A Scalable Location Service for Geographic Ad Hoc Routing

Transcription

1 A Scalable Lcatn Servce fr Gegraphc Ad Hc Rutng Jnyang L Jhn Janntt Duglas S. J. De Cut Davd R. Karger M..T. Labratry fr Cmputer Scence {jnyang, j j, decut, karger, cs.mt.edu Rbert Mrrs Abstract GLS s a new dstrbuted lcatn servce whch tracks mble nde lcatns. GLS cmbned wth gegraphc frwardng allws the cnstructn f ad hc mble netwrks that scale t a larger number f ndes than pssble wth prevus wrk. GLS s decentralzed and runs n the mble ndes themselves, requrng n fxed nfrastructure. Each mble nde perdcally updates a small set f ther ndes (ts lcatn servers) wth ts current lcatn. A nde sends ts pstn updates t ts lcatn servers wthut knwng ther actual denttes, asssted by a predefned rderng f nde dentfers and a predefned gegraphc herarchy. Queres fr a mble nde's lcatn als use the predefned dentfer rderng and spatal herarchy t fnd a lcatn server fr that nde. Experments usng the ns smulatr fr up t 6 mble ndes shw that the strage and bandwdth requrements f GLS grw slwly wth the sze f the netwrk. Furthermre, GLS tlerates nde falures well: each falure has nly a lmted effect and query perfrmance degrades gracefully as ndes fal and restart. The query perfrmance f GLS s als relatvely nsenstve t nde speeds, Smple gegraphc frwardng cmbned wth GLS cmpares favrably wth Dynamc Surce Rutng (DSR): n larger netwrks (ver 2 ndes) ur apprach delvers mre packets, but cnsumes fewer netwrk resurces. 1. ntrductn Ths paper cnsders the prblem f rutng n large ad hc netwrks f mble hsts. Such netwrks are f nterest because they d nt requre any prr nvestment n fxed nfrastructure. nstead, the netwrk ndes agree t relay each ther's packets tward ther ultmate destnatns, and the ndes autmatcally frm ther wn cperatve nfrastructure. We descrbe a system, Grd, that cmbnes a cperatve nfrastructure wth lcatn nfrmatn t mplement rutng n a large ad hc netwrk. We analyze Grd's lca- Jnyang L and Jhn Janntt are supprted by DARPA cntract N Davd Karger s supprted by NSF cntract CCR , an Alfred P. Slane Fundatn Fellwshp, and a Davd and Luclle Packard Fundatns Fellwshp. Permssn t make dgtal r hard cpes f all r part f ths wrk fr persnal r classrm use s granted wthut fee prvded that cpes are nt made r dstrbuted fr prft r cmmercal advantage and that cpes bear ths ntce and the lull ctatn n the frst page. T cpy therwse, t republsh, t pst n servers r t redstrbute t lsts, requres prr specfc permssn and/r a fee. MOBCOM 2 Bstn MA USA Cpyrght ACM //8...$5. tn servce (GLS), shw that t s crrect and effcent, and present smulatn results supprtng ur analyss. t s pssble t cnstruct large netwrks f fxed ndes tday. Prmnent examples nclude the telephne system and the nternet. The cellular telephne netwrk shws hw these wred netwrks can be extended t nclude large numbers f mble ndes. Hwever, these netwrks requre a large up-frnt nvestment n fxed nfrastructure befre they are useful---central ffces, trunks, and lcal lps n the case f the telephne system, rad twers fr the cellular netwrk. Furthermre, upgradng these netwrks t meet ncreasng bandwdth requrements has prven expensve and slw. The fact that large fxed cmmuncatn nfrastructures already exst mght seem t lmt the usefulness f any cmpetng apprach. There are, hwever, a number f stuatns n whch ad hc netwrks are desrable. Users may be s sparse r dense that the apprprate level f fxed nfrastructure s nt an ecnmcal nvestment. Smetmes fxed nfrastructure exsts but cannt be reled upn, such as durng dsaster recvery. Fnally, exstng servces may nt prvde adequate servce, r may be t expensve. Thugh ad hc netwrks are attractve, they are mre dffcult t mplement than fxed netwrks. Fxed netwrks take advantage f ther statc nature n tw ways. Frst, they practvely dstrbute netwrk tplgy nfrmatn amng the ndes, and each nde pre-cmputes rutes thrugh that tplgy usng relatvely nexpensve algrthms. Secnd, fxed netwrks embed rutng hnts n nde addresses because the cmplete tplgy f a large netwrk s t unweldy t prcess r dstrbute glbally. Nether f these technques wrks well fr netwrks wth mble ndes because mvement nvaldates tplgy nfrmatn and permanent nde addresses cannt nclude dynamc lcatn nfrmatn. Hwever, there s a tplgcal assumptn that wrks well fr rad-based ad hc netwrks: ndes that are physcally clse are lkely t be clse n the netwrk tplgy; that s, they wll be cnnected by a small number f rad hps. Grd uses gegraphcal frwardng t take advantage f the smlarty between physcal and netwrk prxmty. A surce must knw the gegraphcal pstns f any destnatn t whch t wshes t send, and must label packets fr that destnatn wth ts pstn. An ntermedate nde nly needs t knw ts wn pstn and the pstns f nearby ndes; that s enugh nfrmatn t relay each packet thrugh the neghbr that s gegraphcally clsest t the ultmate destnatn. Althugh Grd frwards packets based purely upn lcal gegraphc nfrmatn, t s hghly lkely that packets are als apprachng ther destnatn as measured by the number 12

2 f remanng hps t the destnatn. Because ndes nly need lcal nfrmatn, regardless f the ttal netwrk sze, gegraphc frwardng s attractve fr large-scale netwrks. Hwever, t be useful n a larger cntext, a system based n gegraphc frwardng must als prvde a mechansm fr surces t learn the pstns f destnatns. T preserve scalablty, ths lcatn servce must allw queres and updates t be perfrmed usng nly a handful f messages. Of curse, the lcatn servce tself must perate usng nly gegraphc frwardng. t shuld als be scalable n the fllwng senses: 1. N nde shuld be a bttleneck--the wrk f mantanng the lcatn servce shuld be spread evenly ver the ndes. 2. The falure f a nde shuld nt affect the reachablty f many ther ndes. 3. Queres fr the lcatns f nearby hsts shuld be satsfed wth crrespndngly lcal cmmuncatn. Ths wuld als allw peratn n the face f netwrk parttns. 4. The per-nde strage and cmmnncatn cst f the lcatn servce shuld grw as a small functn f the ttal number f ndes. The Grd lcatn servce (GLS) presented n ths paper satsfes all f these requrements. The rest f the paper descrbes the desgn and smulated perfrmance f Grd. Sectn 2 revews exstng wrk n scalable ad hc netwrkng. Sectn 3 descrbes the characterstcs f gegraphc frwardng. Sectn 4 descrbes Grd's dstrbuted lcatn servce algrthm. Sectn 5 descrbes ur mplementatn f gegraphc frwardng and the GLS n detal. Sectn 6 analyzes Grd's rutng perfrmance and scalablty usng smulatns. Sectn 7 suggests areas fr future mprvements. Sectn 8 summarzes the paper's cntrbutns. 