Geo-LANMAR Routing: Asymptotic Analysis of a Scalable Routing Scheme with Group Motion Support

Transcription

1 Go-LANMAR Roung: Asympoc Analyss of a Scalabl Roung Schm wh Group Moon Suppor Florano D Rango, Maro Grla, Bao Zhou, Salvaor Marano D.E.I.S. Dparmn, Unvrsy of alabra, Ialy, mal: drango, ompur Scnc Dparmn, ULA, Los Angls, A 995 -mal: zhb, Absrac Ths papr prsns a novl roung proocoalld Go- LANMAR. Ths roung schm s abl o g full advanags of group moon of mobl nods o rduc h roung ovrhad and offr hgh nwork scalably. Ths proocol nhrs sam advanags of LANMAR proocol rgardng h group moon suppor and s da s o us h long-dsanc go-forwardng for h xra-scop roung such as h Trmnods Roung and h Opmsd Lnk-Sa Roung (OLSR) for h nra-scop roung. Toghr h go-roung forwardng schm, a global upda propagaon schm basd on h Hazy Sghd Lnk Sa Roung (HSLS) bwn landmark nods (clusr hads) s appld. An asympoc analyss of Go-LANMAR proocol s proposd and a rul ha bnds h nra-scop and xra-scop ovrhad cos s found. Th novl roung schm has bn compard wh h sandard roung proocols such as AODV, GPSR and LANMAR.. Inroducon Nwork scalably s a crcal ssu n roung proocols for Ad Hoc nworks. I s mporan o guaran a good scalably proprs o opn sysms or dynamc nwork whn h numbr of nods, h raffc load and mobly ra ncrass. Many scalabl approachs hav bn proposd [-], whch ar basd on hr abl-drvn forwardng or go-forwardng chnqus. Mor spcfcally, n ordr o rduc h conrol ovrhad and o fnd a pah from sourc oward dsnaon, go-roung nsprd schms such as GPSR [] hav bn proposd. Go-roung uss h posons of rours and a pack s dsnaon o mak pack forwardng dcsons [4]. By kpng sa only abou h local opology, go-roung scals br n pr-rour sa han shors-pah. Indpndnly, good scalably rsuls wr also rcnly rpord by h Landmark Roung Proocol (LANMAR) [], usng a oally dffrn approach xplong group mobly and hrarchcal roung. A novl approach basd on h long-dsanc goforwardng and h local lnk-sa roung has bn rcnly proposd and s calld Trmnods Roung [8]. Ths papr, accordng wh rcn advancs n h Ad hoc nworkng roung and scalably ssus, prsns a novl roung schm calld Go-LANMAR ha s basd on h basc da of LANMAR and Trmnods Roung [8,9]. Th proposd proocol maks us of h group moon suppor of h LANMAR roung hrough h clusrng algorhm unl k-hop o lc h clusr-had (landmark nod), and appls also h go-roung schm for long dsancs. A novoncp of Locaon Group Ara (LGA) ha rprsns h ara assocad o h group s nroducd [5] and an opmsd lnk-sa roung calld Hazy Sghd Lnk-Sa (HSLS) Roung [] s appld o manan h locaons of LGAs. Th roung adopd n h local scop has bn h OLSR proocol []. Th proposd proocol prsns good scalably proprs n rspc of h numbr of nods, groups, raffc load and mobly ra. An asympoc analyss s ralsd accordng wh h work n [6,7] and som ruls ha bnd h projc paramrs wh h numbr of groups and group sz ar oband. Smulaon campagns ar assssd and h Go-LANMAR proocol has bn compard wh GPSR, AODV [8] and LANMAR. Th papr s organsd as follows: scon prsns h basc da of Go-LANMAR proocol; an asympoc analyss of Go-LANMAR s ralsd n scon 3; scon 4 offrs h prformanc valuaon and smulaon rsuls; fnally conclusons ar summarsd n scon 5.. Go-LANMAR Th GO-LANMAR s composd by wo roung proocols: lnk-sa and gographc roung proocols. Th lnk sa roung proocol s managd nsd h local scop of a fxd numbr of hops. Th lnk-sa proocol has bn chosn n ordr o prm h calculaon of h shors pah and o manan a good nformaon abou h locaon nformaon nsd h local vw. For any local scop hr s a spcal nod ha ransms som nformaon abou h local scop o h nr nwork. Ths nod s calld Go-Landmark and ransms o h ohr scops h nformaon abou s ID group, abou h poson nfo and h locaon nformaon of h ohr GEO-Landmarks of h nwork. So as showd n fg., h Landmark nod L M ransms h nformaon of all landmarks n h nwork L (x,y), L N-,(x,y), L N (x,y)and s poson L M (x,y) o s on-hop nods. Th poson nformaon s usful n sndng h daa pack ousd h local scop, usng h grdy forwardng chnqu. In fg., f h sourc wans o communca wh a mobl nod D, frs chcks bfor nsd s local scop o s f h dsnaon D can b rachd mmdaly hrough lnk-sa roung. If hr s no nry n rms of IP

