Data-Centric Attribute Allocation and Retrieval (DCAAR) Scheme for Wireless Sensor Networks

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1 Data-Centrc Attrbute Allocaton and Retreval () Scheme for Wreless Sensor Networks Ratnabal Bswas, Kaushk Chowdhury and Dharma P. Agrawal OBR Research Center for Dstrbuted and Moble Computng, Dept. of CCS, Unversty of Cncnnat, Cncnnat, OH 45- mal: Abstract Wreless sensor networks have enabled nformaton gatherng from a large geographcal regon and present unprecedented opportuntes for a broad spectrum of montorng applcatons. In ths paper, we propose a data-centrc storage scheme to determne a dstrbuton of attrbutes over a large-scale sensor network such that the cost of retrevng data s mnmzed. We analytcally determne the condtons under whch the proposed archtecture s benefcal and present smulaton results to demonstrate the same. To the best of our knowledge, ths s the frst attempt to determne an allocaton of attrbutes over a sensor network based on the correlatons between attrbutes. Keywords Allocaton problem, data-centrc storage, aggregaton, n-network processng, mnmum spannng tree, heap, hard threshold, soft threshold, query-drven, event-drven I. INTRODUCTION Recent technologcal advances have enabled dstrbuted nformaton gatherng from a gven regon by deployng a large number of networked tny wreless sensor nodes. However the small form factor of these nodes lmts the sze of the battery or the total power avalable wth each sensor node. Snce data communcaton s the domnant component of energy consumpton at the node level, protocol desgn for sensor networks s geared towards reducng communcaton n the network. Thus we propose a data-centrc storage scheme for storng attrbutes n a sensor network such that communcaton nvolved n queryng the network can be mnmzed. A data-centrc storage scheme [][6][7][8] allows events to be stored at specfc rendezvous ponts wthn the network that queres can access drectly. In ths paper, we have proposed the scheme that determnes an allocaton of attrbutes dependng on the correlatons between them. We have analytcally determned the condtons under whch the scheme should be preferred. Future sensor networks are expected to support several protocols, wth mddleware software allowng a user to select the preferred protocol as per hs requrements. The rest of the paper s organzed as follows. Secton II descrbes a general scenaro where the proposed scheme can be used and lsts the basc assumptons for the scheme. Secton III defnes the allocaton problem and gves an outlne of the proposed scheme. The detaled algorthms are gven n Secton IV. Secton V determnes analytcally the condtons under whch the scheme should be preferred. The smulaton results are dscussed n Secton VI. Secton VII lsts other data-centrc storage schemes, whle Secton VIII concludes the paper wth future research agenda. II. CONTXT In ths secton we frst present a general scenaro where the scheme can be appled and lst some basc assumptons about the sensor networks beng consdered. A. A General Scenaro We have desgned a scheme that can be employed for large scale sensor networks of the future. For example, gven a geographcal area, the user mght want to deploy a sensor network that smultaneously serves multple applcatons lke precson agrculture, weather montorng, ecosystem montorng etc. For each applcaton the user mght want the network to sense specfc physcal attrbutes (e.g. humdty, temperature, lght etc. for weather montorng applcaton; temperature, lght, presence of chemcals etc. for precson agrculture applcaton and so on.) and consequently mght expect the sensor network to respond to specfc queres. Snce such large-scale sensor networks would be expected to serve a substantal number of queres smultaneously for several applcatons, the number of attrbutes sensed by the network would also be substantal. The proposed scheme s desgned for mnmzng cost of data retreval from large-scale sensor networks servng such real-lfe scenaros. B. Basc Assumptons In a sensor network, the nodes whch ssue user queres are called snk nodes. We have assumed that the snk node could be at any random poston n the network. ueres ssued by a snk may be classfed nto two broad categores: ocaton-based query s used when the user s nterested n attrbute values from only a partcular regon of the network and hence the query s routed drectly to that regon. Attrbute-based query s used when the user s nterested n data satsfyng some attrbute-based selecton crtera. Such queres are flooded n the entre network and the relevant nodes route ther data to the user usng aggregaton schemes [4][5]. The motvaton behnd the scheme s to obvate the need for communcaton-extensve floodng n case of attrbute-based queres. The sensor nodes are assumed to be /5/$. 5 I MASS 5