2. Related Wrk Mst exstng ad he rutng systems dstrbute ether tplgy nfrmatn r queres t all ndes n the netwrk. Sme, such as DSDV [16], are practve; they cntnuusly mantan rute entres fr all destnatns. Other technques are reactve, and cnstruct rutes t destnatns as they are requred. Ths ncludes systems such as DSR [1], AODV [15], and TORA[14]. Bfch et al. [4] and Jhanssn et al. [9] each prvde vervews f these ad hc rutng technques, alng wth cmparatve measurements usng small (3-5 nde) smulatns. Grd's man cntrbutn cmpared t these wrks s ncreased scalablty. Mre clsely related t Grd are prtcls that use gegraphc pstns. Fnn's Cartesan rutng [7] addresses each nde wth a gegraphc lcatn as well as a unque dentfer. Packets are ruted by sendng them t the neghbr clsest t the packet's ultmate destnatn. Dead ends are handled by scped fldng. Hwever, Fnn gves n detaled explanatn f hw nde lcatns are fund r hw mblty s handled. Mre recent wrk n gegraphc appraches t rutng ncludes the DREAM [2] and LAR [13] systems. Bth systems rute packets gegraphcally, n a manner smlar t Fnn's Cartesan system. They dffer n hw a nde acqures the gegraphc pstn f a destnatn. DREAM ndes practvely fld pstn updates ver the whle netwrk, allwng ther ndes t buld cmplete pstn databases. LAR ndes reactvely fld pstn queres ver the entre netwrk when they wsh t fnd the pstn f a destnatn. Because they bth nvlve glbal fldng, nether system seems suted t large netwrks. The Landmark system [17, 18] actvely mantans a herarchy t prvde rutng n a changng netwrk. Ndes n a Landmark netwrk have unque permanent Ds that are nt drectly useful fr rutng. Each nde als has a changeable Landmark address, whch cnssts f a lst f Ds f ndes alng the path frm a well-knwn rt t the nde's current lcatn. A Landmark address can be used drectly fr rutng, snce t s smlar t a surce rute. The Landmark system prvdes a lcatn servce that maps Ds t current addresses. Each nde X sends updates cntanng ts current Landmark address t a nde that acts as ts address server, chsen by hashng X's D t prduce a Landmark address A. f a nde Y exsts wth that address, Y acts as X's lcatn server. Otherwse the nde wth Landmark address clsest t A s used. Anyne lkng fr X can use the same algrthm t fnd X's lcatn server, whch can be quered t fnd X's current Landmark address. Ths cmbnatn f lcatn servers and addresses that encde rutng nfrmatn s smlar t the archtecture descrbed n ths paper. Grd, hwever, avds buldng herarches, as they are vulnerable t the mvement f ndes near the tp f the herarchy. 3. Gegraphc Frwardng We use a smple scheme fr gegraphc frwardng that s smlar t Cartesan rutng [7]. Each nde determnes ts wn gegraphc pstn usng a mechansm such as GPS [1]; pstns cnsst f lattude and lngtude. A nde annunces ts presence, pstn, and velcty t ts neghbrs (ther ndes wthn rad range) by bradcastng perdc HELLO packets. Each nde mantans a table f ts current neghbrs' denttes and gegraphc pstns. The header f a packet destned fr a partcular nde cntans the destnatnn's dentty as well as ts gegraphc pstn. When nde needs t frward a packet tward lcatn P, the nde cnsults ts neghbr table and chses the neghbr clsest t P. t then frwards the packet t that neghbr, whch tself apples the same frwardng algrthm. The packet stps when t reaches the destnatn. A packet may als reach a nde that des nt knw abut any ndes clser than tself t the ultmate destnatn. Ths dead-end ndcates that there s a "hle" n the gegraphc dstrbutn f ndes. n that case, the mplementatn descrbed n ths paper gves up and sends an errr message t the packet's surce nde. Recverng frm dead-ends s pssble usng the same neghbr pstn table used n gegraphc frwardng. Karp and Kung prpse GPSR [12], a gegraphc rutng system that uses a planar subgraph f the wreless netwrk's graph t rute arund hles. They smulate GPSR n mble netwrks wth 5-2 ndes, and shw that t delvers mre packets successfully wth lwer rutng prtcl verhead than DSR n netwrks wth mre than 5 ndes. Bse et al. ndependently demnstrate a lp-free methd fr rutng packets arund hles usng nly nfrmatn lcal t each nde. The methd wrks nly fr unt graphs, n whch tw ndes can cmmuncate drectly n exactly the cases n whch they are wthn sme fxed dstance f each ther. 121

3 D t a large number f mble ndes; t can nt allw multple netwrk parttns t each functn nrmally n ther wn parttn; and ndes near t each ther gan n advantages--they must cntact a ptentally dstant lcatn server n rder t cmmuncate lcally. t~ X Number f ndes Fgure 1: Fractn f data packets unable t be delvered usng gegraphc frwardng wth a perfect lcatn servce, as a functn f nde densty. The smulatn area s 1 km Effect f Densty Gegraphc frwardng wrks best when ndes are dense enugh that dead ends are nt cmmn. We present a smple evaluatn f the effects f nde densty usng the ns [6] netwrk smulatr. The smulated ndes have 2 Megabt per secnd EEE rads [5] wth ranges f abut 25 meters; each nde transmts HELLO messages at 2 secnd ntervals, and rutng table entres expre after 4 secnds. Ndes mve cntnuusly at 1 m/s; each nde mves by selectng a randm destnatn, mvng tward t, and selectng a new destnatn when t reaches the ld ne. Each nde sends packets t three destnatn ndes selected at randm; each cnversatn starts at a tme selected randmly ver the 3 secnd lfe f the smulatn. A cnversatn nvlves sendng 6 packets f 128 bytes each at quarter secnd ntervals. Senders knw the crrect gegraphc pstns f destnatns. Fgure 1 s the result f smulatns ver a range f nde denstes. n each smulatn, the ndes are placed at randm n a 1 km 2 square. The graph reprts the fractn f packets that were nt delvered fr each nde densty. n ths scenar, gegraphc frwardng wrks well fr mre than 5 ndes per square klmeter. f 5 ndes are evenly placed n a 1 km 2 square, the nter-nde spacng s 141 = 1/x/5 meters, whch s wthn rad range. Mre generally, the smulatn results agree wth a mathematcal analyss f randm ndes dstrbuted thrughut the unt square: ne can prve that f the cmmuncatn radus s r and