent. uch a process contnues untl the center node completes the updatng. o better understand the network ntalzaton process, we provde an example n Fgure 4. Intally, 0 s selected to be the center node because t s the closest one to the moble snk. 0 broadcasts a beacon denoted by B. In Fgure 4(a), 1 and 2 receve such a message. ght now, they do not have ther own parent nodes and thus return messages YE to 0. hen 1 broadcasts a new beacon. 2, 3 and 4 wll receve 1 s beacon. o far, 2 already has a parent node. As a result, t responds a message No to 1. On the other hand, snce both 3 and 4 do not have ther parent nodes yet, they send out messages YE. In Fgure 4(b), 2, 3, and 4 do not receve any YE message and they enter phase 2. In phase 2, 2, 3, and 4 nform ther parent nodes the number of sensor nodes n ther own routng subtrees. Once 1 successfully obtans such nformaton from all ts chld nodes (.e., 3 and 4 ), t mmedately updates ts own local vew of the network topology and sends the updated result to ts parent node (.e., 0 ) as shown n Fgure 4(c). he 288

8 two-phase ntalzaton s completed when the center node 0 gets responses from all ts chld nodes. After the network ntalzaton, the nformaton stored at each sensor node ncludes ts locaton, workload (.e., the number of sources n all the subtrees rooted at ts chld nodes), parent node s locaton, and chld node s locaton. We defne the workload of a sensor node as the total number of nodes n the local routng tree rooted at ths node tself. We take node 1 for example, where 1 = { locaton: (x 1,y 1 ); workload: 3; parent node: 0 (x 0,y 0 ); chld nodes set: { 3 (x 3,y 3 ), 4 (x 4,y 4 ) } }. B. Optmzng the endezvous Pont Placement o determne the locaton of each P n P-LB-D, the moble snk teratvely elmnates the workload bottleneck va allowng the current busest P to nvte another nearby node as a new P to share ts burden untl the trajectory length reaches ts maxmum movng dstance L. Essentally, the strategy breakng the workload bottleneck n P-LB-D s rather smlar to the strategy growng the medan subtree towards the largest branch n P-LB. In P-LB-D, the moble snk only knows the nformaton of locaton and workload of Ps. For nstance, n Fgure 4(a), the moble snk ntally selects the center node 0 to be the frst P. In such a case, the current P s nformaton obtaned by the moble snk s: P-lst = { P 1 :(locaton: 0 (0,0); workload: 5)}. hen the moble snk moves to the P wth the heavest word load and asks t to nvte one neghborng node wthn the range of d to serve as a new P. 3 he neghbor wth the largest workload wll be selected as the new P and ts own nformaton (ncludng ts locaton and workload) wll be mmedately sent back to the moble snk. In Fgure 4, the busest P s 0 and t nvtes 1, who has the largest load 3 among all ts chld nodes, as a new P. After becomng a new P, 1 can collect data from 3 and 4, whch largely mtgates the orgnal heavy workload of 0. Updates on the routng tree should also be done at ths tme,.e., now 1 does not have a parent node and ts receved data wll thus not be relayed. 0 deletes 1 from ts chld nodes lst and does not wat for the data from 1. At the begnnng, the moble snk nvtes the nearest node (center) to become the frst P. It then executes the P-LB-D algorthm to recrut the new Ps. he moble snk keeps movng towards the P wth the heavest workload untl the length of the trajectory reaches the maxmum movng dstance L. After reachng ths P, the moble snk asks t to nvte one nearby node to be a new P. Once the new P s selected, some necessary updates should be performed at both the sensor and the moble snk sdes. After the trajectory s determned, the moble snk traverses along the formed movng trajectory and collects data at each by vstng all selected Ps. ensory data are sent along the chld-to-parent path unless reach the correspondng P. 3 he range d can be computed by d ( L P( ))/2, where s the set of Ps retreved from P-lst, and P() s a P solver returnng the length of the P tour that vsts all nodes n. Clearly, d s a key parameter guaranteeng the newly ncluded P and orgnal Ps can all be vsted by the new trajectory tour no longer than L. Its correctness can be proven by heorem 3. Fgure 4 An example of network ntalzaton n P-LB-D VI. PEFOMANCE EVALUAION A. mulaton ettngs In ths secton, we evaluate the performance of P-LB and P-LB-D by comparng them wth two well-known mobltyasssted