On Reliability of Dynamic Addressing Routing Protocols in Mobile Ad Hoc Networks

On Reliability of Dynamic Addr essing Routing Protocols in Mobile Ad Hoc Networks Marce llo Caleff i, Gia ncarlo Fe rraiuolo, L uigi Paur a Depa rtme n t of Elect roni c and Telecom municati on Engine ering (DIET) Un iver si ty of Nap l es “F ed eri co II ” via Claudi o 21, Naples , 80125, Ita ly Tel +39 (0)81 7683810 – Fa x +39 (0)81 7683149 {n ame .su r nam e} @u n in a. it Ab stra ct - In this paper , a rel i abi lity anal ysis i s c arr ied out to stat e a p erfo rma n c e com p ar iso n b etw een tw o re cen tly p ro po s ed proac ti ve r outing algor ithm s. These prot oc ols are able to sc ale in ad hoc and sens or net works by resorti ng to dynami c address ing, to f ace with t he topology var i ab ility, w h ich is ty pi ca l o f ad h oc , and se nsor net wor ks. Numeri c al si mulat ions are als o carr ied out to co rro bo ra t e the re sult s o f th e an a ly si s. I. I NTRODUCTION In Mobil e Ad hoc NETworks (MANETs) and sensor netw o rk s th e sc al abi li ty is a cr it ic al r eq uir e men t if th e se tec hnologi es have to reach thei r full potential. However, mo st of expe rime n te d routi ng protocol s have shown to wo rk sa tisf actoril y only up to few hundred nodes [1]. In fact , su ch protoc ol s, b as ed on t raditi onal routi ng proc edure s, assume t ha t node i de ntity e quals node routi ng address exploit i ng so static addre ssing s cheme s, regardle ss thei r belongi ng class (proac tive , reac tive or the hybri d one ). Such an a ssumption is ce rtai nly unacce p ta ble for ad hoc and sensor net works, due to the node mobili t y and/ or link i nstabilit y. The need of trac king each node positi on ( loc ation manage ment proble m) gives rise to a massi ve overhead proble m as the net work signi ficantl y grows. Rec entl y, se v era l works have sugge sted to separate the tim e-i nvariant node i d enti t y from the routing addre ss, which is tr ansie nt and reflect s the node topol ogi cal positi on insi de the net work. Si nce this approach, referre d to a s dynamic addre ssi ng , needs a mechani sm to provi de a scala ble ma pp ing bet ween node identi t y and rout i ng address , Distri bute d Hash Tabl es ( DH Ts) h av e b een u tili zed . Mo re s pe cif ic ally , in [2 - 3 ] a logi cal t ree struct ure, base d on the address spa ce and built on conne cti vit y am ong the node s, is int roduced. Although t h is st ructure all ows one t o p erform a sim ple a nd man age able routi ng procedure , it lac ks for robustness agai nst mobilit y and/ or li nk fail ures and, moreove r, exhi bits unsat is factory route sele cti on flexibil it y [5]. Ver y re cen tly , in or d er to bo th ma in ta in a l igh t m ech an is m for addre ss all ocation and t o fa ce with the a bove menti on ed lac k of c omple te t opol ogical inform ation, a routi ng prot ocol, refe rred to as the Augmented Tree-ba sed Routi ng (AT R) Thi s wor k is par tial ly suppor ted bot h by Nat ional proj ect Wirele ss 8O2. 16 Multi-a nte nn a m Esh Netw ork s (WO MEN ) under grant number 200509 32 48 and by the It ali an M ini str y of Uni versi ty (MI UR) project S.C o.P.E. . protoc ol , has bee n proposed [6]. T h e ATR protoc ol a ugmen ts the t ree-base d address allocat ion scheme of DA RT protocol [4], by s toring i n the node routi ng table s additi onal inform ati on, i.e. multi ple route s towards the same subset of nodes . E ach node ac quire s this i nformati on si mply by using the underl ying nei ghbor di scoveri ng procedure , w it hout inc reasing t he refore the protoc ol overhea d, wit h respect to DART one, and wit h limited cost s in te rms of memo ry requi rement s on the node . The advanta ge of thi s approa ch is tha t a ric her n et work-t opology knowl e dg e can be e xp loit e d to imp lem ent te mporal mul ti- p ath s tr a teg