the number f pnts exceeds (6/r 2) ln(6/r 2 ) per km 2, then dead ends are extremely unlkely t ccur. 4. The Grd Lcatn Servce Cmbnng gegraphc frwardng wth a mechansm fr determnng the lcatn f a nde mplements the tradtnal netwrk layer: any nde can send packets t any ther nde. A trval lcatn servce mght cnsst f a statcally pstned lcatn server. Ndes wuld perdcally update ths server (usng gegraphc frwardng t the server's well-knwn crdnates) wth ther current lcatn. Fr a nde A t cntact nde B, A queres the lcatn server fr B's current lcatn befre usng gegraphc frwardng t cntact B. Usng a sngle lcatn server has a number f prblems. The centralzed server s a sngle pnt f falure; t s unlkely t scale 35 We ntrduce a dstrbuted lcatn servce (GLS) that s desgned t address these prblems. GLS s fault-tlerant; there s n dependence n specally desgnated ndes. GLS scales t large numbers f ndes; ur gal s t prvde a servce that scales t at least the sze f a large metrpltan area. Fnally, GLS perates effectvely even fr slated pckets f ndes. A nde shuld be able t determne the lcatn f any nde that t can reach wth gegraphc frwardng. That s, a lcatn lkup shuld nt nvlve ndes that are t far "ut f the way" f a straght lne trp frm the nde perfrmng the lkup t the nde beng lked up. GLS s based n the dea that a nde mantans ts current lcatn n a number f lcatn servers dstrbuted thrughut the netwrk. These lcatn servers are nt specally desgnated; each nde acts as a lcatn server n behalf f sme ther ndes. The lcatn servers fr a nde are relatvely dense near the nde but sparse farther frm nde; ths ensures that anyne near a destnatn can use a nearby lcatn server t fnd the destnatn, whle als lmtng the number f lcatn servers fr each nde. On the ther hand lng dstance queres are nt dsprprtnally penalzed: query path lengths are prprtnal t data path lengths. n rder t spread unfrmly the wrk f actng as lcatn servers, GLS avds technques such as leader electn r herarchy t determne lcatn server respnsblty. These schemes place undue stress n the ndes unlucky enugh t be elected as a leader r placed at hgher levels n the herarchy. nstead GLS allws a nde X t select a set f lcatn servers that, prbablstcally, s unlke the set f servers selected by ther ndes and des nt change drastcally as ndes enter r leave the netwrk. Ndes searchng fr X are able t fnd X's lcatn servers usng n prr knwledge beynd nde X's D. Ths s accmplshed by carryng ut much the same prtcl that X used t select ts servers n the frst place. Our apprach draws ts ntutn frm Cnsstent Hashng, a technque develped t supprt herarchcal cachng f web pages [11]. T avd makng a sngle nde nt the bttleneck f the herarchcal cache, that paper used a hash functn t buld a dstnct herarchy fr each page, much as we use a dstnct lcatn servce herarchy fr each target. Als lke ur paper, that paper used nested query rad t ensure that queres fr a gven page dd nt g t caches much farther away than the page tself. GLS balances the lcatn server wrk evenly acrss all the ndes f there s a randm dstrbutn f nde Ds acrss the netwrk. GLS ensures that ndes are allcated unque, randm Ds by usng a strng hash functn t btan an D frm a nde's unque name. The name culd be any unquely allcated name, such as nternet hst names, P addresses, r MAC addresses. Fr purpses f dscussng the GLS, a nde's D s mre nterestng than ts rgnal name, therefre when we refer t a nde A, we are referrng t the nde whse name hashes t A. 4.1 Selectng and Queryng Lcatn Servers GLS prvdes fr dstrbuted lcatn lkups by replcatng the knwledge f a nde's current lcatn at a small subset f the net- 122

4 9 3s 391 7~ ~ 45!, t~ 5 t ~ 35 f,,, ,~ ' ~(~ 7-~B: l J Fgure 2: A pece f the glbal parttnng f the wrld. A few example squares f varus rders are shwn wth dark shadng. The lghtly shaded square s shwn as an example f a 2x2 square whch s nt an rder-2 square because f ts lcatn. An rder-n square's lwer left crner's crdnates must be f the frm (a2 n-x, b2 n-l) fr ntegers a,b. wrk's ndes. Ths set f ndes s referred t as the nde's lcatn servers. A nde A hpng t cntact nde B can query ne f a number f ther ndes that knw B's lcatn. Of curse, A must be able t cntact the ndes that knw B's lcatn. Ths means that A's search fr B's lcatn servers and B's rgnal recrutment f lcatn servers ught t lead t the same servers. When B recruts lcatn servers t uses the same nfrmatn that A wll have when searchng fr B's lcatn servers: B's name and certan nfrmatn that all ndes have at startup. At startup, all ndes knw the same glbal parttnng f the wrld nt a herarchy f grds wth squares f ncreasng sze, as shwn n Fgure 2. The smallest square s referred t as an rder-1 square. Fur rder-1 squares make up an rder-2 square, and s n. t s mprtant that nt every square made up f fur rder-n squares s als an rder-(n + 1) square. Rather, t avd verlap, a partcular rder-n square s part f nly ne rder-(n + 1) square, nt fur. Ths mantans an mprtant nvarant: a nde s lcated n exactly ne square f each sze. Ths system f ncreasng square szes prvdes a cntext n whch a nde selects fewer and fewer lcatn servers at greater dstances. Our chce f a grd-based parttn s smewhat arbtrary; any ther balanced herarchcal parttn f the space can be used nstead. Cnsder hw B determnes whch ndes t update wth ts changng lcatn, usng ts D and the predetermned grd herarchy. B knws that ther ndes wll want t lcate t, but that they wll have lttle knwledge beynd B's D. B's strategy s t recrut ndes wth Ds "clse" t ts wn D t serve as ts lcatn servers. We defne the nde clsest t B n D space t be the nde wth the least D greater than B. The D space s cnsdered t be crcular, 2 s clser t 17 than 7s t 17. Fgure 3: The nset squares are regns n whch B wll seek a lcatn server. The ndes that becme B's lcatn servers are crcled and shwn n bld. f we cnsder the tree crrespndng t the grd decmpstn, a nde selects lcatn servers n each sblng f a square that cntans the nde. The exact detals f the selectn are best understd wth an example (see Fgure 3). A nde chses three lcatn servers fr each level f the grd herarchy. Fr example, n the fgure, B recruts three servers n rder-1 squares, three servers n rder-2 squares, and three servers n rder-3 squares. n each f the three rder-1 squares