On the Protection of Multicast Trees in All Optical Networks Using the NEPC Strategy

Transcription

1 On th rottion of Multist Trs in All Optil Ntworks Using th NEC Strtgy Miklós Molnár To it this vrsion: Miklós Molnár. On th rottion of Multist Trs in All Optil Ntworks Using th NEC Strtgy. RR-11022, <lirmm > HAL I: lirmm Sumitt on 27 Jul 2011 HAL is multi-isiplinry opn ss rhiv for th posit n issmintion of sintifi rsrh oumnts, whthr thy r pulish or not. Th oumnts my om from thing n rsrh institutions in Frn or ro, or from puli or privt rsrh ntrs. L rhiv ouvrt pluriisiplinir HAL, st stiné u épôt t à l iffusion oumnts sintifiqus nivu rhrh, puliés ou non, émnnt s étlissmnts nsignmnt t rhrh frnçis ou étrngrs, s lortoirs pulis ou privés.

2 On th rottion of Multist Trs in All Optil Ntworks Using th NEC Strtgy Miklós Molnár Univrsity Montpllir 2, IUT, Dp. of Comp. Si., Lortory LIRMM - UMR CC 477, 161, ru A Montpllir Cx 5, Frn molnr@lirmm.fr Astrt. Du to th hug volum of th rri t in ll optil ntworks, th ility of ths ntworks to op with filurs oms ruil. On of th propos mhnism is th prottion of th routs (lightpths n light trs) with th hlp of promput ns rsrv kup routs prmitting to rpily hng th routs in th s of filurs. Th prottion with p-yls is n ffiint mtho, whih ws originlly propos to prott on-yl n strling links. Rntly th yli prottion ws xtn to prott nos in lightpths n in light trs. As light trs n ontin som rnhing nos whr th inoming light is spitt to svrl outgoing su trs, th prottion of ths kin of trs is mor lit. In opqu ntworks whr th swiths my virtul sours, ffiint yl-s prottion shms n omput sin h no n th sour of nwly insrt light rnhs on n ritrry promput yl. Contrrily, with th pprition of optil swiths n ll optil solutions in or ntworks, th prottion shm shoul orrspon to stringnt optil onstrints. Nmly, th rnhing nos of prottion shm must orrspon to vill splittrs. Tht is, th prottion of multist trs is limit in ll optil omins. Our ppr ims with th formultion of th potntil prottion possiilitis n giv th onitions to pply NEC s prottion. Kywors: ll optil ntwork, multisting, fult-tolrnt routing, p- yl, optil onstrint 1 Introution On th on hn, u to thy hug pity n roustnss, ll optil ntworks r oming inrsingly importnt in or ntworks. On th othr hn, in rnt multimi pplitions, th ommunitions shoul not intrrupt for long tim y filur of link or swith. A filur n implit importnt pkt losss. Sin th uplition of

3 ommunitions using inpnnt routs is xpnsiv, shr ol prottion mhnism is oftn propos s solution. With rout rstortion, whn filur is tt, nw rout to th stintion is rqust, omput n onfigur in rtiv mnnr [12]. This solution my orrspon to high rovry ly. In th s of promput prottions, th routrs n swiths rrout th ommunitions to th prplnn kup routs in s of filur [11]. So, this solution is fstr. To sussfully rirt th fft trffi, suffiint pity shoul llot to promput kup routs. rottion n it to prott som privilg trgts (links n/or nos) n n orrspon to shr prottion shm, whr sm kup possiility my prott ginst iffrnt filurs. Oftn, givn kup rsour my prott svrl primry trgt ut only on trgt t tim. In [13]th uthors stt tht shr prottion provis signifint svings ovr it prottion ut shr prottion is mor susptil to multipl link filurs thn it prottion. Oftn, to hrtriz th qulity of prottion, two msurs of solution r onsir: th rovry ly n th numr of filurs mng [4]. Morovr, th ffiiny of prottion shm n givn y th rtio of th prott primry ommunition pity n th n kup pity. It is thrfor ritil to ru th rovry ly s fr s possil. A goo nit for this rution is prottion shm s on smll yls prmitting fst lol rovris in th s of filurs. Trivilly, singl yl n not prott ginst multipl filurs ut st of yls n. Grovr n Stmtlkis propos in [7] prottion mthos s on pr-onfigur prottion yls (or p-yls) for WDM ntworks. Th p-yls offr th vntgs of oth ring n msh prottion shms. Nmly, rstortion tim n fst s in ring prottion, n prottion ffiiny n high s in msh-prottion shms. p-yls my prott not only on-yl links ut lso strling links of th yl. Morovr, yls n ppli to prform n ffiint shr prottion. To prott trffi pttrn, st of p-yls shoul omput. Sin th optiml p-yl st sign is N-hr [7], svrl huristi sign lgorithms wr propos [6] [3]. Oftn th sign of pr-onfigur prottion yl n m t th sm tim tht th primry rout sign n th optimiztion n onrn oth th primry n th kup rout sign. In ths ss th optimiztions r insprl n w tlk out joint optimiztion of th 2