2 locaton-aware [3]. We also assume that the sensor network has been deployed on a rectangular regon and the nodes are aware of the geographcal boundares of the network. III. TH AOCATION PROBM Sensor networks can be envsoned as a large dstrbuted database where the sensor nodes generate named data aganst user-specfed queres. In ths secton, we defne the Allocaton Problem of dstrbuted databases n the context of sensor networks and present our proposed archtecture. A. Problem Formulaton We defne the Allocaton Problem for sensor networks as follows: Assume that there are a set of sensed attrbutes A = {A, A,, A m } and a network S of sensor nodes whch have to serve a set of queres = {,,, q }. The allocaton problem nvolves n fndng the optmal dstrbuton of A to S. Here the optmalty can be defned wth respect to mnmal energy consumpton and hence mnmal communcaton requred n servng the set of queres. We propose the scheme as a heurstc soluton for the sensor network allocaton problem. We formulate the allocaton problem as follows. et = {,, q } be a set of user-defned queres. We assume that a set of prortes { p, p, p q } for the queres {,, q } s gven. The prorty p of a query could depct ether the probablty wth whch query s ssued per unt tme or the frequency of tuples generated for query per unt tme or a combnaton of both. These values may be set by the system desgner to specfy the relatve prortes of queres and are normalzed such that q p =. ach query k can be = modeled by the set of attrbutes ncluded n the query.e. = A A,, A. As mentoned n Secton II.B., the sensor { },! k nodes are assumed to be unformly deployed over a rectangular regon. Thus our obectve s to dstrbute the m attrbutes over ths rectangular feld of sensor nodes. We do so by splttng the rectangular area nto a grd G of sze m m and each attrbute A s allocated to a partcular grd cell. The allocaton problem thus reduces to fndng an optmal dstrbuton of m attrbutes over a m m grd. et f : A G be an optmal dstrbuton functon. Thus f ( Ak ) = ( xk, yk ), xk {, m}, yk {, m} mples that attrbute A k should be stored n grd cell (x k,y k ) of the deployed rectangular sensor network. The functon f then attempts to mnmze the followng two costs for each query, =,,q: uery valuaton Cost C : Ths s the cost of aggregatng resultant tuples for all the attrbutes { A, A, A k } specfed n the query. For mnmzng ths cost, attrbutes belongng to the same query should be placed near each other n the grd,.e. the cost of the mnmum spannng tree onng the grd cells {( x, y ), ( x, y ), ( x k, y k )} should be mnmzed. uery Access Cost C : Ths ncludes the cost of A query dssemnaton from the snk and result delvery to the snk. In order to mnmze ths cost, the query attrbutes should be placed close to the snk. Thus, the functon f should mnmze the total query evaluaton cost C ( q C = the set of queres. ) and total query access cost C A ( q C A = ) for B. Scheme To determne a good dstrbuton functon f : A G we employ a two-stage heurstc. Note that queres and ther assocated prortes ndrectly defne correlatons between attrbutes. For example, f a query wth a very hgh prorty ncludes attrbutes A and A we can say that A and A have a hgh correlaton snce they are accessed together very frequently. Attrbutes wth hgher correlatons should be placed closer to each other for mnmzng the cost C. Smlarly by placng more frequently accessed attrbutes closer to the center (snce t s equally lkely for the snk to be n any poston), the cost C A can be mnmzed. To dentfy the frequently accessed attrbutes, we calculate the ndvdual access probabltes P(A ) of attrbutes as follows: P q ( A ) = P( ) P( A ), = =, m, where P( ) = p, =, m and P( A ), A = (), A The frst stage of the scheme creates a heap-lke data structure called the correlaton tree that provdes a holstc vew of all the attrbutes n terms of ther access probabltes and correlatons. The second stage uses ths correlaton tree to determne an optmal dstrbuton of the attrbutes to respectve cells of the grd. As an llustraton, Table I lsts a set of gven queres along wth ther prortes. The correspondng correlaton tree and the optmal allocaton of attrbutes are shown n Fg.. Note that snce query 7 has the hghest prorty, attrbutes A, A 35, A 37, and A 39 have been allocated storage cells nearest to the center of the grd and adacent to each other. The algorthms for determnng the functon f are descrbed Secton IV. Snce the algorthms are topology ndependent, each sensor node may