approaches named the Nearest-Neghbor based heurstc (NN) [16] and the endezvous Plannng wth Utltybased Greedy heurstc (P-UG) [17]. Wthout loss of generalty, the P-LB-D algorthm starts from a random ntal poston (.e., the center node) to determne the locaton of sequent Ps. In NN, the moble snk always travels to the nearest source that s closest to the current source that has been vsted. he sources that are not vsted by the snk connect to the closest source on the snk tour. As there s no any P n NN, t serves as the benchmark clarfyng the effectveness of explotng snk moblty n data collecton. P-UG s a recently proposed centralzed network protocol explotng rendezvous nodes and moble elements to mprove the effcency of gatherng data n WNs. hs approach attempts to mnmze the total energy consumpton of data delvery under the assumpton that the cost of sendng a packet s proportonal to ts traversal dstance. As such energy model s also adopted by P-LB and P-LB-D, P-UG can therefore serve as a sutable benchmark to evaluate our proposals n comparson wth the state-of-the-art related work. In P-UG, rendezvous nodes are determned n an teratve manner. In each teraton, P-UG expands the vstng tour for moble element to nclude more source(s) wth the largest utlty servng as the new rendezvous node(s). he utlty s defned as the rato of amount of savng energy to the extended length of tour. As the moble element tour must contan a fxed base staton for uploadng data, we place the staton at a random poston n our network. In smulatons, vared numbers of sensors are densely dstrbuted n a 500m 500m target regon to guarantee the connectvty of network. After the ntalzaton, an M shaped global routng tree has been constructed to connect all sources. A source generates one data sample wthn a data collecton perod and needs to send all accumulated (ncludng receved) samples to ts correspondng P. We set the rado transmsson radus of a sensor as 100m. As the energy consumpton of the wreless transmsson s proportonal to ts Eucldean dstance between the par of source and destnaton nodes, we analyze the energy effcency performance of varous algorthms by comparng ther total dstances of data delvery paths. he network lfetme s quantfed by the tme duraton from the network starts to work untl the frst node depletes ts energy. nce energy s manly consumed by wreless transmsson, energy cost at each sensor sde s 289

9 Fgure 5 otal dstances of data delvery paths vs. Number of source nodes. Fgure 6 otal dstances of data routng paths vs. Length of moble snk vstng tour. Fgure 7 Average maxmum workloads among the Ps vs. Length of moble snk vstng tour. Fgure 8 Workloads on the Ps n dfferent algorthms. Fgure 9 Workloads on sensor nodes n P-LB-D and P-LB. proportonal to ts workload to relay sensory data. We defne the workload of a sensor node as the number of sources n the local routng trees assocated to ths node. Hence, the lfetme of a network s reversely proportonal to the maxmum workload among all the sensor nodes. All the evaluaton results are averaged based on 10 dfferent runs. B. he Performance of P-LB and P-LB-D Fgure 5 compares the total dstances of data delvery paths formed by dfferent algorthms wth vared sze of networks. he sze here s defned as the number of sources deployed. In ths experment, the length of moble snk vstng tour L s set to be 300m. Accordng to Fgure 5, t s clear to see that all rendezvous-based approaches acheve sgnfcant better performances than the one that just explots snk moblty but not rendezvous nodes. In addton, the gap from NN to P-UG or P-LB or P-LB-D s expanded as more source sensors are nvolved. When the network s growng larger, the energy effcences acheved by P-LB and P-LB-D are both boostng. It ndcates that P-LB-D and P-LB can effectvely reduce the energy consumpton by takng advantage of the advanced reference structure,.e. medan subtree, proposed n ths paper. Compared wth the centralzed algorthm P-LB and P-UG, the dstrbuted verson P- LB-D also works well (e.g., ts performance s even better than P-UG n some cases) wth only a slght performance dstorton n terms of the delvery path length summaton. It s because there s not an essental dfference between P-LB and P-LB-D n protocol desgn except the root of medan subtree,.e., the root s the medan n P-LB but a random node n P-LB-D. Moreover, we also fnd that P-LB outperforms P-LB-D