4 (prott) routing shm. Consquntly if th optimiztion of th prottion shm follows th primry rout omputtion, th optimiztion is non-joint optimiztion. Link filurs r mor frqunt, ut gnrlly no filurs impt svrl ommunitions trvrsing th fil no. A no filur n quivlnt to svrl link filurs. Dit prottion shms whih offr sprt solutions for link n no filur rovry r xpnsiv. Aoringly, solutions proposing omin link n no filur rovry r mor intrsting. A goo prottion shm offrs solutions ginst oth link n no filurs. Th xtnsion of p-yl s shms for no filur prottion is on of th is proviing omin prottion. If n on-yl no is fil, thn th yl my trivilly us to prott th ommunitions trvrsing it. Th p-yl onpt ws xtn to pth sgmnt prottion ginst possil no filurs in [14] whr pity optimiztion mol ws lso vlop. Th uthors foun tht using p-yls only smll itionl spr pity is n to hiv goo no-filur prottion. No-nirling p-yls (NECs) my prott no filurs s it is xplin in first mol of th ppr [2]. A singl st of NECs ws propos for omin no n spn prottion. NECs n shr y svrl nos, n h no my us s mny iffrnt NECs s n for pity-ffiint usg of th kup pitis. A iffrnt, filur-inpnnt pth-protting p-yl shm (FI) ws propos in [9], tht xtns th p-yl onpt into pth-orint prottion. In this mnnr, FI p-yls om similr in pity ffiiny to shr-kup pth prottion (SB, f. [8]), supporting filur-inpnnt n-no tivtion n ontrol ginst ithr spn or no filur with fully pr-onnt prottion pths. Our stuy fouss on th ppliility of th NEC strtgy to prott multist light trs. 2 rottion of Multist Trs Multist prottion shms r lssifi in [25] into fiv mjor shms: tr-s, ring-s, pth-s n sgmnt-s prottions. A trivil solution for th prottion of multist tr (originlly in ATM ntworks) hs n propos in [17] s on th xtrtion of ll th pths from th root to h stintion in th multist tr n thn prott h pths with unist prottion shm. This solution 3

5 is sy to rliz in optil ntworks ut is vry xpnsiv sin th shr prottion of th ommon prt of th pths is not rsolv. A prottion shm of multist sssion ginst ny singl link filur in n optil ntwork hs n propos in [16]. A pth-pir (isjoint primry n kup pths) is omput to h stintion y th optiml pth-pir-s shr isjoint pths (O-SD) lgorithm. Th pths n shr gs with lry-xisting pth pirs n lso with othr gs on th primry tr. An improv vrsion ll ross-shring hs n propos in [15] whih improvs th kup shring. It llows to shr vill kup pitis of multipl multist sssions. ortions of kup pths of givn multist sssion not only slf-shrs with its primry tr ut lso ross-shrs with th portions of kup tr of othr sssions. A iffrnt solution for tr prottion is to omplt th primry tr y links prouing runnis n yls n protting ll links n nos in th primry tr. In [5], ul-tr shm for multist fult-tolrnt is propos. In this prottion thniqu, th primry tr lfs r intronnt without th us of ny link or innr no of th primry tr. Th otin runnt shm ontins spnning tr whih n us vn if thr r filurs. Th omputtion of g-isjoint spnning trs for primry n kup routs is lso nturl i [18]. In this s, th kup spnning tr rmins unfft vn if th primry tr is fil. Th topologil onstrint for this prottion shm is vry hr n nssitts th four-onntnss of th topologil grph. Morovr, th g-isjoint pproh os not gurnt vrtx-isjoint trs. ITo filitt th runnt multist routing th uthors in [10] propos to sign two irt r-isjoint trs ( multitr ). In this shm, if ny vrtx or g in th grph lvs, h stintion vrtx rmins to onnt to th sour y t lst on of th irt trs. Dspit th vntgs n th simpliity of this proposition, thr r som isvntgs: th kup pity is qusi-quivlnt with th primry pity n th rirtion prour my omplit n my go k to th sour. Oftn, to formult prottion propositions for optil multisting, it is suppos tht vry swith is of full wvlngth onvrsion pility n optil multisting pility (f. th onition in [20]). Ths onitions r lwys tru in opqu optil ntworks whr vry no my virtul sour. It n hoos th wvlngth ritrry to ontinu th multist forwring in vry outgoing fir. Ths onitions r 4