compute f ndependently. However to reduce the overhead nvolved n performng the same redundant computaton all over the network, the functon f may be computed at the snk and then sent to all the nodes n the network. For now, we assume that such a functon f s avalable to all the nodes n network and present our proposed archtecture for query processng. C. Proposed Archtecture very sensor node s assumed to be aware of ts own locaton as well as the geographcal boundares of the sensor network. Hence every sensor node can dentfy whch grd cell t belongs to. We call the grd cell responsble for storng attrbute A as the zone for attrbute A and denote t by Z. The number of nodes belongng to a zone Z, denoted by N(Z ), depends on the densty and dstrbuton of the sensor nodes over the network. Some of the nodes belongng to each zone

3 have specal functonaltes apart from sensng and routng. Based on the functonaltes assgned to them, these nodes can be classfed nto 3 types vz. control node, storage nodes and replca nodes. The storage nodes of a zone Z are responsble for storng the values of the attrbute A. The number of storage nodes requred n a zone Z s denoted by N(A ) and depends on the total amount of data values correspondng to attrbute A and the memory capacty of each sensor node. For every zone Z, there s one control node that s responsble for fetchng data from the storage nodes usng specalzed ndexes that t mantans. Apart from the control nodes and storage nodes, some of the other nodes n a zone may store redundant or summary nformaton about attrbute values to provde fault tolerance and are hence called the replca nodes. Fg. (b) shows the proposed archtecture where the control node s the node nearest to the center of each zone. The steps nvolved n servng a query are as follows: Snk gets a query { A, A, A k } attrbutes are stored n the zones { Z Z,, Z } = whose,!. k The snk determnes whch zone s nearest to tself, say Z, and sends the query to zone Z. The control node of zone retreve relevant values of Z A The control node of zone uses ts stored ndexes to from the storage nodes. Z also computes the optmal route of dssemnatng the query to the zones storng the remanng query attrbutes. The optmal route for retrevng the attrbutes { A, A, A k } would essentally be the mnmum spannng tree onng the zones { Z, Z, Z k }. The complexty nvolved n calculatng ths route s mnmal (any mnmum spannng tree algorthm may be used) snce a query wll not contan a large number of attrbutes. The computed route s used for routng the query and routng the resultant data tuples back to the snk. Whle routng the data to the snk, the control nodes of the respectve storage zones use aggregaton [4][5] and n-network processng mechansms [9] to further reduce the amount of data transfer n the network. The proposed archtecture acheves effcency n query processng at the cost of mantanng updated values of all the attrbutes n the zones where they are stored. To reduce ths mantenance overhead, a soft threshold scheme may be used: Suppose a sensor node n zone Z senses an attrbute A k. Suppose the soft threshold for attrbute A k s ϕ k. If the dfference between the prevously sensed value and the current value of A k s more than ϕ k, the current value needs to be reported to the storage zone Z k housng A k. However nstead of sendng update messages for every ndvdual node fluctuaton, the sensor node frst sends an update message to the control node of ts own zone Z. TAB I. p IST OF URIS AND ASSOCIATD PRIORITIS p A p k A,A3,A5, A7,A9 A,A3, A5,A7 A9,A, A3 A5,A7, A9 5.5 A3,A A A,A35,A 37,A39 A p k 3.5 A A8 4.6 A3,A A k A4,A, A6 5.5 A 7. A3,A A5 8.7 A A9,A3, A7,A3, A35 A4,A8,A,A39 A6,A, A4 9. A,A9. A A A5,A8,A. A8,A A4,A7.8 A A.7.5 A4,A7,A 3.5 A,A6,A,A6 A,A6, A A8,A6,A 4,A3,A4 A9,A8,A 7,A4 A6,A6,A A6,A36. A33,A36 4. A,A A7.833 (.7,35,7) (.,39,) (.,39,8) (.,39,) (.,39,4) (.3,9,3) (.5,6,3) (.3,9,3) (.,36,33) (.8,5,) (.7,6,) (.5,6,36) (.7,6,) (.8,5,)(.,39,8) (.8,9,4) (.63,5,) (.63,5,8) (.63,5,) (.63,5,8) 9 (.8,9,4) (.5,4,7) (.5,4,7) (.,39,4) (.5,6,3) (.7,35,7) (.,36,33) (.5,6,36) Fgure (a). Correlaton Tree correspondng to queres n Table I. Fgure (b). Allocaton of attrbutes to grd The control node of Z wats for a predefned tme nterval T k. All the update messages for A k that the control node receves from nodes n ts own grd cell durng tme T k are then combned nto aggregate update message(s) and sent to zone Z k housng A k. The duraton T k s called the update epoch for attrbute A k. All the messages (vz. query message, update message or resultant data tuple) can be routed n the network usng geographc routng protocols lke GPSR [].