2 addrss, rs o snd h pack oward h dsnaon D hrough h go-forwardng. Through h knowldg of h group ID s possbl o g h locaon nformaon of h dsnaon landmark L D nsd h local abl. So whou ndng of h spcfc locaon of dsnaon D, w can us h nformaon of h dsnaon landmark. Thn, whn h pack s nar h scop of landmark L D, can b drcly sn hrough h abl-drvn forwardng. S A B LS E Local Scop L Proacv Roung Landmark nod To xplo hs managmn, h nods nsd h local scop nd o sor a local roung abl wh a roung abl ypcal of h lnk sa roung, a landmark abl wh h locaon nformaon and h group IDs of h landmarks n h nworks. Whn a nod nds o snd a pack ousd s local scop, chcks h landmark abl and slcs h nars o h dsnaon nghbour landmark. For xampl, n fg., nod S slcs as h nx nod nsd h local scop and h nars nghbour landmark closs o h dsnaon landmark L D. Whn h daa pack arrvs o E, h nx hop Landmark, ousd h scop, s slcd as h nx arg nod o rach bcaus s h closs o h dsnaon landmark L D Ths procss s rpad unl h las scop, n whch s locad h dsnaon D, s rachd. Go-LANMAR proocol prsns h characrscs lsd blow :. Go-LANMAR Rou Forwardng: s composd of a local abl-drvn forwardng schm and a longdsanc godsc forwardng.. Go-LANMAR roung abls: wo man roung abls. Th frs on nsd any local scop o map h opology of k-hop nghbours and h scond on o gv a coars knowldg of all nwork sa. 3. Go-LANMAR Rou Rcovry Procdur: s appld whn a local maxmum (hol) s rachd. A GPSR-lk chnqu s dployd. Th choc of h nghbour nod o us n h prmr mod s basd on a novl mrc calld Effcv Travlld Dsanc xpland blow. 4. Go-LANMAR upda: roung abl s dffrnad n nra-scop and xra-scop upda. Th frs upda modaly s assocad wh h appld lnksa roung schm. Th scond s assocad wh h ara dfnd by h group moon (Group Ara Lnk Sa Roung Fg.. Local lnk-sa roung and long-dsanc go-roung. Boh of updang (nra and xra-scop) ar proacv. LM LN- LN D Locaon) and s lmd n h spac and n h m such as HSLS n ordr o offr scalably proprs n rms of raffc, mobly and nwork sz. 5. Effcv Travlld Dsanc (ETD): hs rprsns a nw mrc o slc h bs drcon oward dsnaon. Nwork parons and hols can dgrad h prformanc of go-graphc roung. Through h ral ravlld dsanc s possbl o mak h bs choc of h nghbour nod. 6. Hol Dcon: s possbl o avod h hol hrough a long-rang knowldg of h nwork sa. Th proacv nformaon xchang bwn LGAs prm h buldng of a vrual opology wh gocoordnas, whr s possbl o know f hr xs a pah bwn wo LGAs. Ths approach prms h choc of h bs nghbour nod n h rgh drcon oward h dsnaon o occur ofn. 7. Group Mobly Suppor: h clusrng algorhm runnng n h local scop prms h lcon of a landmark nod as h rprsnav nod of h group nods. Ths clusr ladr gvs nformaon abou h Group Ara Locaon o h nr nwork n ordr o prm h us of h go-roung. 8. Hgh Group Scalably: h lnk-sa roung lmd whn h scop rducs h roung ovrhad. Opmzd lnk-sa roung wh spaal and m dvrsy n h vrual opology of LGAs offrs a hghr scalably rducng h nd o upda local opology changs. Mor dals abou h LGA and h basc da of Go- LANMAR w rfr o [5]. In h followng, ohr aspcs of h novl roung schm ar addrssd.. Effcv Travlld Dsanc In h upda pack s nsrd h poson of h landmark as rfrncs for h LGA and a fld dsanc calld Effcv Travlld Dsanc (ETL) ha accouns for h ral ravld dsanc bwn h landmark ha snds h upda pack and h landmark nod ha rcvs h pack. To snd h upda pack o h ohr landmark n h nwork h grdy forwardng s usd and h prmr mod can b rggrd n h cas of rcovry from local maxmums, hols or obsacls. Lx Travlld dsanc gomrc dsanc Fg.. Ral ravlld dsanc n h vrual opology. Imagn ha h numbr of nods usd for h grdy or prmr mod ar n. In hs cas h ETL bwn wo Ly