that, alng wth B's wn rder-1 square, make up an rder-2 square, B chses the nde clsest t tself n D space as a server. The same lcatn server selectn prcess ccurs n hgher rder squares. n the three rder-2 squares that cmbne wth B's rder-2 square t make an rder-3 square, B selects 26, 31, and 43 as lcatn servers. Fgure 4 shws the state f a Grd netwrk nce all ndes have prvded ther crdnates t the ndes that wll act as ther lcatn servers. Wth the cmplete netwrk state as reference, we can return t the prblem f hw A fnds the lcatn f B. T perfrm a lcatn query, A sends a request (usng gegraphc frwardng) t the least nde greater than r equal t B fr whch A has lcatn nfrmatn. That nde frwards the query n the same way, and s n. Eventually, the query wll reach a lcatn server f B whch wll fward the query t B tself. Snce the query cntans A's lcatn, B can respnd drectly usng gegraphc frwardng. The lcatn query s frwarded all the way t B s that B can respnd wth ts latest lcatn. Fr llustratve purpses we have gnred an mprtant btstrappng ssue. We have assumed that ndes select ther lcatn servers apprprately and send ther crdnates t them. Ths appears t assume that a nde can scan an entre square (f arbtrary sze) and chse the apprprate nde t act as ts server. n fact, ndes rute update packets t ther lcatn servers wthut knwng ther denttes. Assume that a nde B wshes t recrut a lcatn server n sme rder-n square. B sends a packet, usng gegraphc frward- 123

5 ~ ! ] ',5,6,','2 [ s2,84,s7,4,3?,62.7 :9 + ' 3:~ ,~,ff/ n.~.~, sls ,62'?,9 l,5,,6,37,39 1,2,16,37,62[ [35,39,45,5 41,43,45,5 7,9,91 [ $ 1"35,6, ,.98, ! 35,4., ,,? ,,7.~ , "23'2~" ',32'3,5537,39 161, ! H.23.3 L32! 2'12'26.8"/ [,.,7.23, Z 1~.16 ~ g43,35'61'631,82+84,[98 87,98 [ 23,63~,.~ +t 23'2~'41'72?6, ! 61+ +,++ hl 19.35"37A5 5,5, [ ~,,55~1 16z 'm 11 t.2,5.6.t.t 21 ] 26.2s.3t,32 t4.16a?.82 51,2 u.st.~.91 1 n ,55.61,62! ,76, [ B : T [ ~ ! ,.32~].87 12,43., "43, , ~.2~"-!991 5',6' ,9' ~!6,1 12, , ;+'3++2,12.,++.. m,~l?.~ ,43 [... +'~.4... ;N..- 51,63.'/,72 [ , ,6,,63.8' 72 l 72"76,8LS ,39,41, ! 31 6, 43!,,, 12 + A:76 84! Fgure 4: An entre netwrk's lcatn server rganzatn. Each nde s shwn wth the lst f ndes fr whch t has up t date lcatn nfrmatn; B's lcatn servers are shwn n bld. Tw pssble queres by A fr B's lcatn are shwn. ng, t that square. The frst nde L n the square that receves the packet begns a lcatn update prcess that clsely resembles a query fr B's lcatn; but ths update wll actually carry the current lcatn f B alng wth t. As we wll demnstrate belw, the update wll arrve at the least nde greater than B befre leavng the rder-n square cntanng L. Ths s exactly the apprprate destnatn fr the lcatn update t g t; the fnal destnatn nde smply recrds B's current lcatn and becmes a lcatn server fr B. The nly requrement fr B t dstrbute ts lcatn t the apprprate server n an rder-n square s that the ndes cntaned n the square have already dstrbuted ther lcatns thrughut that square. f we magne an entre Grd system beng turned n at the same tme, rder-1 squares wuld exchange nfrmatn usng the lcal rutng prtcl, then ndes culd recrut ther rder-2 lcatn servers, then rder-3, etc. Once the rder-n lcatn servers are peratng, there s suffcent rutng capablty t set up the rder- (n + 1) lcatn servers. 4.2 Effcency Analyss When ndes are nt mvng, the number f steps taken by a lcatn query frm A t B s n mre than the rder f the smallest square n whch A and B are clcated. A lcatn query step s dstnct frm a sngle hp n the gegraphc frwardng layer; ndeed, each lcatn query step s lkely t requre several gegraphc frwardng hps. n Fgure 4, the entre dagram s an rder-4 square. Therefre all queres can be perfrmed n n mre than fur lcatn query steps. At each step, a query makes ts way t the best (clsest n D space t the destnatn) nde at successvely hgher levels n the grd herarchy. At the start, the query s frwarded t the best nde n the lcal rder-1 square usng the lcal rutng prtcl. Frm ths pnt n, each step mves the query t the best nde n the next larger cntanng square; when that next larger square cntans the destnatn nde, the best nde (clsest t the destnatn D) must be the destnatn tself. Thus the query's next step s t the destnatn. Ths behavr nt nly lmts the number f steps needed t satsfy a query, t als bunds the gegraphc regn n whch the query wll prpagate. Because the query prceeds nt larger and larger squares that stll cntan the surce, the query wll stay nsde the smallest square cntanng the surce and the destnatn. T understand why each step brngs the query t the best nde n a larger square, we wll frst cnsder the query frm nde A (76) fr the address f B (17), shwn startng n the lwer rght f Fgure 4. Our abbrevated tplgy has n mre than ne nde per square, s the query trvally begns at the best nde, tself, n ts rder- 1 square. The query mves t the best nde (21) n A's rder-2 square, because 76 happens t knw the pstns fr all the ndes n ts rder-2 square. Ths s an artfact f ur sparse layut, s the next step tells the mprtant stry: why 21 knws the lcatn f the best nde n the next hgher rder square. Recall that 21 s the best nde n ts rder-2 square. Ths guarantees that n ndes n that square have Ds between 17 and 21. Nw, cnsder a nde X smewhere n nde 21's rder-3 square, but nt n 21's rder-2 square. Recall that X had t chse a lcatn server n nde 21's rder-2 square. f X's D s between 17 and 21 then X must have chsen nde 21 as a lcatn server snce there are n better ndes n nde 21's rder-2 square. Thus, nde 21 knws abut all ndes n ts rder-3 square that le between 17 and tself, ncludng the mnmum such nde. n ths case, that nde s 2. At the next step, nde 2 must knw abut all ndes n the rder- 4 square between 17 and tself. Snce ndes 2 and 17 share the same rder-4 square (the entre fgure), nde 2 knws abut nde 17, and the query s fnshed. The abve example demnstrates why nde 21 knew nde 2's lcatn and was therefre able t mve the query frm the best nde n ts rder-2 square t the best nde n ts rder-3 square. One may wnder, hwever, why nde 21 des nt knw abut sme ther nde whse D s between 17 and 2, and whch les at a dstant lcatn. Ths wuld be undesrable as nde 21 wuld then frward the packet far away smply because, fr example, t mght knw the lcatn f nde 19. But