and P-UG especally n the case that the network s not so bg. However, ther performance gaps are gradually narrowed wth the ncrease of network sze. uch phenomenon s consstent wth the mplcaton of the approxmaton rato of P-LB drven n ecton IV.D. We then evaluate the performances acheved by dfferent algorthms wth dfferent data delvery deadlnes. As we have mentoned above, such delay bound s equal to the snk traversal tme, and can be fnally mapped to the length of snk tour gven the snk movement speed n average. Fgure 6 llustrates the relatonshp between the total dstances of data delvery paths and the length of snk tour. 200 source nodes are randomly deployed. All algorthms performance becomes better when the snk moblty s enhanced. Consstent wth the result n Fgure 5, P-LB s superor to other three compettors. Although P-LB-D s a dstrbuted algorthm, ts performance s very close to the one ganed by P-UG. hs s another ndcaton of the effectveness of P-LB and P- LB-D to reduce the energy consumpton, whch mples that the network can enjoy a longer lfetme n P-LB or P-LB-D compared wth other two algorthms. Fgure 7 shows the relatonshp between the average maxmum workloads among Ps and the length of snk tour. mlar to Fgure 6, 200 sources are randomly deployed n the feld as well. Accordng to Fgure 7, the average maxmum workload ncurred by three rendezvous-based algorthms all decrease wth the ncrease of L. More specfcally, when the tour s short, the load s extremely heavy n P-UG and P-LB-D,.e., ther workload all exceed 160. As load balancng s not consdered n P-UG, the 290

10 bottleneck node could not be elmnated even when a source s recruted to be a new rendezvous node. However, as L ncreases, P-LB-D rapdly cuts down ts maxmum workload and largely narrows the gap wth P-LB. hs mples that the dstrbuted load balancng strategy n P-LB- D can effectvely mtgate the workload on the bottleneck P. o further verfy the effectveness of our proposals, we show the snapshot of the workload on each P n three dfferent protocols. In ths experment, every node has been assgned a unque ID number beforehand. 300 source nodes are randomly deployed and the tour length s set to be 600m. In Fgure 8, the varance of the workload on dfferent Ps s very large n P-UG, whch s not as smooth as P-LB-D or P- LB. Our proposals are manly benefted from the workload balancng consderaton n trajectory plannng. In Fgure 9, we take a fne look at the dfference between P-LB-D and P-LB. Fgure 9 compares the workload of each sensor node n P-LB-D wth that n P-LB. Accordng to the result, the workload of sensor nodes n P- LB s more unform than that n P-LB-D. he reason for ths phenomenon s that P-LB-D expands the trajectory from the node wth the shortest dstance to the moble snk s ntal locaton whle P-LB expands the trajectory from the medan. In addton, Fgure 9 shows that the workload of sensor nodes s well balanced n both P-LB and P-LB-D as expected by the optmzaton objectve n our orgnal problem defnton. VII. CONCLUION In ths paper, we study the data collecton problem for the moble snk n wreless sensor networks. We formulate such a problem as a jont optmzaton problem of both moble snk trajectory plannng and network load balancng. We prove that such a problem s NP-hard and propose an approxmaton algorthm P-LB to approach the optmal soluton. We prove that P-LB satsfes energy savng and sustanable desgn requrements. Moreover, the derved approxmaton rato valdates the performance of P-LB. o further enhance the applcablty of the proposed algorthm, we relax the assumpton of the locaton nformaton of each sensor node s obtaned by the moble snk and propose a localzed, fully dstrbuted verson P-LB-D. Compared wth exstng works, the proposed P-LB guarantees low total energy consumpton over the network and acheves much more balanced overhead across dfferent Ps. In the future, we wll mplement and evaluate our algorthms on real testbeds. ACKNOWLEDGEMEN hs work s supported by the NFC under grants No and No , the key research project of Mnstry of Educaton grant No , the fundamental research fund for the Central Unverstes No and No.K , COE UG/ 20Aug /14 n Nanyang echnologcal Unversty of ngapore, and key technologes of electromagnetc spectrum montorng based on wreless sensor networks grant No. 2010ZX EFEENCE [1] Yanmn Zhu and Lonel M. 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