3 nghbour landmarks L x and L y s calculad n h followng way: n ( L, L ) = ( x x ) + ( y y ) x y = + + ds () Ths nformaon s propagad n h lnk-sa pack ransmd by h landmark nod. To calcula h oal ral ravlld dsanc bwn h landmark L X and L D, rspcvly k hop far, as shown n fg., h ETD can b calculad as follows: ETD = d k x d = = ds ( L L ), () +. Hol Dcon omparng h ETD d x-d wh h ucldan dsanc L xl D, hr can b dfnd a nw ndx α showd n q.8 rprsnng h dvaon of h ral physcal dsanc from h gomrc dsanc. LX α = = k ETD ( xx xd ) + ( yx yd ) ds ( L, L + ) = h ndx α can chang n h rang [,]. If α h ravlld dsanc s so much hghr han h gomrc dsanc ha a hol prsnc, nwork paron or vry long pah can b m. If α h ravlld dsanc s h shors pah. Typcally f h α valu of h pah s lowr han.5, s no suabl o snd h daa pack on hs pah bcaus h dvaon from h shors pah s hgh. Through h nfo xprssd n q.9, s possbl o dc h hol a LGA lvl. In hs cas, s possbl o slc anohr nghbour Landmark n h nwork ha can avod h hol. An xampl s shown n fg.3. LS LX Vrual pah bwn LGAs LY LZ Hol Fg.3. Vrual pah bwn LGAs. Through h ral ravlld dsanc s possbl o dc h hol In fg.3, h nod L X rcvs h upda pack from h dsnaon landmark L D and can dc a vod or a sub-opmal pah bcaus h gomrc dsanc L X << ds( LX, ). So, f h drcon oward h L Y landmark s slcd, s possbl o go oward a subopmal pah. In hs cas, h L X landmark slcs h nghbour wh h hghs α valu (shors ravlld Landmark nod (3) upda pack dsanc STD) oward L D. n fg.3 h pah passng for L Z s slcd..3 Roung Updas In ordr o offr a br scalably n rms of proocol ovrhad, a vrual opology bwn LGAs s dfnd. Ths opology s bul o hav a knowldg of h locaon of h LGAs and o us h gographc forwardng bwn LGAs. I s prfrrd o apply h lnk-sa nfo propagaon bwn LGAs bcaus, hs guarans o hav a rfrshd nformaon of h locaon nfo and a go-forwardng can b mor ffcvly appld. Accordng wh [8,,,3], bcaus h poson nfo can b mly rfrshd for long dsancs and can b rfnd approachng o h dsnaon, o rduc h ovrhad of h lnk-sa propagaon o h nr nwork w us a lnk-sa roung lmd n h scop and n h m. Th lnk-sa propagaon bwn LGAs can offr h advanags of h lnk-sa roung o h macro-lvl (LGA lvl) n rms of h vrual pah avalably n a small amoun of m n comparson wh h racv roung schms. Through h lnk-sa propagaon, s also asr o chck h lnk-sa n ordr o dploy load balancng or QoS rsrvaon. Anohr mporan rason s avodng h Locaon Srvr managmn. Bcaus any nod can know h zon locaon LGA D whr h dsnaon can b found, s no longr ncssary o g h poson locaon of h dsnaon hrough a qury n a srvr dssmnad n h wrlss ad-hoc nwork. Th proposd approach rs o localz h qury rqus nsd h local scop whr runs h lnk-sa roung runs (.g. OLSR, fshy c) and lmnas h upda procss of a Locaon Srvr n ordr o manan accura locaon nfo abou ach nod n h nwork. A furhr advanag of h lnk-sa propagaon of LGAs locaon s o offr a knowldg of h group poson avodng o rqus h nfo of a spcfc dsnaon whr forwardng h daa pack bu ndng only of h locaon of h group ara whr forwardng h pack. Thr s also anohr problm assocad wh goforwardng ha can b ovrcom by h lnk-sa propagaon of h LGAs poson. Go-roung, as n GPSR [,3] and GEDIR [4], s blnd for h long dsancs bcaus of h local opology knowldg and h local opology vw. Ths can drmn, somms, n lss dns nworks, and ofn n spars nworks, h choc of h bad pah owards h dsnaon. A no suabl pah s m f a rcovry procdur by h local maxmum s appld ofn. So, h lnk-sa propagaon of h poson and h vrual lnk sas can b usful n makng br dcsons abou h drcon n whch o snd h daa pack. Ths mchansm rs o rduc h frquncy of h local maxmum rcovry procdur and, n h cas whr h rcovry procdur s appld, a mor suabl nghbour nod basd on h mnmum ravlld dsanc s chosn for h prmr forwardng.

4 .3. Global Updas Th updang mchansm s nhrd by h HSLS approach whr h lnk-sa proocol s mad mor scalabl hrough spaal and m ra dffrnaon. Bfor xplanng h lnk-sa propagaon, may b usful o gv som dals abou h vrual opology nwork bwn LGAs. I s sad ha hr xss a vrual lnk bwn wo LGAs f, consdrng rspcvly hr avrag rangs r and r (hy can b g rfrrng o q.6), h followng condon s vrfd: ( x x ) + ( y y ) mn( r, r ) d = < (4) L L L L As shown n fg.4 h vrual opology bwn LGAs s consdrd. LS L L7 L r L8 L3 r L L9 L4 L L5 L6 L4 L L3 Fg.4. Vrual opology bwn landmarks. -hop nghbours (=) lnk-sa pack L L7 Each landmark nod, rprsnanv of a group, ransms a lnk-sa pack wh s locaon. If h q. s no rspcd h nry n h roung abl s s o nfny. onsdrng h landmark s opology, as shown n fg.5, h propagaon ra s rducd for an ncrasng numbr of hops and h opologcahangs n h landmark s nwork ar aggrgad and ransmd n som parcular nsan of m. Only h upda of h frs landmark s vn-basd, hn h upda unl o k hop wh k> s ransmd afr a m nrval. Th HSLS algorhm s appld o propaga h lnksa pack among h landmark