6 not tru in ll optil ntworks. W isuss th spifiitis of ll optil ntworks in Stion 4. As it is til in th nxt stion, p-yls n lso us with suss for multist tr prottion. 3 Cyl Bs Link/No rottion of Optil Multist Trs Th multist tr prottion y yls is s on th ft tht if link or no in th tr fils, th nighor nos of th fil lmnt my inform th ntwork ontrol pln n this lttr n initit to swith to kup pr-onfigur yls. Th prour must ronnt th isonnt prts of th fil trs y forming nw multist trs (or n quivlnt multist rout, f. ltr). Th most signifint rfrns on yl s solutions r prsnt in th following. F. Zhng n W. D. Zhong propos th pplition of p-yls to ynmi provisioning for multist sssions in WDM ntworks in [19]. Th sign of p-yl s prottion for stti survivl multist sssions ws isuss in [25] whr svrl joint n non-joint optimiztions n huristi lgorithms r ompr. In ths works, only link filurs wr onsir. In [25] n [23] Intgr Linr rogrmming (IL) s mthos n IL s huristis wr formult for optiml n qusi-optiml p-yl prottion shms rsptivly n oth in joint optimiztion n non-joint optimiztion ss. Th no nirling p-yl thniqu my ppli with suss vn if th no is rnhing no of multist light tr. Th ppr [23] propos p-yl s solution for omin no n link filur rovry whih n ppli to prott light trs. Furthr no n link filur prottion shms for multist trffi prottion using th p-yl onpt wr propos n nlyz in [21]. An ffiint huristi lgorithm for p-yl s multist tr prottion hs n propos in [20]. In this propos vrsion, p-yls prott light trs on n n-to-n sis, inst of protting h link n no. In th s of link filur, trs whih r r-isjoint with th yl, hving th sour n th stintion nos on th yl n prott. Th solution prmits th rovry ginst intrmit no filurs. Th uthors lso isuss th onitions how th fft trs n shr th prottion yls. Sin th n-to-n prottion of lrg trs ns lrg p-yls, n it my iffiult to fin this kin of p-yls, 5

7 th ppr propos tr prtition lgorithm to solv th prottion of su trs inst of th whol tr. In th prsnt p-yl s prottion shms it is lwys ssum tht vry no is of full wvlngth onvrsion pility n optil multisting pility. Morovr th light trs r irt n th yls shoul omplt th trs in th s of filur y irt pths. Th most snsil n omplit s orrspons to th filur of rnhing no of light tr. Th si i of th propositions s on no nirling n rsum s follows (suh sitution is shown in Figur 1). Th yl nirls th no whih is rnhing no in th irt tr T: thr is n nstor no of in th tr whih is lso on th yl (it is th no ) n ll of th su trs of r root y n on-yl no (th nos, n in our xmpl). Whn filur of is ourr, nw onnt light tr n otin using th rovry pity of th yl s it is init in th figur (n ritrry irt pth on th yl spnning th sussor nos of is prsnt in th xmpl). Noti tht th ntwork is n opqu ntwork n th nos, n hv multisting pility n n virtul sours of th orrsponing su trs. Fig.1. A yl my prott ginst th filur of rnhing no in multist tr in n opqu optil ntwork Originlly, th no nirling p-yl (NEC) onpts ws propos in [2]. Th yl prsnt in Figur 1 is onsir s simpl NEC. Th uthors stt if th ntwork grph is t lst two-onnt, 6