ies , w h ic h g u aran t e e bet ter pe rformance a nd a hi gher rel iabili ty [7]. Howeve r, with a lit tl e effort, ATR could be eas ily exte nded to s plit data tran sf ers on mu l tip le p ath s in the s pa tia l domain, in order to reduc e conge stion and end-to-e nd delay. This pape r presents a rel iab il ity asses s men t ana ly si s to sub s tan tiat e th e eff ec tiv ene s s of the multi -pa th approa ch of the AT R prot ocol and its supe riorit y wit h respect t o the shortes t-pat h one of DA RT. Th e ou t lin e o f the p ap er i s th e f ollo w in g : in S e ct ion I I, w e short ly pres ent the ATR and DART prot ocols under anal ysis. In Secti on III a framework for carrying out the relia bility ana lysi s is int roduced, whereas in Secti on IV numerical performa nce a nalysis a nd comparis on, using t he framework pres ented in Sect ion III and via si mulati ons, are pres ented. Fi nall y, in Secti on V conclusi ons are drawn. II. D YNAMIC A DDRESSING R OUTIN G P ROTO COLS We give here onl y essential i nformati on on DART and ATR protoc ol s, and remi nd to [4,6] for detai l s. In few words, ATR and DART are based on the same addre ss space structure whic h can be repre sente d by a binary tree of l+ 1 lev el s, wh ere l is the number of bits used for an addres s (Fig. 1) ATR and DART protocols di ffer from the packet forwardi ng proc ess and from t h e way in which the node routi ng ta bles are popula ted. More spec ifi call y, in DART each node m ainta ins onl y one pos sible next hop tow ar d th e fin a l des tinat ion, defining so a uni que route along t he tree st ructure of the addres s space, whereas i n ATR each node maintains and e xplores all the pos sible ways to reach the fi nal des tinat ion, t hrough i t s neighbors . T his is equi vale nt t o us e a n augment e d tree struc t ure to perform forwa rd ing, obtai ned wit hout a dd iti onal overhea d with res pect t o DART. The goal of th is p a per is to s ta te the ef f e ctiv en ess o f th e m u lt i- pa th approa ch, wit h respect t o c la ssic s hortest-pa t h one, by a theo r e tica l r el iab il ity ana ly s is. Fi g u re 1 - A d dr e s s sp a ce s t ru ctu re III. T HEORETICAL R ELIA BILI TY A NA LYSIS A. Defi nit ions and ass umptions Wit h reference to unica st routing, let us defi ne the te rm in a l pair routi ng reli abil ity a s the probabil ity that at least one route bet ween a coupl e of node s e xist s: R st ( G P ) = P (nodes s and t ar e connect ed) (1) wh ere s is the sourc e node , t is th e d est in a tio n o n e a nd G p =(V,E) is t h e proba bil istic di rect gra ph tha t repre sent s the net work t opology, in whi ch a verte x v i  V denote s a node bel ongi ng to t he network, an edge e ij  E denote s the com municat i on link bet ween nodes v i and v j th at o p er at es w i th probabi l ity p ij . The f ailu re ev ents of the ed ges e ij are a ssu m ed to be stati sti call y inde pende nt of eac h other with proba bilit y q ij =1-p ij , wh ile the v er tex es ar e con s id er ed to b e f law les s, i. e . opera tive with probabil it y one [8]. Alt hough in real networks, there may also be outage due to fini te capacit y effec ts cause d by physi cal -la y er a nd link-l a yer cons trai nt s, as well as routi ng rela ted one s, netw ork reli abilit y as sumes that there i s no routing or capa city c onstrai nt on the net work. If at least one route exi sts topol ogicall y bet ween s and t , tha n it is assumed t he packets will discove r and use it. More over, we suppos e tha t the network t opol ogy is static, nam e ly th e p acke t d e liv er y ti me in t erv al s ar e sma l ler th an th e topol ogy varia tion ones [12]. With s uch a n as sumpti on, we us e re li abi li ty m easur e as v alu ab le too l to an a lyze t h e tol e rance of routing prot oc ols agains t the route failure s. B. Exact algor ithm for rou ting re liability To e valuat e the net work re lia bility from a rout i ng point of vie w, we should disti ngui sh be tw een physical a nd o ver l ay gr ap hs rela ted to a n e tw or k . L et’s st art w ith an ex amp le . I n Fig . 