nods. HSLS blongs o h famly of h Fuzzy Sghd Lnk Sa (FSLS) and s an opmzd vrson of hs class. In h FSLS LS Vrual opology bwn LGAs (landmarks) L5 L L3 L6 L L8 L L9 L 4-hop nghbours (=; propagaons unl hops ach - ) Fg.5. Lnk-sa updas dffrnad n h m and n h spac. L4 L L3 algorhms h Tm o lv (TTL) s usd n ordr o lm h spaal propagaon of h lnk-sa upda (LSU) pack and h ransmsson s dffrnad n m. A h bgnnng, h TTL valu s s o a spcfc valu ha s a funcon of h currn m. Afr on global LSU ransmsson (whn TTL valu s s o nfny), a nod waks up vry sconds (obsrvaon m) and snds a LSU wh TTL s o s f hr has bn a lnk saus chang n h las sconds. A lnk-saus chang occurs f h q. s no rspcd and a vrul lnk braks. Th nod waks up vry sconds and ransms a LSU wh TTL s o s f hr has bn a lnk-saus chang n h las. In gnral, an LSU s ransmd wh TTL s o s f hr has bn a lnk saus chang n h las sconds. In addon, o guaran a LSU ransmsson also n low mobly scnaros, a sof sa procon s nroducd n h algorhm and a LSU s sn also whou a vrual lnk brakag vry b scond whr >>. b Th abov approach guarans ha nods ha ar s hops away from a rfrnc nod wll larn abou a lnk saus chang a mos afr sconds HSLS algorhm rs o mnmz h oal ovrhad producd by h LSU propagaon. I s rcalld ha oal ovrhad s rprsnd by h ovrhad assocad wh h proacv upda xchang and h ovrhad assocad wh h sub-opmal pah. Afr a lnar opmzaon problm prsnd n [6,7]. I s found ha for fxng h m a br valu of s valu (TTL) s s =..3. Local Upda Insd ach group a smpl lnk-sa roung algorhm can b appld (nra-scop roung). Ths s du o h rducd numbr of nods blongng o h group n comparson wh h oal numbr of nods n h nwork. In our analyss a full lnk-sa roung and an opmsd lnk-sa roung (OLSR) hav bn appld. In h nx scon, an asympoc analyss whr h ffc of nrascop roung on h ovrall ovrhad cos of h Go- LANMAR s accound. 3 Asympoc analyss of GEO-LANMAR In hs scon, n accordanc wh analyss of auhors n [6,7], an asympoc analyss of GEO-LANMAR proocol s carrd ou. In ordr o dsgn a scalabl proocol n rspc of h mos mporan nwork paramrs, s mporan o s f, whn h numbr of nods, h raffc load, h spd of mobl nods and h numbr of groups ncras, whhr or no h prformanc of proocols can dgrad. Hr, bfor gvng an da of h proocol bhavour, h sam assumpons proposd n [6,7] ar rcalld. L N b h numbr of nods n h nwork, G h numbr of groups n h nwork, d h avrag n-dgr,

5 h avrag lnk-brakag ra (numbr of lnk brakags pr scond), h avrag raffc gnraon ra, and S h avrag ssson gnraon ra, Th assumpons n buldng h modl ar as follows:. Whn h nwork sz ncrass, h avrag ndgr d rmans consan.. L A g b h ara covrd by a group of nods, and σ g = b h group avrag dnsy. Th A numbr of nods nsd h ara A g s σ g A. g 3. Th maxmum and h avrag pah lngh (numbr of groups) n h vrual nwork Θ g n a subs of g groups or as ncras as ( ) ( G ) Θ n all nwork. 4. Th raffc ha a nod gnras n a scond s ndpndn of h nwork sz N. As h nwork sz ncrass, h oal amoun of daa ransmd/rcvd by a sngl nod wll rman consan, bu h numbr of dsnaon ncrass. 5. For a gvn sourc nod, all possbl dsnaons (N- nods) ar quprobabl and h raffc from a nod o a parcular dsnaon dcrass as Θ. N 6. Lnk saus changs ar drcly proporonal o h nra-group mobly for local lnk-sa roung and du o h group mobly. 7. Tm scalng for h mobly modl: l f ( x, y) b h probably dsrbuon / funcon of a nod poson a m, gvn ha h nod was a h orgn (,) a m. Thn, h probably dsrbuon funcon of a nod a m gvn ha h nod was a h poson x y a m s gvn by ( ) f, n / ( x, y, x, y ) = f x x y y, n ( ) / n To br undsand h assumpons lsd abov, w rfr o [6]. Only for assumpons 5 and 6 w rcall ha hy can b jusfd by h bhavour of h xsng nwork. As h nwork sz ncrass, h raffc of usrs dvrsfs rahr han ncrass. I s possbl o hnk of h ncrasng n sz and conn n h Inrn; can produc mor wb pags o b vsd (dsnaon s dvrsfs) bu h amoun of bandwdh and m avalabl for h usr s fxd. In wrlss nworks, hs can b dffrn. Anyway, hs assumpon s usd o smplfy h analyss. Th oal ovrhad cos assocad o h FSLS famly of proocols s xprssd as follows: n = c LSU sz s R + (5) pro n = n = + αβγσl n sub MR ln( R) ln( s ) (6) N 4 = o = pro + (7) sub whr { s } s h spac whr h LSU s propagad, R s h radus of h nwork, s