4 A p p p p A (p ) A p A (p+) A k Fgure. Shows ntal tree for query = { A A! A }. D. Advantages and mtatons As wth all data-centrc storage schemes, the scheme obvates the need for floodng queres n the network. The user response tme for queres s also mnmzed. Moreover mnmzes both query access cost and query evaluaton cost. In addton to these benefts, havng all values of an attrbute at one place provdes helpful global context for evaluatng local data. For example, sensed temperature values could be compared aganst the average temperature value of the network to detect fres or other local temperature spkes. Furthermore, user-defned parameters lke soft threshold and update epoch allows the user to tune the performance of the system as per hs requrements. The scheme works well as long as the overhead of sendng update messages to storage zones does not supersede the advantage of mnmzng the query cost. That s, f the attrbutes are such that they have very frequent fluctuatons or fluctuatons contnually occur all over the network but the queres are not frequent enough, then more energy may be expended n proactvely mantanng updated values n storage zones. However snce most real-lfe physcal phenomena are localzed, the fluctuatons can be consdered to be mostly local and not too many. Consequently the scheme should perform well n most real-lfe stuatons. IV. AGORITHMS In ths secton we present the algorthms CreateCorrelatonTree and AllocateGrd that have been employed n the two stages of the scheme. A. Algorthm CreateCorrelatonTree Input: st of queres and assocated prortes p Output: Correlaton Tree/ Forest Ths s the frst stage of the heurstc whch creates a heaplke data structure called the correlaton tree to represent the correlatons between attrbutes as well as the relatve orderng of attrbutes n terms of ther access probabltes. The ntalzaton phase of the algorthm constructs a tree for each query as shown n Fg.. The query attrbute wth hghest access probablty s made the root of the query tree. Thus for query n Fg., A has hghest probablty.e. ( A ) { P( A ), P( A ), P( A )} max! p k p P =,. The weght of an edge n tree T onng the attrbutes A and A s denoted by w T (A,A ) and depcts the probablty of A and A beng n the same query. At each teratve phase, a query tree T s chosen from ths ntal lst n ascendng order of query prortes, and combned wth the partal soluton PS (.e. the partal correlaton tree/forest at that teraton phase) as shown n the pseudocode. The trees are combned usng usual tree unon algorthms. The case that requres specal attenton s when an k attrbute A x has dfferent parents n PS and T and thus algorthm AdustCorrelatonTree s nvoked. PSUDOCOD : CreateCorrelatonTree Sort query trees n ascendng order of ther query probabltes Choose query tree T = query tree wth lowest query probablty PS = T // ntal partal soluton = query tree wth lowest query probablty For ( each remanng query tree T from sorted lst of query trees ) do { If ( (attrbutes of T) (attrbutes n PS) = φ) then { // no attrbute of T s present n PS PS = PS +T // add query tree T to exstng partal soluton PS } lse { // some of the attrbutes n T are present n partal soluton PS A p = root of T If ( A p PS ) then // A p s not present n partal soluton PS { PS = {A p} + PS // add A p to PS as a sngle node tree } For ( each chld node A x n T ) do { If ( A x PS ) then { Add A x as chld of A p n PS Set w PS(A p,a x)= w T(A p,a x) } lse // f A x s present n PS { If ( A x has no parent n PS ) then { Set A x as chld of A p n PS Set w PS(A p,a x) = w T(A p,a x) } lse // A x has parent n PS { If ( parent of A x n PS s also A p ) then { w PS(A p,a x)= w PS(A p,a x)+w T(A p,a x). // ncrease correspondng edge weght } lse // A x has dfferent parent n PS { A q = parent of A x n PS Call PS = AdustCorrelatonTree(PS,T,A x,a p,a q) } } } } } } Return PS // PS s the fnal correlaton tree/forest B. Algorthm AdustCorrelatonTree Input: PS - Partal soluton, T - uery tree to be added, A x - Attrbute present n both PS and T, A p - Parent of A x n T, A q - Parent of A x n PS. Output: PS New partal soluton Ths algorthm makes the parent (A p or A q ) that has a hgher correlaton (.e. edge weght) wth A x as the parent of A x n the new partal soluton, whle the other parent s made a sblng of A x. We reason as follows. Algorthm AllocateGrd always stores an attrbute as close to ts parent as possble and thus A x s made chld of the parent wth whch t has hgher correlaton. Also snce algorthm AllocateGrd stores every chld attrbute near ts parent, sblng attrbutes also end up beng stored farly close to each other n the grd. Ths ustfes makng the other parent a sblng of A x n the new partal soluton. A trplet of values called the vrtual weght s assgned to both attrbutes to sgnfy that they have a correlaton even though they do not share a parent-chld relatonshp n the tree (nes 9,7). Note that the heap property of the correlaton tree should be preserved at all tmes.e. f attrbute A s the parent of A, then P( A ) P( A ) (nes 4,). If necessary, the algorthm Bubble (smlar to a usual heap-creaton algorthm) s nvoked to adust the tree so as to mantan the heap property (nes 7,5). Before deletng any edge, a cost-beneft analyss s performed to ensure that beneft > cost, where cost and beneft are defned as follows, Cost = Sum of effectve weghts of deleted edges ()

