A DISTRIBUTED ALGORITHM FOR MULTIPATH COMPUTATION

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1 A DISTRIBUTED ALGORITHM FOR MULTIPATH COMPUTATION SRINIVAS VUTUKURY Computer Scences Deprtment Unversty of Clforn Snt Cruz, CA J.J. GARCIA-LUNA-ACEVES Computer Engneerng Deprtment Unversty of Clforn Snt Cruz, Clforn Networng n Securty Center Sun Mcrosystems Lortores Plo Alto, Clforn Astrct Toy s Internet routng protocols ether prove sngle pth etween ech source-estnton pr, or multple pths of equl length. Furthermore, the pths prove y RIP n OSPF re not free of loops urng tmes of networ trnston. Sngle-pth routng lgorthms re nherently slow n responng to congeston n temporry trffc ursts; consequently, the elys experence y pcets n these networs re fr from optml. Recently, we evelope frmewor for esgnng routng lgorthms tht offer ner-optml elys; ey component n ths frmewor conssts of usng fst responsve routng protocol tht uls multpths for ech estnton n the computer networ, such tht they re loop-free t ll tmes. Ths pper stues the performnce of MPATH (multpth routng lgorthm) y smulton n compres t gnst the performnce of other stte-ofthe-rt routng lgorthms. I. INTRODUCTION The elys experence n the networs tht use routng lgorthms such s RIP[10] n EIGRP[1] re fr from optml, ecuse these lgorthms prove only sngle pth etween ech source-estnton pr for pcet forwrng. OSPF[14] llows router to choose from more thn one pth to the sme estnton only when multple pths of mnmum cost ext, whch mens the full connectvty of the networ s stll not use for pcet forwrng. To relze mnmum-ely routng[4], the pcet forwrng tles must represent recte-cyclc grph nste of tree, wth the estnton s the sn noe. Recently, we escre prctcl frmewor to otn ner-optml elys [21] n ynmc networs. A ey component of ths frmewor s fst responsve routng lgorthm tht computes multple pth etween ech sourceestnton pr, such tht they nee not ll hve the sme length n re loop-free t every nstnt n stey stte s well s urng networ trnstons. By lo-lncng trffc over these multple pths, congeston cn e reuce n elys cn e sgnfcntly ecrese. Unfortuntely, most routng lgorthms o not ul loop-free multple pths. In [8], we performe lo-lncng over loop-free multpth compute usng the stnce-vector routng lgorthm Ths wor ws supporte n prt y the Defense Avnce Reserch Projects Agency (DARPA) uner grnts F n F C DASM [22], n reuces elys rmtclly. In [21], we presente the frst ln-stte lgorthm tht computes loopfree multpths n use t to mplement the ner-optml frmewor. Recently, we ntrouce new loop-free multpth routng lgorthm clle MPATH [19] n prove ts correctness n nlyze ts complexty. In ths pper, we contnue the stuy of MPATH y comprng ts control messge overhe n convergence tme through smultons wth two other routng lgorthms. The pper s orgnze s follows. Secton II escres the MPATH routng lgorthm. Secton III gves survey of vrous lgorthms n proves comprtve stuy wth respect to MPATH. The smulton results n comprsons re presente n Secton IV. Secton V proves conclung remrs. II. MPATH ROUTING ALGORITHM Ths secton llustrtes the mn concepts n the routng lgorthm MPATH. For etle forml escrpton, correctness proofs n nlyss, the reer s referre to [19] n [21]. The sc pproch conssts of noes frst computng shortest stnces to estntons n then usng the stnces long wth certn constrnts (whch we cll loopfree nvrnts) to otn loop-free routng grph for ech estnton. Let N represent the noes n the networ n N e the set of neghors of n rtrry noe, nletsj enote the set of next-hop choces (or successors) t noe for forwrng pcets estne to noe j. Then the gol of MPATH s to mntn the routng grph enote y the ln set SG j = f(m; n)jn 2 Sj m ; m 2 N g n presence of chngng ln costs, such tht t s recte cyclc grph t every nstnt. In contrst, the successor sets n OSPF s efne s S j = f 2 N j D j + l = D j g,whered j n D j re the shortest stnces of noes n to j, nl s cost of ln (; ). In sngle-pth routng protocols (e.g., RIP n EIGRP), the set Sj s restrcte to t most one memer, nctng tht the routng grph SG j s sn-tree roote t j. The ey e s to generlze the shortest-pth trees to shortest-multpths; thts,s j = f 2 N jd j + l = D j g