h basc obsrvaon m,, σ and N ar dfnd abov, and β s a consan assocad wh h numbr of nods a a dsanc k or lss from nod S. LSU sz s h avrag sz of a LSU pack. M s a consan assocad wh mobly, L s h ransmsson rang of a nod, α s h mnmum dsanc bwn S and s nghbours, γ (,3) s a consan, and n s h smalls ngr, so ha n R. A soluon ha mnmzs h oal ovrhad cos s s = max, mn R, H whr gvn for { { } H αβγσlmr = 4 N c LSU sz. Through h soluon of a Lnar Programmng rlaxd problm, s obsrvd ha can b fxd o. So, n a HSLS ha uss h opmzd LSU propagaon, h valu of s can b fxd o s =. onsdrng h wors suaon n whch ach s dcd n a lnk-chang, an LSU pack s ransmd unl s =. So, o accoun for proacv ovrhad, assumng ha HSLS s run n h vrual nwork (landmarks nwork), h followng consdraons can b mad.. Each landmark compus s maxmum dsanc MD x o any ohr landmark and f h valu of s TTL s grar han h maxmum dsanc, wll broadcas h LSU pack (TTL s s o nfny) and hn rs s counr o zro.. If < MDx R, for ach R x x h landmark broadcass LSU and rss h counr o zro. 3. Th bandwdh consumpon for broadcas n LSU s LSU sz G whr N G =. 4. If TTL s s o R x, h LSU ransmssons ar sr x = Θ( R x ) whr s < R x G and h bandwdh consumpon s LSU sz s. 5. For TTL qual o R x, h gnraon ra of LSU doubls bu h numbr of ransmssons pr LSU s rducd by a facor +. Th cos of h proacv ransmssons for a sngl landmark can b summarzd as follows:

6 LSU sz G LSUszs LSUszs LSU s sz proacv = = G+ s (8) R x consdrng ha R x = Θ( G ) and sr x < G, only h frs rm n q.5 gvs a conrbuon so h proacv cos can b xprssd as:.5 HSLS LSU sz G G = Θ (9) landmark G f h numbr of groups (landmarks) n h nwork s G, h oal proacv cos s: G G Θ G = Θ N = Θ..5 HSLS landmarks 5 () Anohr conrbuon of h landmarks o h ovrhad s h cos of sub-opmal rous, du o h bad nx-hop dcson cos. A bad nx-hop dcson happns f h gomrc dsanc for a ransmng nod o h dsnaon s no rducd. I s asy o undrsand ha, n a dns nwork, hr s an hgh probably ha a nod wlhoos as h nx hop a nod ha ncrass h dsanc oward h dsnaon. Ths s bcaus go-roung s abl o fnd h shors pah. In a suaon n whch h nwork s spars, hs vn can b mor frqun and hs can produc mor local-maxmum rcovry procdurs. onsdrng ha h probably of a nod ncurrng a bad dcson s p, hn -p s h probably of h nod gong n h rgh drcon oward h dsnaon. If w assum ha wo succssv roung dcsons ar ndpndn procsss, s possbl o assum ha h probably of addrssng h pack n h rgh drcon, mnmzng by on hop h dsanc oward h dsnaon, s. Morovr, h numbr of opmal p ransmssons s, so bandwdh consumpon s gvn by p f daasz, whr f s a consan ha accouns for p h numbr of nods nsd h local scop of h landmark, and ha ncrass h shors pah. If w l L rprsn h dsanc n rms of landmark hops away from h dsnaon, h avrag wasd bandwdh s xprssd as follows: landmarks bad nx hop p = f G daasz L = Θ p consdrng ha L Θ( G ) ( f GL) () =, h cos of a bad nx-hop can b summarzd as: landmarks N = Θ f = Θ G f () bad nx hop ( ) To br spcfy h q.9, s mporan o obsrv ha h probably p dpnds on h mobly ra and, consqunly, on h lnk-chang ra and on h m lapsd lapsd of h las LSU pack wh h rgh nformaon abou h dsnaon. Assumng an analogy wh a cllular sysm, h probably p can assumd o b lpsd c L p = and, consqunly, h sub-opmaos s as follows: landmark sub opmal = c c lc lapsd 3 L G (3) Bcaus HSLS snds prodcally a LSU pack, h nod S wll rcv h updad nfo abou h nod D afr almos sconds. On h avrag, s possbl o assum ha nod S wll xprnc a dlay of So, subsung hs uppr bound wh h lapsd valu, h q. can b wrn agan as follows: 4. 5 ( c ) G opmal = c (4) landmark sub 3 whr c 3 and c 4 ar consans. Th oal ovrhad assocad wh propagaon n h vrual nwork of LGAs (landmarks) s xprssd as: c lc 4 ( ) N + c3 landmarks N HSLS = f (5) If h xponnal approxmaon ( x x )s usd, h ovrhad can b xprssd n h followng way: landmarks HSLS N N N (6) = + c l c = + c l c 3 c 4 3 c 4 Th valu ha mnmzs h ovrhad cos s = Θ and landmarks N HSLS = Θ l. c l c l Th approxmaon abov s vald only f c (for and ). If, = Θ and h oal ovrhad s landmarks N HSLS = Θ. c. 5 l Anohr conrbuon o h oal ovrhad nsd h nwork s gvn by nra-scop roung. In hs cas, w gv an da of h ffc of lnk-sa roung whn h local scop, rfrrng o h OLSR proocol.