2 w e h av e r ep res en ted the ad ja cency m atr ix es ass oc ia t ed wit h the physi cal and ove rlay graphs re ferring t o the same net work wit h 8 nodes. These matrixe s differ onl y from the numbe rs of ‘1’ (communicati on li nks). The mat rix on the left refe rs t o the phys ical gra ph, i.e . t he gra ph in whi ch t he e dge e ij is pre sent i f a physical comm unicati on link is prese nt between the nodes i and j . Th e oth er tw o ma tr ixe s r ep re s ent th e o v er l ay gr ap hs b uilt upon the physi cal n et work by DART a nd ATR route di scovery proc esse s. The absence of ten e dges (‘1’) in the DART matri x, with re spect t o the phys ical and ATR ones, evi dence s the ina bili ty of shortes t-pat h routing protoc ols to buil d a comple te topol ogica l view of the net work Figu re 2 - Adja cenc y ma tr ix fo r a 8 no d es net wor k. The ed ge s e t E of an overla y graph could be de fined as: E = E st s , t  V  (2) wh ere E st = e ij  P st {} and P st is t he col lecti on of s-t paths dis cove red by the routi ng prot ocol. Fi g. 3 shows the overla y graphs as sociate d w it h the diffe rent route discove ry results for th e same full-mesh 4 nodes net work. M ore specif ical ly, t he gra phs show t he routes from eac h node towa rds two destina tions , say node ‘2’ a nd ‘4 ’. Thi s kind of re presenta ti on underli nes some nota ble as pect s of the r ou t e d is cov ery p ro c ess . Th e fir s t is th e pr esen ce ( o r n o t) of mu lt ip l e pa th s tow ard s th e s a m e d es tin at ion . F ur th er, it all ows one to rec ognize if the multi p le paths are di sjoi n t or part ia lly dis joint a nd how m any li nks are sha red by the routes. Fi nall y, it s hows that a hiera rchical s hortest -path routing protoc ol as DART one does not f ind eve ry time the shortest ro ute, du e to its hi er arch ic al na tu re ( in the ex a mp l e, t he short est route is the si ngle hop one). Figu r e 3 – G r a phs re f err in g to ro ute di sc over y pr oces s. Our approa ch to evaluate the routing reli abili t y is base d on enum erati ng all the mi n imal e dge cut s ets of the graph rep res en tin g the n e tw or k , wh er e a m in im al cu t s e t is d efin ed as a mi nimal s et of elem e nts whos e fai l ure im plie s that some nodes cannot c ommunicate . We have gene ralize d the al gorit hm prese nted in [9] i n order to obt ain a sym bolic expre ssion for the routi ng relia bilit y, which is function of the link fa ilu r e pr o ba bi l ity . T his al lo w s o ne to easy ev alu at e th e reli abili t y in diffe rent e nvironm ental c ondi tions . An aly tic a lly , th e m ean ter m in a l- pair ro u ting r el iab il ity is : R = z st R st t  s  s  n ( n  1) (3) wh ere n = V , z st is the proba bilit y of a dat a flow bet ween { s,t } and R st is the termina l pair routi ng rel iabil ity de fine d as: R st ( G , p ) = 1  C i ( G , s , t ) p m  i (1  p ) i i = c m  (4) wh ere m = E , G=(V,E st ) is the overla y graph gene r ate d by the routi ng discove ry proces s, p  p ij is the l in k su c ces s pr o ba bili ty ( a ssu m ed f o r s im p li ci ty the s a me f o r an y p air of nodes ), c is the mini mum cut of the gra ph b et ween { s , t } a nd C i is the num ber of { s , t } cu t s ets co mp o sed ex a ct ly b y i ed g e s. Li sti ng 1 shows our proposal to exact compute both symbol ic and nume rical relia bili ty (4). Furthe r detail can be found in [9]. Lis tin g 1 – R ecu rsiv e(G , HA S H,S S ,n,t ,no tR e l,sy mb) // Re li abilit y = 1 – Rec ursive (…) out put // G is th e ad jac e ncy ma tr ix re la ted to th e o ve rl ay gr ap h // H A SH is a col le c tio n of min im al cut s