ths cannt happen because nde 2 acts as a sheld fr nde 21 durng lcatn server selectn. That s, fr any nde utsde f the lwer rght quadrant f fgure 4, nde 21 s guaranteed nt t be the best chce fr lcatn server; nde 2 wll always be preferable. n addtn, because every lcatn query s labelled wth ts surce, ntermedate query steps knw what level f the herarchy the query s currently n, and can refran frm sendng queres t far away. Havng bult an ntutn, we nw gve an nductve prf that a query needs n mre than n lcatn query steps t reach ts destnatn when the surce and destnatn are clcated n an rder-n square. Furthermre, the query never leaves the rder-n square n whch t starts. We assume, wthut lss f generalty, that the destnatn nde's D s. We then prceed nductvely t prve the fllwng equvalent clam: n n r fewer lcatn query steps, a query reaches the nde wth the lwest D (.e clsest t ) n the rder-n square cntanng the surce. Snce the destnatn s nde, when the query reaches the rder-n square that cntans bth the surce and the destnatn ndes, t must reach the destnatn. 124

6 Base case (rder-1 square): The query begns at a nde X. Nde X may r may nt be the nde wth the lwest D n ts rder-1 square. f s, the query trvally reaches the lwest nde n the rder-1 square after zer lcatn query steps. fx s nt the nde wth the lwest D, then X wll knw the lcatn f the nde wth the lwest D n the rder-1 square, Y, thrugh the lcal rutng prtcl. Nde X wll nt knw f any ther ndes wth Ds lwer than Y. Any such nde wuld nt have selected X as a lcatn server as Y wuld always have been the better chce. Therefre the lwest nde that X s aware f s Y and the query wll be frwarded there n ne lcatn query step. nductve step (rder-(n + 1) square): We clam that fa query s at the nde X wth the lwest D n ts rder-n square, then X wll rute the query t the nde Y wth the lwest D n ts rder-(n + 1) square wth ne r zer lcatn query steps. f X has the lwest nde D n the rder-(n + 1) square, then ur clam s trvally true. f nt, X wll knw the crdnates f Y and wll nt knw the crdnates f any nde lwer than Y utsde the rder-(n + 1) square. Nde X wll knw the crdnates f Y because Y wll have selected X as a lcatn server. Nde Y must have selected a lcatn server n X's rder-n square because Y's rder-n square s a part f the same rder-(n + 1) square as X's. Nde Y must have selected X because X s the lwest nde n ts square that s greater than Y. Nde X wll nt knw the lcatn f any nde lwer than Y utsde f ts rder-(n + 1) square because when any such nde sught a lcatn server n X's rder-(n + 1) square, Nde Y was the better chce. Therefre the lwest nde that X s aware f s Y and the query wll be frwarded there n ne lcatn query step. [2 t s mprtant t remember hwever, that ths prf apples nly t a statc netwrk. Addtnal technques, descrbed n Sectn 5, help Grd t deal wth the prblems cereated by mblty. These sectns descrbe Grd's apprach t keepng lcatn servers up t date n the face f nde mtn and Grd's recvery technques when, despte updates, lcatn nfrmatn s fund t be ut f date. 5. mplementatn Ths sectn descrbes the detals f the gegraphc frwardng and GLS prtcls. 5.1 Gegraphc Frwardng The gegraphc frwardng layer uses a tw hp dstance vectr prtcl. Ths helps allevate hles n the tplgy and ensures that each nde knws the lcatn f all ndes n ts rder-1 square. Each nde mantans a table f mmedate neghbrs as well as each neghbr's neghbrs. Each entry n the table ncludes the nde's D, lcatn, speed, and a tmestamp. Each nde perdcally bradcasts a lst f all neghbrs t can reach n ne hp, usng a HELLO message. When a nde receves a HELLO message, t updates ts lcal rutng table wth the HELLO message nfrmatn. Usng ths prtcl ndes may learn abut tw hp neghbrs--ndes that cannt be reached drectly, but can be reached n tw hps va the neghbr that sent the HELLO message. The rutng table s als updated every tme a nde receves a packet, usng the packet's last hp nfrmatn. Each entry n the neghbr table expres after a fxed tmeut. Hwever, when an entry expres, the nde estmates the neghbr's current pstn usng ts recrded speed. f t wuld lkely stll be n range, the entry may stll be used fr frwardng, but t s nt HELLO Surce D Surce lcatn Surce speed Neghbr lst: Ds and lcatns Frwardng pnters Fgure 5: HELLO packet felds. reprted as a neghbr n further HELLO messages. Ths specal treatment s justfed by tw prpertes f the MAC layer. Frst, bradcast packets are mre lkely t be lst n the face f cngestn than uncast packets. Thus t s nt unusual t mss HELLO messages frm a nde that s stll nearby. Secnd, uncast transmssns are acknwledged. f the neghbr has actually mved away, the transmttng nde wll be ntfed when t attempts t frward packets thrugh the mssng nde. The nvald neghbr entry s then remved mmedately and a new frwardng path s chsen. T select a next hp, ndes frst chse a set f ndes frm all ndes n ther neghbr table. Ths set cnssts f the best ndes t mve the packet t, as defned by the shrtest dstance t the destnatn frm the canddate ndes. All ndes whse dstances t the destnatn are nearly equal are cnsdered n ths set. Call ths set B. f B cntans any sngle-hp neghbrs, remve duble-hp neghbrs frm B. A nde, X, s then chsen at randm frm B. f X s a sngle-hp neghbr, the packet s frwarded t X, therwse, snce X may be reachable frm any number f sngle hp neghbrs, the best such neghbr s chsen and the packet s frwarded t that nde. f the transmssn fals, the chsen nde s remved frm cnsderatn and the packet s reprcessed, startng wth the rgnal B (wth X remved f t was a sngle-hp neghbr). 5.2 Updatng Lcatn nfrmatn GLS mantans tw tables n each nde. The lcatn table hlds the nde's prtn f the dstrbuted lcatn database; each entry cnssts f a nde D and that nde's gegraphc lcatn. The lcatn cache hlds lcatn nfrmatn that the nde learns by lkng at update packets t frwards. A nde nly uses the cache when rgnatng data packets. Because each nde uses the neghbr table mantaned by the gegraphc frwardng layer t learn abut ther ndes n ts rder-1 square, the nde des nt need t send nrmal GLS updates wthn ts rder-1 square. As a nde mves, t must update ts lcatn servers. Ndes avd generatng excessve amunts f update traffc by lnkng ther lcatn update rates t ther dstance traveled. A nde updates ts rder-2 lcatn servers every tme t mves a partcular threshld dstance d snce sendng the last update; the nde updates ts rder- 3 servers after each mvement f 2d. n general, a nde updates ts rder- servers after each mvement f 2~-2d. Ths means that a nde sends ut updates at a rate prprtnal t ts speed and that updates are sent t dstant servers less ften than t lcal servers. n addtn, ndes send lcatn updates at a lw rate even when statnary. Lcatn update packets (see Fgure 6) nclude a tmeut value that crrespnds t the perdc update nterval, allwng the servers t nvaldate entres shrtly after a new entry s expected. The tme at whch the lcatn update packet s generated s als ncluded n the update packet s that the freshness f lcatn nfrmatn btaned frm dfferent ndes fr the same destnatn can be crn- 125