5 Beneft = Sum of effectve weghts of new edges (3) where effectve weght w T ( A, A ) of an edge ( A, A ) w ( A, A ) = w T (A,A ) + Σ{vrtual weghts of A } (4) T and value of a vrtual weght (v,a y,a z ) s, (v,a y,a z ) = v f A y and A z are sblngs = otherwse (5) PSUDOCOD : AdustCorrelatonTree ne. If ( w T(A p,a x) > w PS(A q,a x) ) then ne. { // A x has more correlaton wth A p than wth A q ne 3. Make A x chld of A p and set w PS(A p,a x)= w T(A p,a x) ne 4. If ( P(A p) P(A q) ) then ne 5. { Make A q chld of A p provded beneft>cost } ne 6. lse ne 7. { Call TempTree = Bubble(PS,A p,a q) ne 8. PS = TempTree provded beneft>cost } ne 9. Add vrtual weght (w PS(A q,a x), A q,a x) to A q and A x } ne. lse // A x has more correlaton wth A q than wth A p ne. { // A x remans chld of A q n the new partal soluton ne. If ( P(A q) P(A p) ) then ne 3. { Make A p chld of A q provded beneft>cost } ne 4. lse ne 5. { Call TempTree = Bubble(PS,A p,a q) ne 6. PS = TempTree provded beneft>cost } ne 7. Add vrtual weght (w PS(A p,a x), A p,a x) to A p and A x } C. Algorthm AllocateGrd Input: CT - Correlaton tree created by CreateCorrelatonTree st of attrbutes A wth access probabltes P(A ) Output: Allocaton of attrbute set A to grd G PSUDOCOD : AllocateGrd ne. Sort attrbutes n descendng order of access probabltes ne. Choose A x = attrbute wth hghest probablty ne 3. Assgn A x to central-most grd cell ne 4. For ( each remanng attrbute A x from sorted lst of attrbutes ) do ne 5. { If ( A x has no parent n CT ) then ne 6. { opt_lst = Call FndNearestCells(Center) ne 7. zone x = Call FndMnChldren(opt_lst) ne 8. Assgn A x to grd cell zone x } ne 9. lse // A x has parent n CT ne. { A p = parent of A x n CT ne. If ( w CT(A p,a x) = P(A x) ) ne. { zone p = Assgned grd cell of A p ne 3. opt_lst = Call FndNearestCells(zone p) ne 4. opt_lst=call FndFarthestCenter(opt_lst) ne 5. zone x = Call FndMnChldren(opt_lst) ne 6. Assgn A x to grd cell zone x } ne 7. lse ne 8. { // A x has correlatons wth other attrbutes also ne 9. attr_lst = Call FndCorrelatonAttrbutes(A x) ne. attr_corr_lst = Call FndCorrelatons(A x) ne. attr_cell_lst = Call FndStorageCells(attr_lst ) ne. ne 3. opt_lst = Call FndOptonCells(attr_cell_lst) zone x=call FndBestCell(opt_lst, attr_cell_lst, attr_corr_lst) ne 4. Assgn A x to grd cell zone x } ne 5.} } Ths s the second stage of the scheme. Ths algorthm allocates attrbutes to grd cells whle tryng to preserve the correlatons between attrbutes as represented by the correlaton tree. The algorthm begns wth the attrbute A x havng the maxmum access probablty and allocates A x to the s, central-most grd cell. It then teratvely assgns attrbutes n descendng order of ther access probabltes as shown n the pseudocode (nes 4-5). For each attrbute A x, the algorthm fnds out from the correlaton tree CT the attrbutes that A x has correlatons wth and then determnes ts optmal poston n the grd. If the A x has no parent n CT, t s placed as close to the center as possble (nes 5-8). However there may be multple avalable grd cells at the same dstance from the center. In that case, the optmal grd cell s the one for whch adacent already-allocated attrbutes have mnmum number of unassgned chldren (ne 7). The ustfcaton for choosng such a cell s that f a cell C s surrounded wth attrbutes that have more number of unassgned chldren attrbutes, then t would be preferable to leave C for those unassgned chldren attrbutes when other optons are avalable. Next the algorthm handles the case where the correlaton that A x has wth ts parent A p s the same as ts access probablty P(A x ) (ne - 6). Ths mples that any query that accesses A x also accesses A p and thus A x should be stored close to A p. Fnally the algorthm consders the case where A x has correlatons wth multple attrbutes (nes 7-4). The algorthm FndBestCell returns the optmal cell for assgnng A x by scannng the lst opt_lst for the cell whch mnmzes the value Σ{dstance(opt_lst[],attr_cell_lst[])*attr_corr_lst[]) }. The complexty of the algorthms CreateCorrelatonTree and AllocateGrd s O(mlogm), snce CreateCorrelatonTree s smlar to creatng a heap of m attrbutes whle AllocateGrd s smlar to traversng the heap. V. ANAYSIS The energy consumpton n scheme s compared wth that of TAG [5], where an aggregaton tree spannng all the sensor nodes s formed n a dstrbuted manner. For both the schemes, we assume that only those readngs greater than the hard threshold are reported to the snk. Further for the scheme we