2 s extene to Sj = f 2 N jdj < Dj g. Fg. 1(A) shows n exmple of networ wth shortest-pth tree for c n Fg. 1(B) n the shortest-multpth n Fg. 1(C). For ulng shortest multpths, we requre strute lgorthm to compute shortest stnces for ech sourceestnton prs. Though there re mny lgorthms for shortest-pth computton, we present new shortest-pth lgorthm. In ln-stte lgorthms such s OSPF, ech router stores n forwrs costs of ll lns n the networ. It ws shown n LVA [6] n MPDA [21] tht t s suffcent for ech noe to store the costs of only those lns tht re on the shortest pth tree. Smlrly n MPATH, noe stores costs of lns on ts shortest pth tree n copy of ech neghor s shortest-pth tree. However, nste of communctng ln costs rectly s n MPDA, noes n MPATH exchnge stnces to estntons long wth the ress of the secon-to-lst, or preecessor, noe on the shortest pth to the estnton le n LPA [7]. MPATH trnsltes ths nformton to ln costs n nternlly wors wth lns rther thn stnces, n when chnges to topologes hve to e reporte, the nternlly represente topology s trnslte c to stnces n preecessors. In Fg.1(B), for exmple, s the preecessor noe on the shortest pth from to c. Usng stnces n preecessors for ll noes,, c n, the complete tree cn e esly constructe t the recevng neghor. Fg. 2 shows nformton mntne t two rtrry jcent noes n. T s the shortest pth tree of noe n T s the copy of the shortest pth tree T of neghor. Smlrly t, T s copy of the tree T.The sc strute shortest-pth lgorthm s smple n s s follows. Ech noe repetely executes the followng two steps untl there re no more chnges to ts shortest-pth tree T. 1. Construct the noe s shortest pth tree T from the costs of the jcent lns n the shortestpth trees T reporte y the neghors 2 N. 2. Report the new shortest pth tree T to ll ts neghors usng stnces n preecessor nformton. Note tht noe lwys hs the current cost of the jcent ln costs n step (1). However, the noe hs no wy to vlte the costs of non-jcent lns reporte y the neghors. Therefore, the noe trusts the ln-cost reporte y neghor s long s t s not n jcent ln n oes not conflct wth the cost reporte y nother neghor for the sme ln. If two neghors report the cost of the sme ln whch re fferent, the noe must resolve the conflct n choose the cost t consers most ccurte. The followng conflct resoluton rule s use. If two or more neghors report conflctng nformton regrng the sme ln, then the noe must eleve the neghor tht offers the shortest stnce to the he of the noe c 1 (A) c (B) Fg. 1. Shortest-pth tree n Shortest multpth Fg. (2) vsully llustrtes the resoluton rule. Assume the ln (m; n) sreportey two neghors p n q wth fferent ln costs. Then the cost of the ln (m; n) reporte y p s use to upte the mn tle f the stnce D p m + l p s less thn D q m + l q. The remrle fct s tht ths greey pproch to ln-cost vlton s suffcent for purgng outte ln nformton from the networ. We generlze tht rule to lns of ny costs n pply t n the context of propgtng prtl topologes. After mergng ll the neghor trees nto composte grph, the shortest-pth lgorthm s run on the grph to otn the tree T. The proof tht the topology T t ech noe converges to the correct shortestpth tree s presente n [21]. Smlr resoluton rule s use n SPTA[2] n the context of unt ln costs n rocstng complete topology. It s not necessry to report the complete tree s step (2) nctes; only chnges to the shortest-pth tree nee to e reporte s escre n MPDA [21]. p q Tp p m n q Tq m n T T T Fg. 2. Noe nformton Loop-free Invrnts Constructng the set Sj = fjdj < Dj ; 2 N g s not strght forwr. The vlue Dj s not n noe s locl memory. It s vlue communcte (rectly or nrectly) y the neghor n store n the locl vrle Dj n the tree T. Accorngly, noe cn only compute Sj = fjdj < D j ; 2 N g. However, ecuse of non-zero propgton elys, the vlues of Dj n D j cn e nconsstent urng networ trnstons. Smlrly, the copy of stnce Dj t neghor, D j, cn e nconsstent wth Dj except n stey-stte. In stey-stte, ssume tht c (C) T neghor s usng s successor for estnton j. Then Dj = Dj >D j = Dj.LetD j ncrese to vlue greter