8 it is lwys possil to rw t lst on logilly nirling non-simpl yl whih n prott no filur. Suh non-simpl yl = (,,,,,f,) is prsnt in Figur 2. This kin of non-simpl NEC ws propos for no prottion in light-pths, ut th shm n pt for light trs s it is illustrt y th son prt of th figur. This figur shows th us of irt non-simpl wlk (,f,,,) longing to th non-simpl yl to stlish th prottion ginst th filur of no. Evn if th sm wvlngth is us in th multist tr n in th kup multist rout, this wvlngth n ross swith from iffrnt inoming ports to iffrnt outgoing ports, n th illustrt non-trivil multist rout n stlish ftr th rovry. Th finlly otin kup strutur is not light tr ut light hirrhy whih hs n propos in [26]. f f Fig.2. A non-simpl NEC whih my prott ginst th filur of rnhing no Trivilly, in n opqu ntwork p-yl my rovr th filur of rnhing no, vn if th fil no is on th yl. Th onition of th rovry is tht ll su trs of th fil no must ontin ommon no (sussor of th prott rnhing no) on th yl. Suh sitution is illustrt y Figur 3 (th yl in ott lin psss through th no ). roprty 1. A yl is n NEC (simpl or not) n n us to rovr th filur of th nirl no iff ll th nighor nos of r in th yl. 7

9 Fig.3. In n opqu optil ntwork, yl my prott ginst th filur of n on-yl rnhing no Noti tht th sgmnts (,), (,), (,), (,),... n ontin intrnl nos whih r not stintions nor rnhing nos. To simplify, w suppos tht thy r simpl links. To otin mor lrg prott prts, p-yl n offr th prottion ginst th filur of nos n links of n nirl su tr s it is init in Figur 4 (in this s, th yl is not n NEC nirling only on no). Noti tht th nirl su tr must fr of stintions. If thr is stintion in th su tr, th rovry s on th yl n rgring th irtion of th links in th su tr n not ssum th onntion to this stintion no. If th wist, th yl s prottion n ppli from th sour no n n onrn th stintions on th yl s it is th s of th filur inpnnt pth-protting (FI) p-yl pprohs ppli for multist trs [21]. In ll ss, th nirl su tr n not ontin ny stintion, only th on-yl stintions n th stintions tht r outsi th yl n simply prott. Oviously, mor th prott prt n th yl r wi, mor th ronfigurtion is omplit n slow. Morovr, only th intrmit no filurs n rovr y th yl n sour n stintion no filurs nnot rstor y ny prottion lgorithm. Th sour no prottion nssitts th uplition of th sour s it is xplin in [22]. For th prviously prsnt yl-s prottions, opqu ntworks with multist pl nos wr suppos. In th following, w nlyz 8

10 f Fig.4. A yl my prott ginst th filur of ny link n no of su tr limit y it th light tr prottion possiilitis y NECs in ll optil ntworks whr th optil swiths o not oligtory ontin splittrs. 4 rottion of Brnhing Nos of Light Trs unr Optil Constrints In trnsprnt ll optil ntworks, whr th nos r optil swiths n th O/E/O onvrsion in ths swiths is not sirl, th multist routing must stisfy itionl optil onstrints. All of th optil swiths n not split th inoming light. To prform th multist routing with light tr, th rnhing nos of th tr must oini with swiths hving spil light splittrs. In ition to th uniqunss of th wvlngth in th firs, th sm wvlngth shoul us long th light-pths n light trs. Th wvlngth n only hng if thr is wvlngth onvrtr in th trvrs optil swith. Sin our nlyz prolm fouss on th sprs splitting onstrints for th multist routing, without loss of gnrlity, w suppos tht thr r no onvrtrs in th ntwork (in th rnt stuy, th onflits on th wvlngth ssignmnt r not nlyz). Hr, w fous on th first, strong onstrint orrsponing to th splitting pity of th optil swiths. In ll optil ntworks, no 9