assume that the update messages are sent only when the soft threshold ϕ s crossed. We assume that the snk s at the centre of the network as shown n Fg. 3. We also assume that the communcaton between nodes of a grd cell and ther respectve control nodes, the snk and the control nodes, as well as nodes n dfferent levels of the aggregaton tree all pack avalable data n the fewest possble packets. The parameters used n the analyss are lsted n Table II. TAB II. PARAMTRS USD IN ANAYSIS N total Total number of nodes n the network A() Area of sub-regon at depth R Transmsson radus ength of a sde of the deployed regon Hard Threshold ϕ Soft Threshold Rato of nformaton generated by a sngle ξ node to sze of data packet P Transmsson cost of a sngle packet d ength of a sde of the sub-regon N Nodes reportng a readng > N Nodes reportng a readng > D(sk,stg) Dstance between snk and storage regon Frequency of attrbute value crossng Frequency of attrbute value crossng ϕ uery Frequency f

6 (a) (b) Fgure 3. Aggregaton Tree and A. nergy cost of Aggregaton Tree (AT) The queres are propagated downwards tll every leaf node n the AT s reached. The AT s rooted at the snk and spreads outwards from the center of the regon. For best case performance, we assume that the AT spans the regon unformly. We dvde the entre area nto n concentrc square regons, each of wdth r as shown n Fg. 3(a). The nodes present n the th concentrc regon are assumed to be at a depth n the AT. Thus n s the depth of the tree where nr =. Area of regon s A( ) = 4( ) r, =,, 3,, n. Thus, the probablty that a node les n regon s gven by A ( ) ( ) p =. Smlarly, out of N nodes, the number of such nodes n the th regon s gven by Np ( ). Thus the energy cost ncurred at each level s ( ) = I ( ) ξ P and the total energy s gven by: Data( AT ) = ( ) n =. We now calculate I(), the total number of packets transmtted at level of the aggregaton tree. Ths ncludes the total number of packets generated at level as well as the packets arrvng at level from level +. We thus obtan a recursve relaton as: r 4 r I ( n) = N (n ), I ( n ) = 4N(n 3) + I( n),, r I ( ) = 4N + I( ) Thus the total ncurred communcaton cost: n = Data( AT ) I ( n) ξ P = Through algebrac calculatons, I r ( ) = 4N ( n), I ( ) = 4N [( n) ],, r I ( ) = 4N [( n) ( ) ], n = r ( n) ξ P = r 3 n( n )( n 4N P n ) I ξ (6) 6 Snce each node forwards the query exactly once, the ntal cost of propagatng the query down the tree s gven by: = N r uery AT total P (7) ( ) For query-drven systems, nformaton s sent to the snk only n the event of a query. Hence, total cost of query dssemnaton and aggregaton s, Total ( AT) f ( ) = + (8) P uery( AT ) Data( AT ) The total cost ncurred n event-drven systems s dependent on the number of reports generated by the system wth =. In ths case, the cost s, uery( AT ) Total ( AT ) Data( AT ) =! R B. nergy cost of Scheme et us assume that the storage regon X n Fg. 3(b) stores the values for the desred query attrbute. The squares marked represent the frst ter of surroundng sub-regons, those marked ndcate the second ter and so on. We approxmate the dstance from any node of the th ter to the center of X as d and ths dstance s traversed n d/r hops. Thus the probablty of a node lyng n regons marked, s, 8d 6d p ( ) =, p ( ) = up to / d ters. Hence, 8d p ( ) = where =,,, / d N ' number of nodes report update messages to control nodes of ther own grd cell. In the worst case scenaro, the reportng nodes are furthest away from the control node at a dstance of d/r hops. Thus energy spent n ths update s, d Update = N' P r Number of nodes reportng update of attrbute values n ter s N ' p( ). nergy cost assocated wth all control nodes n ter reportng aggregated update message to regon X s, N d d r 8 ' ( ) ξp (9) = Thus n one reportng event, total energy spent by all control nodes n reportng data to the storage regon hostng that attrbute s gven by, Data( DS ) = / d = / d = = 8N' d r / d ( ) = ξp 3 = 3 N' d ξ () 3r ( ) = P [( / d)( /d + )( / d + ) ] The storage regon receves queres from the snk wth a frequency f and ncurs a query cost of D(sk, stg) uery ( DS ) = P. r The consequent reply from the storage regon to the snk ncurs a cost of D(sk,stg) Reply ( DS ) = NξP r The total energy expended n our scheme s gven by, Total ( DS ) = f ( + ) + + ) µ!!!!!!!!!!()! uery( DS ) Reply ( ( DS ) Data( DS ) Update