3 thn Dj ue to networ event. Noe shoul now use s successor, ut ng n the successor set Sj wthout restrnt woul result n loop. Therefore, the neghor must frst remove from ts successor set efore cn put n ts successor set. Ths requres neghor-to-neghor synchronzton. Noe frst reports ts new stnce to the neghor n cn to ts successor set only fter cnowleges the new stnce n removes from ts successor set. To ccomplsh ths, we use new vrle FDj, clle the fesle stnce, to compute the successor sets. FDj closely follows the vlue of Dj whle lwys stsfyng the followng loop-free nvrnts. FD j(t)» D j(t) 2 N S j(t) = f j D j(t) <FD j(t)g Whenever Dj ncreses neghor-to-neghor synchronztonsusesothtfdj s ncrese to D j only fter the copy of Dj s properly upte t the neghors. It s prove n [19] tht the LFI contons ensure loop-freeom of the successor grphs SG j t ll tmes. The lgorthm MPATH ensures tht t convergence FDj = Dj = Dj for ll n j n 2 N, whch mples tht the routng grph t convergence s the requre shortest-multpth. III. COMPARISON WITH OTHER ALGORITHMS A. Dstnce-vector lgorthms RIP[10] s se on the Dstrute Bellmn-For (DBF) lgorthm for computng the shortest-pths to estntons. In networs tht use RIP, noes exchnge only stnces to estntons n hve no nowlege of the networ topology, n ue to lc of ths nformton they suffer from the nfmous countng-to-nfnty prolem[2]. Severl technques hve een propose to tcle ths prolem. DUAL[5], whch s the lgorthm use n EIGRP [1], uses ffusng computtons [3]. In ton to DUAL, severl lgorthms se on stnce vectors hve een propose tht use ffusng computton to overcome the countng-to-nfnty prolem of DBF [17], [13], [12], [22]. Jffe n Moss[12] llow noes to prtcpte n multple ffusng computton of the sme estnton, whch requres use of unoune counters. In contrst, DUAL restrcts noe to prtcpte n only one ffusng computton t ny one tme for ny estnton. All these routng lgorthms prove only one loop-free pth to the estnton. Zumen n Grc-Lun-Aceves [22] presente DASM, whch s the frst stnce-vector lgorthm tht proves loop-free multpths. DASM s shown to perform etter thn DUAL, whch ws prevously the est stnce-vector lgorthm. All the lgorthms mentone ove use ffusng computtons tht potentlly spn the whole networ. In contrst, MPATH uses only sngle-hop synchronzton,.e., noe nees xto synchronze only wth ts neghors. It s nterestng to see how these synchronzton mechnsms nfluence the convergence tmes. For ths reson, we chose DASM s the cnte routng lgorthm se on stnce vectors wth whh to compre MPATH. B. Ln-stte lgorthms In ln-stte lgorthms, full topology nformton s flooe through the networ. When peroc uptes re me s n the cse of ner-optml routng, the overhe s very hgh. Routng protocols se on topology-rocst (e.g., [18], [15] ) ncur too much communcton overhe, whch forces the networ mnstrtors to prtton the networ nto res connecte y cone. Ths mes OSPF complex n terms of router confgurton requre. A couple of routng lgorthms hve een propose tht operte usng prtl topology nformton (LVA [6],ALP [9]) to elmnte the mn lmtton of topology-rocst lgorthms. In the ove ln-stte lgorthms noes stngush new n ol ln nformton usng sequence numers, whch re not only n e overhe ut lso requre to e reset o occsons. Inste of sequence numers, MPATH uses novel upte rule to stngush ol n new nformton. Le the ln-stte lgorthms MPATH s free from count-to-nfnty prolem. In OSPF, multple equl-cost pths re compute to ech estnton f they exst. However, these pths re not loop-free urng networ trnstons, n even f short-lve, these loops my cuse ncorrect ln-cost mesurements. In contrst, MPATH mntns multple pths tht nee not e of equl cost n whch re loop-free t every nstnt. Severl strute shortest-pth lgorthms [11], [16], [7] hve een propose tht use the stnce n secon-to-lst hop to estntons s the routng nformton exchnge mong noes. These lgorthms re often clle pth-fnng lgorthms or source-trcng lgorthms. Though they exchnge stnces le the