11 pl to split th inoming light is ll s Multist Cpl (MC) no, othrwis it is Multist Inpl (MI) no [24]. On n suppos tht ny no (lso n MI no) t lst hs th Tp n Continu ility to tp into th inoming signl for lol usg n forwr it to only on output [1]. So, ny no n n intrmit stintion on light tr ut only th MC nos n rnhing nos. Svrl propositions hv n formult to omput light trs orrsponing to ths onstrints (f. Rrout-to-Sour, Rrout-to-Any, Mmr-First n Mmr-Only lgorithms in [24]). Typilly, if thr is not singl light tr stisfying th onstrints, st of trs ( lightforst ) is omput orrsponing to thm. As rsult of th onstrints, not only th primry light trs ut lso th kup routs otin ftr th rovry must stisfy th mntion onitions. Tht is, ftr th rovry, th vntul rnhing nos of th nw light tr must orrspon to splittrs (to simplify, t first tim, w suppos tht th nw optil rout ftr th rovry lso orrspons to light tr). Unfortuntly, th splittrs my sprs in n ll optil ntwork. In som ss, pning on th ntwork topology, on th vilility of th splittrs n on th lotion of th primry light trs, som of th lttr n not prott y th NEC thniqu s it is illustrt y Figur 5. In th figurs, th MI nos r rprsnt y squrs n th MC nos r irls. Sin th nos, n r MI nos, nw optil multist rout ovring ll of th su trs of th no n rspting th onstrints on th splittrs n not uilt whn th no is fil. Figur 6 prsnts two iffrnt rprtitions of th multist pl nos in th sm ntwork n for th sm light tr. In ths nw situtions, th prottion with th hlp of th ylginst th filur of no is possil u to th onnt MC nos. Our prinipl qustion is th following: Whn is it possil th prottion of rnhing no of light tr using th pity of n no nirling p-yl? Th following proposition givs nssry n suffiint onition for this prottion. Rmmr, thr is no wvlngth onvrsion in th ntwork n th sm wvlngth shoul us ftr th rovry. Lt G = (V,E) n unirt grph rprsnting th ll optil ntwork topology with two typ of nos. Lt T = (W,F) light tr n rnhing no in th tr. Lt n NEC nirling in th topology grph. To simplify w not lso y th st of nos on th yl. Lt S = W \{} th st of nos in th intrstion of th tr 10

12 MI no MC no Fig.5. A onfigurtion of MC n MI typ nos on th yl whih os not prmit th prottion ginst th filur of th rnhing no of multist tr Fig.6. A yl whih my prott ginst th filur of rnhing no in multist tr ppli in n ll optil ntwork n th yl xpt (s is n NEC, S orrspons to th nighor nos of in th tr T). Noti tht th p-yl my ontin svrl nos whih r not in S. Ths nos r only rly nos in th s of filur rovry n so thy r not rlvnt for us. Our nlysis fouss on th nos in S. At first, w giv th onition to prott rnhing no with simpl NEC ginst filur. 11

13 roposition 1. A simpl NEC n prott ginst th filur of th no, iff it ontins pth ovring th no st S suh tht os not ontins ny intrnl no of typ MI longing to S. roof. Lt us suppos tht to prott th tr T ginst th filur of, su-pth of th yl is us ftr th rovry. In th nw optil multist rout (in th nw light tr), trivilly, th xtrmitis of th pth hv gr 2 (n so ths nos n MI or MC nos) ut th intrnl nos longing to S shoul rnhing nos hving on or mor su trs whih shoul onnt to th sour). Th onition is nssry. Lt us suppos tht ll pths in n ovring th no st S ontin n MI typ intrnl no. Without loss of gnrlity, lt suh pth n lt v S th MI typ intrnl no in this pth. v sprts th nos of S into two non mpty no sts n th pth into two su pths. To otin th onntivity of th two su pths n lso th su trs root in v, v shoul hv gr 3 or mor ftr th rovry, ut v is of MI. Th onition is suffiint. If thr is pth suh tht h intrnl no of longing to S is n MC no, thn ths nos n th nw rnhing nos of th kup multist strutur. A non-simpl NEC n xtn th prottion ginst rnhing no filur of multist tr. Th iffrn twn simpl n nonsimpl yls is tht non-simpl yls MAY ontin svrl tims sm no ( sm no n hv svrl ourrns in th yl). So, th onnt susts of th non-simpl yl r not oligtory pths ut my wlks rturning svrl tims t sm no. To stisfy th onstrints on th vilility of splittrs, ll th no ourrns in th wlks shoul onsir. Figur 7 illustrts two ss, whr nonsimpl NEC n us for th prottion. In th first xmpl, th non-simpl NEC = (,,,,,f,) n prott th rnhing no (ll of th nighor nos of r on this non-simpl yl). In this yl, two firs twn th nos n r rsrv. Th nos n r MI nos. Thr is no simpl pth in th yl stisfying th prvious onition (f. roposition 1). Th figur init how th wlk (,,,,) in this yl n us to rt kup light hirrhy to rovr th filur. As it ws shown in th simpl s, th xtrmitis of th wlk (th nos n ) hv gr 2. Th prtiulrity of this prottion is tht th no is prsnt twi in th wlk. Byon th ourrn orrsponing to n xtrmity of th ppli wlk, th 12