7 Thus the scheme should be preferred only when Total ( DS ) < ( AT ).e. Total f ( uery DS ) + Reply )< ( ( DS ) + Data + ) µ ( ( DS ) Update ( ) f + uery ( AT ) Data ( AT ) (vent-drven) () To valdate our models of the aggregaton tree and our proposed scheme, we smulated a testbed of nodes dstrbuted randomly n an area of 6 6 square unts. A node at (x,y) was gven an ntal attrbute value calculated by the functon Z = ( + sn( R) / R), where R = x + y +. 5.We allowed 5 possble fluctuatons n the sensed attrbute, but the decson to undergo a change was taken locally at each node wth probablty.3. The magntude of change was ±.8 and a functon of a unformly dstrbuted random varable. At the end of the smulaton we obtaned an average of 34 nodes crossng =.7 at each fluctuaton and those that were over = averaged at 38. The other constant smulaton parameters are as descrbed n Secton VI. The calculated and observed values are summarzed n Table III and are n good agreement thus valdatng our model. As predcted by quaton (), has lower energy cost under these condtons and s the preferred choce. VI. SIMUATION RSUTS Usng Smava, a dscrete event smulator, we have conducted smulatons to compare our scheme wth the aggregaton tree (AT) algorthm of TAG [5]. A. Smulaton nvronment In our study, we dspersed nodes randomly n a square area of 6 6 unts, each wth a transmsson range of 4 unts to form a connected network. ach packet of bytes s transmtted over a kbps channel, ncurrng a cost of.8mw and.3mw for transmsson and recepton respectvely. To nvestgate the performance of the scheme, we splt the area nto 49 subregons, each of sde 9 unts. We measured the energy consumed by all the nodes for dfferent topologes. We have measured ths by varyng both the rate at whch queres are nected nto the network by the snk and the rate at whch the sensed attrbute shows a varaton n ts magntude. The control nodes n ndvdual subregons, as well as and the nodes n the aggregaton tree try and pack all avalable data n the fewest possble packets thus mantanng an economy of transmsson. For both schemes, the snk s assumed to be at the center of the network. To evaluate the best case of our scheme, we assume that the attrbute quered s stored n the central grd cell (near snk). To measure the worst case performance, we consder the stuaton when the snk (whch s at the centre of the regon) queres an attrbute that s stored n a grd cell further away from the centre of the network. TAB III. (uery-drven) Data(AT)µ!! NRGY COST IN mj Aggregaton Tree Smulaton Calculated Smulaton Calculated B. ffect of uery Rate on Performance We frst keep the rate of fluctuatons constant and vary the query rate. From Fg. 4(a), we observe that the scheme shows margnal performance degradaton at lower query rates. As the snk nects progressvely greater number of queres per unt tme, the scheme performs ncreasngly better than the AT algorthm. We reason as follows. The cost of floodng the query down to the leaf level of the AT and then retrevng the nformaton essentally requres O(n) transmssons. In our proposed scheme (and more so for our consdered topology), ths s accomplshed n a sngle transmsson between the control node n the storage regon and the snk, as s evdent from the mnmal - uery energy cost. There s however, a constant overhead of updatng the storage regon for the nodes whch show a varaton n the sensed attrbute. Ths s reflected n the almost constant -Update energy cost. Fg. 4(b) shows results for the scenaro where the attrbute stored at a subregon far from the snk s accessed by a perodc query. Here the breakeven pont s reached when the query rate s (unlke 8 n the best case) after whch performs much better than AT. C. ffect of Fluctuaton Rate on Performance In ths experment (Fgs. 4(c) and 4(d)), we vary the rate of fluctuatons whle keepng a steady query rate of queres/smulaton tme. We observe that wth an ncrease n the number of fluctuatons, the scheme s no longer preferable to the AT scheme after the break-even pont. The AT performs at a steady energy cost as nodes, whle sensng the changed attrbute values, see no need of reportng t unless a query message s receved. The mnor ncrease n energy cost of AT happens because, wth ncreasng rate of fluctuatons, the number of attrbute values more than the hard threshold ncrease and hence more number of nodes report data to the snk. On the other hand, the rapd fluctuaton and ts assocated cost n mantanng updated nformaton n the storage regon strans the scheme whch explans the steady ncrease n -Update cost and hence total cost. ven then, n the best case scenaro (Fg. 4(c)), the scheme performs better than AT tll the fluctuaton rate reaches a consderable value of 6 fluctuatons /smulaton tme. VII. RATD WORK There have been dfferent approaches for storng data n sensor networks. arler sensor network systems stored sensor data externally at a remote base staton (xternal Storage) or locally at the nodes whch generated them (ocal Storage). Shenker et al. [8] proposed the Data-Centrc Storage scheme and have shown that DCS outperforms other approaches such as xternal Storage and ocal Storage under certan crcumstances. Ratnasamy et al. [7] have also proposed a Geographc Hash Table (GHT) to hash events nto geographc coordnates. In DIFS [], Greensten et al. have desgned a spatally dstrbuted ndex to facltate range searches over attrbutes, whle et al. [6] have bult a dstrbuted ndex (DIM) for multdmensonal range queres of attrbutes.