et in it ia lized to em p t y // S S is the under ana l y si s minimal cut set init iali zed to em pty // n i s in i ti al iz ed to s if ( n = = t) r etu rn ; merge (G, SS, n); // Me rging node n in SS abs orb(G, SS, t); // Abs orbing re dundant node s in SS if ( HA SH .is P res en t( SS )) r etu r n ; HASH.i nsert(SSt); find a cuts et C of S S; symbT emp = “(1-p)^” + C.si ze.toSt ring; te mp = 1.0; symbTe mp = symb + " + p * ( “ + symb Te mp; fo r each ed ge in C tem p = pFaile d * temp; end fo r each node a djace nt t o SS Re cur siv e(G ,HA SH ,SS ,n ,t ,tem p, s ymb ) ; tem p = pSucce ss * te mp; end symbTe mp = sy mb Temp + “)”; notRe l = no tRe l + tem p; C. C onside rati ons on comput a ti onal ti mes The problem of calc ulati ng the routi ng reli abili ty as te rminal-pai r reliabil ity is c omputati onally ha rd, even in spe cial ca ses, since it belongs to t he cla ss of #P  co m ple t e pr ob lems [ 1 0] , wh ich ar e at le ast as d iff icu l t as th e o n es in t h e clas s of NP -complete proble ms. There fore, we are l ooking f or some useful bounds , whic h make easy to analyze the gai n of a mu lt i-p a th ap p ro ach w ith re sp ec t to the tr ad itio n a l sh or t es t- pat h one. Work is in progress t o prove that the reli abili ty of any s hortest -pat h routi ng protocol coul d be upper bound by a power of p , whe re the expone nt is relat ed to t he number of nodes in t he net work. Moreove r, we a re tryi ng to bound t he reli abili t y for a mult i-pat h rout ing prot ocol wit h a pol ynomial expre ssion. IV. R OUTING PER FORMANCE ANALY SIS In thi s s ec tion , w e an a ly ze th e p erf or man ce of D A R T an d ATR protocol s by ass essi ng the relia bilit y (3) a nd we ve rify that th e re su l ts o f su ch theo r e tica l an a lys is ag re e w i th th e on es bas ed o n a tr ad i tion a l me tr i c su ch as th e p ack et d eliv er y r a t io obta i ned via numeric al si mulati ons. A. Exact algor ithm for rou ting re liability The Listing 1 ta kes a s input t h e adja cenc y matrix as sociate d with th e ov erl ay g rap h , wh ich is, as i llu s tra ted in S ec tio n I II , the ove rlay graph is the result of the route di scovery process performe d by the routi ng prot o col . In order to ge n erate the overl ay graph, we have tested DART and AT R via ns -2 net work simulator [11] (see Section IV.B for further details ) wit h stat ic t opologie s. T h en we have ext racte d from each node the p ath s in fo r mat ion em bed d ed in th e rou ting tab le . Th is inform ati on has been exploite d to build the overla y gr aphs util iz ed to c o mput e the mea n network rel iabil ity as i n (3) and it s standa rd deviati on as functi on of p. Fi g. 4 c o mpar es the mea n network re liabil ity (3) of DAR T and ATR for a full-m esh topol ogy wit h four nodes. The res u lts con fir m th e cap abi li ties of A TR mul ti- path ap p ro ach to ta k e adva ntage of redundant rout e s als o in presence of a few nodes. The ef f e c tiv en ess o f th e mu lt i-p ath app r oach is p art icu lar ly marke d for values of p near ‘0 .5’ . F i gu r e 4 - Reliabili t y for 4 no des full m esh t opology In Fi g. 5 we present the relia bili ty (3) for a random topology wit h 16 node s and a densit y of 64 node s/ Km 2 . T h is fi gure shows t hat the ATR signi fica n tl y outperform s DA RT, thanks to th e av a il ab il ity o f m u lt ip l e p a th s. Mo r eo v er, w e o b ser ve tha t the reli abilit y of ATR for the 16 nodes topol ogy (Fig. 5) is highe r t han that obt aine d for a t opol ogy with 4 node s (Fi g. 4) for any va lue of p . T his fact cl ea rl y e vide nce s that t he m ulti - path ap pr oach b ecom es mo r e ad van tageo u s wh en th e n um b er of redunda nt pat hs scales . Figu re 5 – Re l i ab i l ity f o r hi g h dens ity 1 6 no de s to p o l o gy Fi g. 6 ill ustrates the relia b ili t y (3) for a random