7 LOCATON UPDATE Surce D Surce lcatn Surce tmestamp Update destnatn square Update tmeut Next lcatn server's D Next lcatn server's lcatn Fgure 6: GLS update packet felds. LOCATON QUERY Surce D Surce lcatn Ultmate target D Next lcatn server's D Next lcatn server's lcatn Tmestamp frm prevus server's database Fgure 7: GLS query packet felds. pared. GPS recevers can prvde every nde n the netwrk wth clsely synchrnzed tme. When frwardng an update, a nde adds the update's cntents t ts lcatn cache. The nde asscates a relatvely shrt tmeut value wth the cached entres regardless f the recmmended tmeut value carred n the update packet. Ndes pggyback ther lcatn nfrmatn n data packets, s that tw ndes wh are cmmuncatng always knw hw t reach each ther. n the case f ne-way cmmuncatn, ndes als perdcally send ther pstn nfrmatn drectly t ndes wh are sendng them data. 5.3 Perfrmng Queres When a nde S rgnates a data packet fr destnatn D, t frst checks ts lcatn cache and lcatn table t fnd D's lcatn. f t fnds an entry fr D, t sends the packet t D's recrded lcatn usng gegraphc frwardng. Otherwse, S ntates a lcatn query fr D usng the GLS. GLS wll eventually delver the query packet (Fgure 7) t D, whch wll gegraphcally rute a respnse t S that ncludes D's current lcatn. f S had t ntate a GLS query, t stres the data packet n a send buffer whle t wats fr the reply frm D. Nde S rentates the query perdcally f t gets n reply, usng bnary expnental backff t ncrease the tmeut ntervals. 5.4 Lcatn Query Falures A lcatn query may fal fr tw reasns. Frst, a nde may receve a query packet fr D, and nt knw the lcatn f any nde wth an D clser t D than tself. Ths type f falure s relatvely uncmmn. t ccurs when a lcatn server has nt recently receved a lcatn update fr a nde t shuld knw abut. Because the server has tmed ut the nde's prevus update, t has n way t frward the query packet. There are ways t allevate these falures, such as usng stale lcatn data n a last dtch effrt t frward a query packet f the query wuld therwse fal. The secnd type f query falure ccurs when a lcatn server frwards a packet t the next clsest nde's square, but the nde s n lnger n that square (that s, the lcatn nfrmatn at the prevus lcatn server s ut f date). Because ths falure mde s mre cmmn, Grd cntans a specalzed mechansm t allevate the prblem. Cnsder a nde D that has recently mved frm the rder-1 square st t the rder-1 square s2. Nde D's lcatn servers, partcularly thse that are far away, wll thnk that D s n st untl D's next updates reach them. T cpe wth ths, D leaves a "frwardng pnter" n st ndcatng that t has mved t s~. When a packet arrves n st fr D, t can be crrectly sent n by fllwng the frwardng pnter. D bradcasts ts frwardng pnter t all ndes n st when leavng. Cnceptually, we can thnk f the frwardng pnters as beng lcated n the square st rather than at any partcular nde. Therefre, all ndes that mve nt st shuld pck up the frwardng pnters asscated wth st, and when ndes leave Sl, they shuld frget the crrespndng frwardng pnters. T prpagate frwardng pnters t all ndes n the rder-1 square and keep all newcmers t the square updated, a randmly chsen subset f the frwardng pnters stred at a nde (up t fve n ur smulatn mplementatn) s pggybacked n the nde's perdc HELLO messages. Upn hearng a HELLO message, a nde adds each frwardng pnter n that message t ts wn cllectn f frwardng pnters, but nly f the pnter's rgnal bradcaster was n the same square as the nde. n ths way, frwardng pnter nfrmatn s effectvely and effcently spread t every nde n the square. Wth ths prpagatn mechansm, even f all the ndes that rgnally receved D's frwardng pnter were t leave the square themselves, the nfrmatn wuld stll be avalable n the square. 6. Perfrmance Analyss Ths sectn presents smulatn results fr GLS that shw hw well t scales. Gd scalng means that the amunt f wrk each nde perfrms des nt rse quckly as a functn f the ttal number f ndes. We use tw metrcs fr wrk: the number f lcatn database entres each nde must stre, and the number f prtcl packets each nde must rgnate r frward n rder t rute a gven wrklad. The smulatns shw that these csts scale well wth the number f ndes. Mblty ncreases the wrk requred n tw ways. Frst, a nde that mves must update ts lcatn servers. Secnd, f a nde has mved recently, sme ndes may retan ut-f-date lcatn nfrmatn fr t; ths wll cause queres fr the mved nde t travel farther than necessary, r t fal and need t be resent. Handlng mblty requres a tradeff between the bandwdth used by lcatn updates and the bandwdth avalable fr data. f a mvng nde sends updates aggressvely, ther ndes are mre lkely t be able t fnd t. Hwever, the updates cnsume bandwdth n cmpettn wth data. Wrse, a very aggressve update plcy may cause enugh cngestn that updates themselves are drpped. At the ther extreme, a nde culd send updates nfrequently even when mvng quckly, ncreasng the amunt f bandwdth avalable t data. Hwever, that bandwdth s nt useful f the success rate f lcatn query becmes lw because f naccurate lcatn nfrmatn. The smulatns shw that Grd can acheve a reasnable tradeff fr the chce f update rate. 6.1 Smulatn Scenar The smulatns use CMU's wreless extensns [8] fr the ns [6] smulatr. The ndes use the EEE rad and MAC mdel prvded by the CMU extensns; each rad's range s apprxmately a dsc wth a 25 meter radus. The smulatns wthut 126