stnce-vector lgorthms, they re n to ln-stte lgorthms ecuse they nternlly mntn pth nformton otne usng the preecessor nformton; stnce-vector lgorthm hve no nowlege of networ topology. These lgorthms elmnte DBF s countng to nfnty prolem usng the pth nformton. Some of them [7] re more effcent tht ny of the routng lgorthms se on ln-stte nformton propose to te. Furthermore, LPA [7] s loop-free t every nstnt, ut proves only one pth. MPATH s the frst pth-fnng lgorthm tht uls multple loop-free pths. As n LPA, the synchronzton n MPATH s gere towrs provng loop-free pths. IV. SIMULATION RESULTS The smultons compre the control overhe n convergence tmes of MPATH, topology rocst n DASM. The reson for choosng topology rocst s tht t s the

4 pproch use n OSPF, for whch commercl mplementtons exst n t proves multple pths of equl length. Its convergence tme s frly constnt n epens on the meter of the networ. Ielly, MPATH shoul pproch the convergence tmes of topology rocst, tht s, the extr tme neee to enforce loop-freeom shoul e neglgle. We expect MPATH to hve fr less messge overhe, ecuse of ts relnce on only prtl topology nformton. On the other hn, DASM s the only pror stncevector routng lgorthm tht proves loop-free multpths to ech estnton, n hs een shown to e more effcent thn DUAL, whch s use n EIGRP. DASM cheves loop-freeom through ffusng computtons tht spn the whole networ. In contrst, MPATH uses only neghor-toneghor synchronzton. It s nterestng to see how convergence tmes re effecte y the synchronzton mechnsms. Also, t s not ovous how the control messge overhes of DASM n MPATH compre. The performnce metrcs use for comprson re the control messge overhe n the convergence tmes. The smultor s n event-rven rel-tme smultor clle CPT. Smultons re performe on the CAIRN topology, whch ws lso use n [20]. The topology s flt n we o not use re ggregtons n the smultons. There s no reson to eleve tht the presence of res woul fvor one routng lgorthm over others. Two types of events re trggere n the networ: lnsttus chnges n ln-cost chnges. Ln flures n ln recovery events re clssfe s ln-sttus chnges. In prctce, lns n noes re hghly relle n chnge sttus much less frequently thn ln costs whch re functon of the trffc on the ln. We o not smulte noe flures ecuse of the prolems resultng ue to loss of sequence numers y the noes, whch only effect the functonng of topology rocst here. Specl reset protocols tht scover sequence numers shoul e mplemente for topology rocstng se on sequence numers. We lso restrct ln-sttus chnges to sngle chnge; tht s, only one ln flure or ln recovery cn occur t ny tme urng the mesurement ntervl. Becuse the lns n noes n the networ re hghly relle, smultneous multple topologcl chnges re much less lely to occur n t s resonle to ssume tht tles converge etween topologcl chnges. However, ln costs of multple lns cn chnge smultneously n repetely efore the tles converge to the ltest costs. Ths s the cse when ner-optml ely routng of [21] s use, n whch the ln costs re peroclly mesure n reporte. For these resons, we smulte only sngle ln-sttus chnges n multple ln-cost chnges. Ln-sttus chnges: Ech ln n turn s me to fl n then recover, n the control messge overhe n convergence tmes re mesure n ech cse. The worst-cse n the verges of control messge overhe n convergence tmes for ln flures n ln recoveres re gven n Tle 1. Fgs. (3)-(6) gve the performnce fgures for ech event. For revty, the performnce curves for topology rocst re lele TOPB. For ln flures n recoveres MPATH hs lower verge messge overhe thn TOPB, whch s ue to the use of prtl topologes n MPATH, compre to full topologes n TOPB. However, MPATH ncurs hgher worst-cse messge overhe thn TOPB, ecuse of the synchronzton use n MPATH to prove loop-freeom. MPATH hs lrger overhe (n ytes) thn DASM uner ln recoveres, ecuse nether nvoes synchronzton, ut MPATH exchnges preecessor nformton n ton to stnces. However, DASM requres more messges uner ln-flures ecuse of the multhop synchronzton tht DASM uses. The sme rgument cn e pple for the convergence tmes. TABLE 