7 If D N s h avrag numbr of MPR lnks pr nod, R N h avrag numbr of rransmssons n an MPR floodng, h h ra of hllo ransmsson pr nod, τ h ra of opology conrol gnraon, and d h avrag dgr (numbr of adjacn lnks) pr nod, hn h nrascop conrol raffc s xprssd as follows: OLSR n rascop = ( hd + τ R D ) G (7) In h wors suaon D = d and R =, so h ovrhad s as a full lnk-sa algorhm. Howvr, hrough h sam opmzaon, s possbl o oban D << M and R << d offrng a hgh rducon of nra-scop ovrhad. So, n hs cas, h oal ovrhad of GEO-LANMAR assocad wh h mor mporan projc paramrs s xprssd blow: N hdn + τ R D N + l c = Ο f ( ) OLSR landmarks = n + = (8) o rascop HSLS N hdn + τ R D N + = Ω f ( ) Th followng funcons can b analysd. B f + ( ) = A f ( ). 5 = Ο = (3) o B f + ( ) = A f ( ). 5 = Ω Graphs ha rprsn h ffc of boh local and global updang ar prsnd n fg.6 and fg.7. o = =5 = Fg.6. Go-LANMAR ovrhad cos for fxd A valu (5) and dffrn group dmnson (=, 5, ). Th xprsson abov consss of wo conrbuons: h frs s assocad wh nra-scop roung and h scond on (xra-scop roung) s rlad o h roung bwn LGAs (landmarks). Inra-scop roung ncrass lnarly wh h ncras of h numbr of nods of h group; h roung assocad wh HSLS dcrass as for h ncras n h group dmnson. Th oal ovrhad s: o 3 x = =5 = f ( G ) = Ο( ) N Θ l c = Θ l c o (9) N Θ = Θ ( G ) f = Ω( ) If h conrbuon assocad wh h OLSR ovrhad (nra-scop roung), dpndng by h proocol paramrs, s fxd as follows and R k =: A = hd + τ R D O( ) () k k and h rms assocad o h xra-scop roung (HSLS) s fxd as follows: B = N () B = N () lc Fg.7. Go-LANMAR ovrhad cos for fxd B valu (6) and dffrn group dmnson (=, 5, ). Bcaus wo oppos conrbuons ar obsrvd ncrasng h numbr of nods blongng o groups and mananng fxd h oal numbr of nods n h nwork, a rad-off bwn locaos and globaos assocad o landmark nods can b found. By drva calculaon of h funcons f and f, h valus ha mnmz h cos of Go-LANMAR proocoan b oband: 9 B 5 = wh =, (4) 4 A Th quaon abov prms o oban h omal valu knowng h B and A valus or vcvrsa s possbl o rgula h paramrs of local roung (A) o

8 mnmz h ovrall updang cos of h Go-LANMAR proocol. Bcaus h B rm dpnds from numbr of nods and lnk brakag ra such as shown n q., q.., s possbl only o chang h paramrs assocad o h local lnk-sa roung fxng h numbr of nods blongng o a group. Thus f an opmsd lnk sa roung s appld n h local scop (R <<) an opmal or A valus can b oband, ohrws an ncras n h numbr of group dos no affc h ovrhad assocad o h local scop (h ncras of h cos assocad o h local scop s balancd by h dcras of h cos assocad o h rducd numbr of groups) bu h ovrhad assocad o h HSLS dcrass as xprssd n q.9. 4 Prformanc Evaluaon Th proocol has bn mplmnd n a QUALNET smulaor ha rprsns an xnson of h Glomosm smulaor [9]. Th consdrd channapacy s Mbs/sc. BR sourcs ar usd o gnra nwork daa raffc. Th sourc-dsnaon conncons ar randomly sprad ovr h nr nwork. Durng a smulaon, a fxd numbr of conncons ar manand all h m. Whn on ssson closs, anohr par of communcaons wll b randomly slcd. Thus, h npu raffc load s consanly manand. Th adopd mobly modl s h Rfrnc Pon Group Mobly (RPGM) [,]. Each nod n a group has wo componns n s mobly vcor: h ndvdual componn and h group componn. In our smulaon, h group componn has bn changd n h nrval [- 5 m/s] whl h nra-group movmn has bn fxd o 5 m/s. GEO-LANMAR prformancs hav bn sd undr many scnaros n whch raffc load, mobly ra and nwork sz hav bn consdrd. In ordr o s h scalably of h proocol n rspc o h nwork sz wh group moon a scnaro, whr h numbr of groups s ncrasd, s consdrd. Anohr consdrd scnaro rfrs o a nwork wh havy raffc load and moblby n prsnc of hols. In hs cas, h numbr of conncon pars and h spd of groups ar ncrasd nsd h nwork n ordr o s h scalably of GEO- LANMAR wh rspc o h raffc load and mobly ra. In hs las scnaro h ETD mrc and h hol dcon mchansm hav bn valuad. In summary h consdrd scnaros ar summarzd as follows:. Incrasng Traffc Load: a grd of 5 mrs wh 9 logcal groups s consdrd. Th numbr of conncons s vard bwn 3 and 4 conncons. Each conncon snds packs pr scond and lass 3 sconds.. Mobly wh Hols: n ordr o s h ffcvnss of h novl mchansms (Effcv Travlld Dsanc and Hol dcon) nroducd n GEO-LANMAR, a parcular scnaro has bn bul. In