8 1.8.6 ~,,.4 == Number f ndes 1, x a{ ~, 1.s 8 3 a. 1 t x--- ~ + ~ ~--- ~... ~"... -x ~x". --" " ~s~ ~ l(., ''..x ~...-" Number f ndes Fgure 8: GLS query success rate as a functn f the ttal number f ndes. The ndes mve at speeds up t 1 m/s (abut 22 mles per hur). Each lne crrespnds t a dfferent mvement update threshld. data trafféc use 1 Megabt per secnd rads; the smulatns wth data traffc use 2 Megabts per secnd rads. Each smulatn runs fr 3 smulated secnds. Each data pnt presented s an average f fve smulatn runs. The ndes are placed at unfrmly randm lcatns n a square unverse. The sze f each smulatn's unverse s chsen t mantan an average nde densty f arund 1 ndes per square klmeter. One reasn fr ths chce s that we ntend the system t be used ver relatvely large areas such as a campus r cty, rather than n cncentrated lcatns such as a cnference hall. Anther reasn s that we expect any deplyed system t use rads that allw the pwer level t be decreased n areas wth hgh nde densty. The GLS rder-1 square s 25 meters n a sde. Fr a netwrk f 6 ndes, whch s the bggest smulatn we have dne, the grd herarchy ges up t rder-5 n a square unverse 29m n a sde. Each nde mves usng a "randm waypnt" mdel [4]. The nde chses a randm destnatn and mves tward t wth a cnstant speed chsen unfrmly between zer and a maxmum speed (1 m/s unless nted therwse). When the nde reaches the destnatn, t chses a new destnatn and begns mvng tward t mmedately. These smulatns d nt nvlve a pause tme. 6.2 GLS Results The results n ths sectn nvlve nly GLS (and gegraphc frwardng), wthut any data traffc. The default smulatn parameters fr ths sectn are an rad bandwdth f 1 Megabt per secnd, and a cmmuncatn mdel n whch each nde ntates an average f 15 lcatn queres t randm destnatns ver the curse f the 3 secnd smulatn, startng at 3 secnds. The lcatn update threshld dstance s an mprtant parameter that may need t be tuned. Fr ths reasn we present results fr three values f the threshld: 1, 15, and 2 meters. Fgure 8 shws the success rate fr GLS lcatn queres, as a functn f the ttal number f ndes. Queres are nt retransmtted, s a success means a success n the frst try. As mentned earler, mst falures are due t ether lcatn nfrmatn nvaldated by nde mtn r ndes nt beng crrectly updated because f delayed r lst lcatn updates. The success rate fr data sent after Fgure 9: Average number f Grd prtcl packets frwarded and rgnated per secnd by each nde as a functn f the ttal number f ndes. Ndes mve at speeds up t 1 m/s ' ~ ! Respnse path length Fgure 1: Average query path length (n hps) as a functn f the query reply path length, fr 3 ndes mvng up t 1 m/s. a successful query wuld be much hgher than ndcated here because the endpnts f a cnnectn drectly nfrm each ther f ther mvements. Fgure 9 shws the average number f Grd prtcl packets frwarded and rgnated per secnd per nde as a functn f the ttal number f ndes. Grd generates three types f prtcl packets: HELLO packets that are generated every tw secnds but nt frwarded, lcatn update packets that are als perdc but requre frwardng, and lcatn query and reply packets that als requre frwardng. As lcatn updates are generated by ndes as they mve, the results depend n nde speeds; the smulated ndes mve at speeds unfrmly dstrbuted between and 1 m/s. Fgure 9 s generated frm the same smulatns that prduced Fgure 8. The graph shws that Grd mpses a mdest prtcl traffc lad as the netwrk sze grws. Fgure shws hw the dstance that query packets travel cmpares wth the actual dstance n hps between the surce and the destnatn. We recrd the ttal number f gegraphcal frwardng hps (fr all query steps) that each query takes, as well as hw many hps the reply takes. Snce query reples are sent drectly t the query surce usng gegraphc frwardng, the reply return path ndcates the gegraphcal frwardng hp dstance between 127

9 .= O. "u O O 4O 2!! Average Maxmum ---x--- X / ; / ',, / J / ",, Number f ndes 5 6 == (D == Maxmum speed (m/s) 1 t x ~ Fgure 11: Average and maxmum per-nde lcatn database sze (number f entres) as a functn f the ttal number f ndes. The ndes mve at speeds up t 1 m/s. the surce and destnatn. We averaged the query hp lengths fr all queres wth a gven respnse hp length. The graph shws that n average, query packets nly travel abut 6 hps mre than the gegraphcal frwardng rute between ndes. Als, the dstance traveled by a query between tw ndes s prprtnal t the actual dstance between thse ndes. Our smulatn agrees wth a theretcal analyss that prves that wth a suffcently dense unfrm dstrbutn, the number f hps traveled by the query s prprtnal t the dstance t the destnatn. The smulatn nvlves 3 ndes mvng at speeds up t 1 m/s, wth a lcatn update threshld f 2 meters. Fgure 11 shws the effect f the ttal number f ndes n the sze f each nde's GLS lcatn table. The plts nclude bth the average and maxmum lcatn table sze ver all ndes. The spkes at 15 and 4 ndes ccur because the smulated area des nt exactly fll a herarchy, causng the database lad t be dstrbuted unevenly. At these pnts, the maxmum database sze s larger because the squares that extend acrss the edge f the smulated area cntan relatvely few ndes; these ndes must stre mre than ther far share f lcatn database entres. On the ther hand, the average table sze grws very slwly wth the netwrk sze. Ths hghlghts a prblem that may arse n practce when ndes are nt unfrmly dstrbuted. A small number f ndes n a hghlevel square may end up respnsble fr trackng the lcatns f a large number f ndes n sblng squares. Ths wuld requre large amunts f space n these few ndes. Fgure 12 shws the effect f nde mvement speed n the GLS query success rate, fr 1 ndes. As ndes mve faster, ther lcatn servers are mre lkely t be ut f date. On the ther hand, the ndes als generate updates faster. The net effect s that the query success rate s relatvely nsenstve t nde speed, hwever, the update traffc grws as ndes mve faster. Fgure 13 shws the effect f ndes turnng n and ff. Sme ndes are always n, whle the rest alternate beng n and ff fr ntervals unfrmly dstrbuted frm t 12 and t 6 secnds, respectvely. As we are smulatng nde crashes, ndes d nt d anythng specal befre turnng ff; they smply lse all ther lcatn table data. n practce, f a nde was manually turned ff, t wuld be apprprate t frst redstrbute ts lcatn table t get better per- Fgure 12: GLS query success rate