1 Control messges (ytes) Worst-cse Avg St-ev Ln flures TOPB DASM MPATH Ln recoveres TOPB DASM MPATH Ln-cost chnges TOPB DASM MPATH Convergence tmes (ms) Worst-cse Avg St-ev Ln flures TOPB DASM MPATH Ln recoveres TOPB DASM MPATH Ln-cost chnges TOPB DASM MPATH Multple ln-cost chnges: When ner-optml routng frmewor s mplemente, multple lns chnge costs. To stuy the protocol overhe uner such scenros, multple smultneous ln costs re chnge n the performnce s mesure. Ln costs re chosen rnomly wthn rnge. The verge messge overhe n convergence tmes re shown n the Tle 1. MPATH hs lower worst-cse n verge messge overhe thn TOPB n DASM. MPATH hs lower worst-cse n verge convergence tme thn DASM. The verge convergence tme for MPATH s lso

5 0 MESSAGE LOAD IN BYTES TIME IN MILLISECONDS MESSAGE LOAD IN BYTES TIME IN MILLISECONDS Fg. 3. Ln flures. Messge overhe Fg. 4. Ln flures. Convergence tmes Fg. 5. Ln recoveres. Messge overhe Fg. 6. Ln recoveres. Convergence tmes lower thn TOPB. Only n the cse of worst-cse convergence tme, MPATH showe hgher vlue thn n TOPB, whch s gn ue to synchronzton use n MPATH. V. CONCLUDING REMARKS The performnce of new loop-free multpth routng lgorthm clle MPATH [19] s compre wth two stte-ofthe-rt routng lgorthms. The lgorthm hs low control messge overhe ecuse of ts relnce on reportng only prtl topology nformton. By vrtue of ts one-hop synchronzton, the convergence tmes of the lgorthm re etter thn those of stnce-vector routng lgorthms tht use ffusng computton tht potentlly spn the entre networ. The multple successors t noe me vlle y the lgorthm cn e use for trffc lo-lncng n cn prove vlule n the nternet for hnlng congeston n mnmzng elys. REFERENCES [1] R. Alrghtson, J.J. Grc-Lun-Aceves, n J. Boyle. EIGRP-A Fst Routng Protocol Bse on Dstnce Vectors. Proc. Networl/Interop 94, My [2] D. Berses n R. Gllger. Dt Networs. Prentce-Hll, [3] E.W.Djstr n C.S.Scholten. Termnton Detecton for Dffusng Computtons. Informton Processng Letters, 11:1 4, August [4] R. G. Gllger. A Mnmum Dely Routng Algorthm Usng Dstrute Computton. IEEE Trns. Commun., 25:73 84, Jnury [5] J.J. Grc-Lun-Aceves. Loop-Free Routng Usng Dffusng Computtons. IEEE/ACM Trns. Networng, 1: , Ferury [6] J.J. Grc-Lun-Aceves n J. Behrens. Dstrute, sclle routng se on vectors of ln sttes. IEEE Journl on Selecte Ares n Communctons, Octoer [7] J.J. Grc-Lun-Aceves n S. Murthy. A pth-fnng lgorthm for loop-free routng. IEEE/ACM Trns. Networng, Ferury [8] J.J. Grc-Lun-Aceves, S. Vutuury, n W. Zumen. A Prctcl Approch to Mnmzng Delys n the Internet Routng Protocols. ICC 99, [9] J.J. Grc-Lun-Aceves n M. Spohn. Sclle ln-stte nternet routng. Proc. Interntonl Conference on Networ Protocols, Octoer [10] C. Henrc. Routng Informton Protocol. RFC, 1058, june [11] P. A. Humlet. Another Aptve Dstrute Shortest Pth Algorthm. IEEE Trns. Commun., 39: , June 91. [12] J. M. Jffe n F. H. Moss. A Responsve Dstrute Routng Algorthm for Computer Networs. IEEE Trns. Commun., 30: , July [13] P. M. Merln n A. Segll. A Flsfe Dstrute Routng Protocol. IEEE Trns. Commun., 27: , Septemer [14] J. Moy. OSPF Verson 2. RFC, 1247, August [15] R. Perlmn. Fult-tolernt rocst of routng nformton. Computer Networs n ISDN, 7, [16] B. Rjgopln n M. Fmn. A Responsve Dstrute Shortest- Pth Routng Algorthm wth Autonomous Systems. Internetworng: Reserch n Experence, 2:51 69, Mrch [17] A. Segll. Optml strute routng for vrtul lne-swtche t networs. IEEE Trns. Commun., 27: , Jnury [18] J. Spnell n R. Gllger. Event Drven Topology Brocst wthout Sequence Numers. IEEE Trns. Commun., 37: , [19] S. Vutuury n J.J. Grc-Lun-Aceves. An lgorthm for multpth computton usng stnce-vectors wth preecessor nformton. Proc. of ICCCN, Oct [20] S. Vutuury n J.J. Grc-Lun-Aceves. A Sclle Archtecture for Provng Determnstc Gurntees. Proc. of ICCCN, Oct [21] S. Vutuury n J.J. Grc-Lun-Aceves. A Smple Approxmton to Mnmum Dely Routng. Proc. of ACM SIGCOMM, Sept [22] W. T. Zumen n J.J. Grc-Lun-Aceves. Loop-Free Multpth Routng Usng Generlze Dffusng Computtons. Proc. IEEE IN- FOCOM, Mrch 1998.