parcular, a grd wh som obsacls has bn consdrd as shown n fg.8. Th mor commonly usd mrcs o valua roung proocols for wrlss ad hoc nworks hav bn consdrd: Pack Dlvry Rao: s h numbr of daa packs dlvrd o h dsnaon nod ovr h numbr of daa packs ransmd by h sourc nod. Avrag nd-o-nd daa pack dlay: ncluds h dlay assocad wh MA rransmssons, quung dlays, pah dour dlay whn local maxmum rcovry procdur s appld for h go-roung and buffrng dlays assocad wh h AODV proocol. Normalzd Roung Ovrhad: s h oal numbr of ransmd conrol packs for ach dlvrd daa pack; for packs sn ovr mulpl hops, ach pack ransmsson (on ach hop) couns as on ransmsson. S3 S S Fg.8. Grd wh obsacls n h mddl of ara. Smulao paramrs ar summarsd n abl I: TABLE I: SIMULATION PARAMETERS Inpu Paramrs Smulaon ara 5x5 m Traffc sourcs BR Numbr of conncons 3-4 Sndng ra packs/s Sz of daa packs 64 bys Transmsson rang 5 m Smulaon Tm 5 s Mobly Modl Mobly Modl RPGM Paus m s Mobly group spd rang [-5 m/s] Mobly nra-group spd 5 m/s Traffc parn Pr-o-pr Smulaor Smulaor QUALNET Mdum Accss Proocol IEEE 8.b Lnk Bandwdh Mbps onfdnc nrval 95% D D D Sourc- Dsnaon Hol Grd whr nods can mov mobl

9 4. Smulaon Rsuls Prformanc valuaons of wo scnaros, such as xpland abov, ar prsnd n h followng: AODV [], LANMAR wh nra-scop OLSR proocol, and GEO-LANMAR wh wo knds of nra-scop roung (OLSR and FSR). 4. Incrasng Traffc Load In hs scnaro, GEO-LANMAR s sd n a suaon of havy raffc load. 3 conncons ar consdrd n fg.9 and fg.. Group mobly s slcd unformly n h rang [- m/s] and h numbr of groups s ncrasd from 4 o 36. For a havy raffc load, LANMAR and GEO-LANMAR prform br han AODV as shown n fg.3. Th racv proocol (AODV) prforms wors bcaus of h ncras n h conrol raffc n buldng h pah oward h dsnaon. Th proocol producs a lo of rou rquss (RREQs) ha consum bandwdh n sp of daa raffc. Th daa pack dlvry rao s prsnd n fg.4. Undr a havy raffc load, LANMAR and GEO-LANMAR ouprform AODV. Furhr, GEO-LANMAR ouprforms LANMAR bcaus manags br h conrol raffc hrough upda rducon n m (upda dffrnad n h valu) and n spac (LSU propagad unl s ). Normalzd onrol Ovrhad Daa Pack Dlvry Raon (%) Numbr of groups Numbr of groups AODV LANMAR GOAL Fg.9. Normalzd onrol Ovrhad vs ncrasng numbr of groups. Th numbr of conncons s 3. Fg. Daa Pack Dlvry Raon vs ncrasng numbr of groups. Th numbr of conncons s 3. AODV LANMAR GOAL Th avrag nd-o-nd dlay s shown n fg.5. kbps corrsponds o 5 conncons whl 8 kbps corrspond o 5 pars of conncons. Th daa pack dlay ncrass for hgh raffc load du o quung dlay. LANMAR and GEO-LANMAR bhav smlarly and hy ouprform AODV bcaus h accuracy of h rou o h landmark provs o b vry cos ffcv, n sp of a possbl mnor dour oward h dsnaon. GEO- LANMAR prforms br han ohr proocols bcaus h go-roung schm wh h rfrnc pon rprsnd by h LGAs prms rachng h dsnaon a a low cos. Avrag nd-o-nd daa pack dlay (msc.) Offrd Load (kbs/sc.) Fg.. Normalzd onrol Ovrhad vs ncrasng raffc load. Th offrd load s ncrasd by ncrasng h numbr of conncons. 4.3 Mobly n prsnc of Hols AODV LANMAR GOAL In hs scnaro, w hav consdrd groups wh 5 nods for ach group. Th group spd, n accordanc wh Random Way Pon modl, s unformly chosn among h followng valus [, 5,, 5, ]m/s. Th moon nsd ach group s characrzd by a spd unformly slcd n h rang [-5m/s]. Th consdrd grd s 5x5m and h ransmsson rang for ach nod s 5 mrs. GEO-LANMAR proocols ar xpcd o prform wll also n mor ralsc scnaros n whch h nod movmn s no oally fr n spac, bu whr hr ar obsacls or nwork parons ha can occur. In hs cas, GEO-LANMAR proocoan mak us of h novl proposd mrc ha accouns for ral ravlld dsanc, and of h hol dcon mchansm. Th capably of sng ovr h local scop hrough lnk-sa propagaon bwn LGAs prms h dcon of a pah no conncd o h dsnaon ha avods long dours. GPSR, on h ohr hand, maks only local dcsons, applyng prmr forwardng ofn. Ths producs long dours for h daa pack and a consqun ncras of nd-o-nd daa pack dlay, as shown n fg.6. LANMAR proocol offrs a lowr dlay han AODV and GPSR proocol. Ths s du, wh rfrnc o AODV, o s hgh conrol ovrhad, whch producs a lo of collsons n h wrlss channl, hus dlayng h daa pack. Insad, h grdy forwardng of GPSR, basd on gomrc dsanc, slcs h wrong nghbour ha, alhough gomrcally nars o h dsnaon, s nar a hol or obsacls, as shown n fg.3. 5 onclusons A novl roung proocol for scalabl wrlss ad hoc nworks wh group moon has bn dvlopd. Th