topol ogy wit h 64 node s and a de nsity of 25 node s/ Km 2 . In t his ca se, a lowe r numbe r of redunda nt pat hs, com p are d with t he 16 nodes topol ogy (Fi g. 5), give s rise to l ower values of ATR reli abilit y. Simila rly, the DA RT p erformance is low er then tha t as sociat ed w it h respect to the higher node densit y case (Fig. 5). F i gu r e 6 - Reliabilit y for low d e nsi t y 64 nod es to polo g y B. Simulation r esults In this sub-secti on, we present result s of a performanc e ana lysi s of the propose d routing prot oc o ls , ac hieve d by nume rical expe rime n ts carrie d out by resorting to ns-2 (vers ion 2. 30) network simula t or [11]. W e adopt t he standard val ues for bot h the physica l and t he li nk layer t o simulate an IEEE 802. 11a Lucent network inte rface with Two-Ray Ground as channel m odel (whe re the li nk success probabili ty is ‘1’ in the tr an s mis s ion r ang e) . Here , we prese nt only sim ulati on res ults to veri fy that t he res ul ts o f th e th eor et ic al r e li abi li ty an aly s is p rev io u s ly report ed agree with the one s based on traditi ona l routing metr ic , s uch as p acke t d e l iver y ra tio . A m or e d eta il ed performa nce compa rison of the two prot ocols can be found in [6]. For all t he simula tions , we a dopt the Random Waypoi nt mobi lit y model, with the speed val ues randomly taken in the [0.5m/ s; 5m/s ] range, and the pa use time in [0s ; 100s]. Alt hough much more reali stic mode ls are availa ble in lit e rature, w e have adopte d t h e Random Waypoi nt one si nce, due t o it s sim plici t y, it ha s bec ome a st anda rd choice . Each tria l is 750 sec onds long, with t he first 450 free of mobilit y and da ta t ra ffic, dedica ted t o t h e a ddres s a lloca tion process. The size of sim u lat ion area is chosen in orde r to keep steady the node density. Sim ulati on result s r efer to a density of 64 nodes /km 2 , which corres ponds to a node connecti vit y degree of 12; this value guara ntees for most of the cases a conne cted topol ogy. The data tra ffic is model ed as CBR flows over UDP protoc ol and t he global t hroughput is kept cons tant a t 250Kb it/s . The s tar t and th e en d t im e of ea ch f lo w a r e randoml y selecte d in the i n te rval [450s; 730s] acc ording to a uniform dist ributi on, and t he number of flows grows wit h the number of node s N . Since we do not de al wit h DHT laye r, this is replac ed in the sim ulati ons by a globa l known table . Here we compare DART and ATR using the packet del i v ery rati o. Fig. 7 shows the rati o of correctl y delive red pack e ts w ith r esp e ct to th e to ta l nu m b er o f se n t p a ck ets f o r both DART and ATR, normali zed t o the ATR value s, versus the number of node s. The experiment al res ults show that AT R sc ale s always bette r than DART in terms of packet del i v ery rati o, due to it s multi -pat h charact eris tic. Let us underli ne that , as the number of nodes grows, the link failures , due to mo bil ity an d/o r col li sio n effe c ts, m ak e the mu lt i- p a th approa ch more effe cti v e with respect to the shortest -path one, confi rmi ng so the reli abili t y anal ysis res ults of Sec tion 4. A. Fi g u re 7 - N o r m a l ized p a ck et de l iv e ry ra t i o V. C ONCLUSIONS AND F UTURE W ORKS In th is p ap e r, a th eo r et ic al r e liab il ity an a ly sis o f rec en t ly propose d DART and ATR rout ing protoc ols for MANETs and se nsor networks is pre sented. An effective met hod t o eval uate routi ng re lia bility i s proposed, a nd it is used t o compare the two c onside re d protoc ols. The result s of the t heoreti cal ana lysi s are also in agreeme nt with thos e based on a trad i tion al m etr ic, s uch as th e p ack e t de liv ery r a tio o b t ain ed by n u mer ic al s im u la tio n s . 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