8 6 5 AT uery Update 6 5 AT uery Update nergy cost (mj) 4 nergy cost (mj) ueres / Smulaton tme Fgure 4(a). ffect of uery rate (Best Case) ueres / Smulaton tme Fgure 4(b). ffect of uery Rate (Attrbute far from snk) 4 35 AT uery Update 6 5 AT uery Update nergy cost (mj) nergy cost (mj) Fluctuatons / Smulaton tme Fgure 4(c). ffect of Fluctuaton rate (Best Case) In ths paper, we have proposed a data-centrc storage scheme that dffers from the exstng data-centrc approaches [][6][7] n that t dstrbutes attrbutes nstead of specfc user-defned events. We reason as follows. If an attrbute s ncluded n many events, then values for that attrbute have to be replcated and stored at dfferent places n the network for each ndvdual event. In our proposed approach, the attrbute need not be replcated at multple places and hence saves communcaton cost nvolved n storng and replcatng data. Instead every attrbute s stored at a predefned locaton wthn the network such that attrbutes that are a part of the same query are stored near each other to facltate data retreval. VIII. CONCUSIONS The proposed scheme s a data-centrc storage scheme for allocatng attrbutes to a large-scale sensor network dependng on the correlatons between them. We have proposed a communcaton archtecture that mnmzes the cost of mantanng and retrevng data from such a system and have determned analytcally the condtons under whch the archtecture should be preferred. We have conducted smulatons that compare performance wth other aggregaton schemes. As a part of future work, we plan to develop detaled protocols for query dssemnaton, data update and data retreval. We also need to ensure that these protocols are fault-tolerant and perform load balancng. RFRNCS [] B. Greensten, D. strn, R. Govndan, S. Ratnasamy, and S. Shenker, DIFS: a dstrbuted ndex for features n sensor networks, Frst I Fluctuatons / Smulaton tme Fgure 4(d). ffect of Fluctuaton Rate (Attrbute far from snk) Internatonal Workshop on Sensor Network Protocols and Applcatons, pp , May 3. [] B. Karp and H.T. Kung, GPSR: Greedy Permeter Stateless Routng for Wreless Networks, Sxth Annual ACM/I Internatonal Conference on Moble Computng and Networkng (Mobcom ), Boston, Massachusetts, August. [3]. Doherty, K. S. J. Pster and.. Ghaou, Convex Poston stmaton n Wreless Sensor Networks, I Infocom, pp , Alaska, Aprl. [4] C. Intanagonwwat, R. Govndan, and D. strn, Drected Dffuson: A Scalable and Robust Communcaton Paradgm for Sensor Networks, Sxth Annual ACM/I Internatonal Conference on Moble Computng and Networkng (Mobcom ), Boston, Massachusetts, August. [5] S. Madden, M. J. Frankln, J. M. Hellersten and W. Hong, TAG: a Tny AGregaton Servce for Ad-Hoc Sensor Networks, 5th Annual Symposum on Operatng Systems Desgn and Implementaton (OSDI), Boston, MA, December. [6] X., Y. J. Km, R. Govndan and W. Hong, Mult-dmensonal range queres n sensor networks, st nternatonal conference on mbedded networked sensor systems, Nov. 3. [7] S. Ratnasamy, B. Karp,. Yn, F. Yu, D. strn, R. Govndan, and S. Shenker, GHT: A Geographc Hash Table for Data-Centrc Storage, Frst ACM Internatonal Workshop on Wreless Sensor Networks and Applcatons (WSNA ), Atlanta, GA, September,. [8] S. Shenker, S. Ratnasamy, B. Karp, R. Govndan and D. strn, Datacentrc storage n sensornets, ACM SIGCOMM Computer Communcaton Revew, Volume 33 Issue, January 3. [9] Ram Kumar, Vlasos Tsatss, Man B. Srvastava, Computaton Herarchy for In-network Processng, nd ACM Internatonal Conference on Wreless Sensor Networks and Applcatons, San Dego, CA, September 3.