as a functn f maxmum nde speed n a netwrk f 1 ndes. 5 m/s s abut 11 mph Fractn f stable ndes 1 J x ~--- =.8 Fgure 13: The effect f turnng ff ndes n the query success rate. The X axs ndcates the fractn f ndes that are always n; the remanng ndes cycle n and ff fr randm perds up t 12 and 6 secnds, respectvely. The smulatns all nvlve 1 ndes mvng at speeds up t 1 m/s. frmance. Each pnt n the graph represents a smulatn n whch a dfferent fractn f ndes are always n. The smulatns nvlve 1 ndes, each mvng wth a maxmum speed f 1 m/s. The statstcs are lmted t queres addressed t ndes that are turned n; n queres are generated t ndes that are ff as these queres wll always fal. When a nde turns ff, a part f the dstrbuted lcatn database s lst; when a nde turns n, t wll nt be able t partcpate crrectly n the update and query prtcl fr a whle. The graph shws that even a great deal f nstablty des nt have a dsastrus effect, and that the query success rate degrades gracefully as ndes turn n and ff. 6.3 Data Traffc The smulatns n ths sectn measure Grd's behavr when frwardng data traffc. The rad bandwdth s 2 Megabts per secnd, and the lcatn update threshld dstance s 2 meters. The data traffc s generated by a number f cnstant bt rate cnnectns equal t half the number f ndes. N nde s a surce n mre than ne cnnectn and n nde s a destnatn n mre than three cnnectns. Fr each cnnectn fur 128-byte data packets are sent per secnd fr 2 secnds. Cnnectns are ntated at randm tmes between 3 and 28 secnds nt the smulatn. Fr 128

10 O >= ~,.,,,-- -~ - - -Jr... ~-... ~ ' ' " -... X... K t- O 3 = t )SR 4,, Grd ---x--- ~- 2s " r- 2 zl O Number f ndes DSR, Grd ---x E l K... -l~... K Number f ndes Fgure 14: The fractn f data packets that are successfully delvered n smulatns fr ncreasng numbers f ndes. The ndes mve wth a maxmum speed f 1 m/s. purpses f cmparsn we nclude results fr the DSR [1] prtcl. Ths may nt be a far cmparsn snce DSR s ptmzed fr relatvely small netwrks [3]. Fgure 14 shws the fractn f data packets successfully delvered. Mst f the data packets that Grd fals t delver are due t GLS query falures; these packets never leave the surce. Once Grd fnds the lcatn f a destnatn, data lsses are unlkely, snce gegraphc frwardng adapts well t the mtn f ntermedate ndes. Belw 4 ndes, mst f the DSR lsses are due t brken surce rutes; at 4 ndes and abve, lsses are manly due t fldng-nduced cngestn. Grd des a better jb than DSR ver the whle range f numbers f ndes, especally fr large netwrks. Fgure 15 shws the message verhead f the Grd and DSR prtcls. Only prtcl packets are ncluded. n the case f Grd, these are HELLO, GLS update, and GLS query and reply packets. n the case f DSR, these are rute request, reply, cached reply packets etc. DSR prduces less prtcl verhead fr small netwrks, whle Grd prduces less verhead fr large netwrks. At 4 ndes and abve, DSR suffers frm netwrk cngestn. Almst half f the rute reply and cache reply messages are drpped due t cngestn whch causes DSR t nject even mre rute requests nt the netwrk. Als, as the netwrk grws larger and cngestn bulds up, the surce rute s mre vulnerable t falure whch wll als nduce DSR surce ndes t send mre rute request packets. DSR's verhead drps at 6 ndes because t culd nt send much mre packets n the presence f cngestn. We present verhead n terms f packets rather than bytes because medum acqustn verhead dmnates actual packet transmssn n 82.11, partcularly fr the small packets used by Grd. 7. Future Wrk One area f the GLS prtcl that culd be mprved s the handng f nde mblty. Accurate mvement mdels may allw us t ntegrate mvement predctn nt the GLS prtcl. Our current system makes lttle effrt t predct the mvement f ndes ver lng tme perds because ur mvement mdel s randmzed, but n the real wrld a nde may nt need t update a lcatn server as ften f ts velcty s cnstant r predctable. Currently the GLS prtcl makes lttle effrt t practvely cr- Fgure 15: The number f all prtcl packets frwarded per nde per secnd as a functn f the ttal number f ndes. N data packets are ncluded. The ndes mve wth a maxmum speed f 1 m/s. rect ut-f-date nfrmatn when, fr nstance, a nde crsses a grd bundary lne. Practve updates may reduce the ncdence f query falures. Hwever, the tradeff s bvus---care must be taken nt t cnsume t much bandwdth wth the updates. An alternate strategy t address the same prblem s t place less trust n lcatns btaned frm dstant lcatn servers. Rather than trust a dstant lcatn server t pnpnt the rder-1 square n whch a nde s lcated, a query culd be mved t, fr nstance, the surrundng rder-3 square. There the query can be restarted wth the fresher nfrmatn avalable n that square Anther ptental area f mprvement s adaptng t nde densty. f an rder-1 square becmes t crwded, each nde wll get less bandwdth frm the shared rad spectrum, and each nde wll have t wrk harder t keep ts neghbr table up t date. Rads wth varable pwer levels wuld help allevate ths prblem by changng the effectve densty f ndes wthn rad range. n addtn, each square n the GLS may make a lcal decsn abut hw fnely t sub-dvde tself; dstant areas need nt agree n the sze f the rder-1 square. Fnally, as we nted earler, the chce f a grd based system s smewhat arbtrary. n fact, certan parttnng schemes ffer the pssblty f better scalng. The number f lcatn servers that a nde must recrut s equal t the number f neghbrs per level n the gegraphc herarchy multpled by the number f levels n the herarchy. Fr a grd based system, ths means that a nde must mantan 3 lg 4 n servers n a netwrk that s n tmes the sze f the cverage area f a sngle rad. t s pssble, hwever, t splt the wrld n half at each level, rather than n furths, by usng rectangles wth an aspect rat f 1/x/2. At successve levels, each such rectangle may be dvded nt tw such rectangles. Ths leads t a netwrk n whch ndes must recrut nly lg s n lcatn servers, r 2/3 the number f servers needed n a grd based apprach. 8. Cnclusns Wreless technlgy has the ptental t dramatcally smplfy the deplyment f data netwrks. Fr the mst part ths ptental has nt been fulflled: mst wreless netwrks use cstly wred nfrastructure fr all but the fnal hp. Ad he netwrks can fulfll ths ptental because they are easy t deply: they requre n nfrastruc- 129