10 proposd proocol, calld GEO-LANMAR, assmbls mor characrscs blongng o many roung proocols. I uss h da of LANMAR roung o suppor group mobly; appls h roung schm of Trmnods o apply lnk-sa roung for shor dsancs and longdsanc go-forwardng. Th concp of Locaon Group Ara (LGA) s nroducd and a vrual opology of LGAs (landmarks) s bul. Th opology updas of LGAs ar rgulad by HSLS roung. An asympoc analyss of GEO-LANMAR proocol s carrd ou and shows h hgh scalably of h proposd roung schm for ncrasng numbr of groups and nods Avrag nd-o-nd daa pack dlay (msc) Daa Pack Dlvry Rao (%) AODV GPSR GOAL + ETD + Hol Dcon LANMAR GOAL + Hol Dcon 5 5 Maxmum Group Spd (m/s) Fg.. Avrag nd-o-nd daa pack dlay vs ncrasng group spd. Th nra-group mobly spd s 5 m/s. Rrfrncs AODV GPSR GOAL + ETD + Hol Dcon LANMAR GOAL+ Hol Dcon+Ovrhad 5 5 Maxmum Group Spd (m/s) Fg.3. Daa pack dlvry rao vs ncrasng group spd. Th nra-group mobly spd s 5 m/s [] M. Mauv, J. Wdmr and H. Harnsn, A Survy on Poson-Basd Roung n Mobl Ad-Hoc Nworks, IEEE Nwork, no. 6, Novmbr/Dcmbr pp [] B.arp, H.T.ung, GPSR: Grdy Prmr Salss Roung for Wrlss Nworks, Procdngs of h Sxh Annual AM/IEEE Inrnaonal onfrnc on Mobl ompung and Nworkng (Mobom ), Boson, MA, Augus,, pp [3] I. Sojmnovc, X. Ln, Loop-Fr Hybrd Sngl- Pah/Floodng Roung Algorhms wh Guarand Dlvry for Wrlss Nworks, IEEE Transacon on Paralll and Dsrbud Sysms, Vol., n, Ocobr pp.-. [4] J.L, J.Janno, D.D ouo, D.argr, R.Morrs, A Scalabl Locaon Srvc for Gographcal Ad Hoc Roung, Proc.Mobcom,. [5] R. Ramanahan, M. Snsrup, Hrarchcally-organzd, mulhop mobl wrlss nworks for qualy of srvc suppor, Mobl Nworks and Applcaons Journal, pp.- 9, 998. [6] S.-. M. Woo, S.Sngh, Scalabl Roung Proocol for Ad Hoc Nworks, Wrlss Nworks Journal, vol.7, pp.53-59,. [7] G.P, M.Grla, X.Hong,.-.hang, A Wrlss Hrarchcal Roung Proocol wh Group Mobly, IEEE Wrlss ommuncaons and Nworkng onfrnc,. WN99, vol.3, pp , Sp [8] L.Blazvc, J.-Y. L Boudc, S.Gordano, A Locaon-Basd Roung Mhod for Mobl Ad Hoc Nworks, IEEE Transacon on Mobl ompung, vol.3, no.4, Oc.-Dc.4. [9] L.Blazvc, S. Gordano, J.-Y. L Boudc, Anchord Pah Dscovry n Trmnod Roung, nd IFIP-T6 Nworkng onfrnc (Nworkng ), Psa, 9-4 May [] G.P, M.Grla, X.Hong, LANMAR: Landmark Roung for Larg Scal Wrlss Ad Hoc Nworks wh Group Mobly, Proc. of h s AM nrnaonal symposum on Mobl ad hoc nworkng & compung, Nov.. [].A.Sanvanz, R. Ramanahan, Hazy Sghd Lnk Sa (HSLS) Roung: A Scalabl Lnk Sa Algorhm, BBN Tchncal Mmorandum No.3, Mar.3. [].Jacqu, A.Laou, P.Mn, L.Vnno, Prformanc of Mulpon rlayng n ad hoc mobl roung proocols, Proc. of h nd Inrnaonal IFIP-T6 Nworkng onfrnc on Nworkng Tchnologs, Srvcs, and Proocols, pp ,. [3] G. P, M. Grla, T.-W. hn, Fshy Sa Roung n Mobl Ad Hoc Nworks, Procdngs of Workshop on Wrlss Nworks and Mobl ompung, Tap, Tawan, Apr.. [4] P.Bos, P.Morn, I.Sojmnovc, J.Urrua, Roung wh Guarand Dlvry n Ad Hoc Nworks, Wrlss Nworks Journal, vol.7,. [5] F.D Rango, M.Grla, B.Zhou, S.Marano, GoLANMAR: Go Asssd Landmark Roung for Scalabl, Group Moon Wrlss Ad Hoc Nworks, h Inrnaonal onfrnc on Tlcommuncaons (IT 5), apown, Souh Afrca, May 5. [6].A. Sanvanz, R.Ramanahan, I.Savrakaks, Makng Lnk- Sa Roung Scal for Ad Hoc Nworks, Proc. of nd AM nrnaonal symposum on Mobl ad hoc nworkng & compung, pp.-3, Long Bach, A, USA, [7]. Sanvanz, Asympoc Bhavour of Mobl Ad Hoc Roung Proocols wh rspc o Traffc, Mobly and Sz, TR-DSP--5, Dparmn of Elcrcal & ompur Engnnrng Norhasrn Unvrsy, Bosonm MA, Oc.. [8] J. L, Elzabh M.B.-Royr,.E.Prkns, Ad Hoc on Dmand Dsanc-Vcor Roung Scalably, AM SIGMOBILE Mobl ompung and ommuncaons Rvw, vol.6, ssu 3, Jun. [9] M.Taka, L.Bajaj, R.Ahuja, R.Bagroda, M.Grla, Glomosm: A Scalabl Nwork Smulaon Envronmn, Tchncal Rpor 997, Unv.of alforna a Los Angls, ompur Scnc Dparmn, 999S.- [] X. Hong, M. Grla, G. P, and.-. hang, A Group Mobly Modl for Ad Hoc Wrlss Nworks, Procdngs of AM/IEEE MSWM'99, Sal, WA, Aug [] X.Hong, M.Grla, Dynamc Group Dscovry n Ad Hoc Nworks, n Procdngs of h Fourh IEEE onfrnc on Mobl and Wrlss ommuncaons Nworks (MWN ), Sockholm, Swdn, Sp.