14 othr ourrn of this no is simpl rly no in th otin light hirrhy. Th gr 2 of h ourrn orrspons to th ft tht it is n MI no. Aftr th filur rovry, th optil swith is trvrs twi: t first from to n sonly from to its singl xisting su tr. Of ours, s is n MI no, it n hv only on su tr in th primry tr. Finlly, th gr of h no ourrn orrspons to th typ of th givn no (MC or MI). Th son xmpl in th figur proposs n othr non-simpl NEC = (,,,f,,,,) using two firs twn th nos n n lso twn n f. To rovr th filur of th no in th init tr ( hs four sussors in th tr:,, n f), for instn, th wlk (,,,f,,,) n propos. Th wlk rturns thr tims to th no n h ourrn of in th rsult light hirrhy hs gr 2. Ths rturns using th wlk r lso illustrt in Figur 8. Th gnrliztion of th rsults is summriz y th following. f f Fig. 7. Non-simpl NECs prmit th prottion ginst th filur of th rnhing no using wlks on th NEC roposition 2. A non-simpl NEC n prott ginst th filur of th nirl rnhing no, if it ontins wlk ovring th nighor no st S of suh tht th intrnl MI nos longing to S in hv lso n xtrmity ourrn of. In othr worl: n MI typ no n rpt in th wlk svrl tims, if it lso hs n xtrmity ourrn in th wlk. 13

15 su tr f su tr su tr su tr Fig.8. Th til wlk of th son xmpl roof. Lt us suppos tht to prott th tr T ginst th filur of, wlk in th non-simpl yl is ppli. Rmmr tht in wlk, no my ppr svrl tims (svrl ourrns of th no my long to th wlk). In th nw optil multist rout (in th nw otin light hirrhy), trivilly, th xtrmitis of th wlk hv gr 2. Th intrnl nos of longing to S r ithr rnhing MC nos hving on or mor su trs or thy r simpl rly nos. Lt s i ns n intrnl rly no, n lt T s its su tr in th originl multist tr. Lt us suppos tht s hs rly no ourrn in pth. Thr is two ss: 1. This no s hs n ourrn in th wlk lot t th xtrmity of th wlk. This xtrmity no ourrn n onnt th su tr T s to th nw multist rout. 2. Thr is no xtrmity no ourrn orrsponing to s. In this s, th su tr T s n not onnt to th nw multist rout. Th onition is nssry (f. 2). Th onition is suffiint. If it is tru, ll of th su trs longing to th nos in S n onnt to th nw multist rout. Trivilly, s wlk hs two xtrmitis, only ourrns of ths two nos (if thy r MI nos) n rpt in th wlk us to rovr th no filur. 14

16 5 A rtiulr rottion Shm Using Non-Simpl Cyls Non-simpl yls xtn th prottion possiilitis of rnhing nos in ll optil light trs. In th prviously prsnt yl-s prottion shms, th yl (simpl or not) is us to th filur rovry in th following mnnr. If no filur ours, thn squn of som onsutiv nos in th yl (i.. wlk) is us to r-onnt th su trs of th fil optil multist tr. Lt = (x 1,x 2,x 3,...,x n,x 1 ) yl (rprsnt y irulr list of nos) with n no ourrns (if th yl is non-simpl yl, thn svrl ourrns orrspon to sm no of th topology grph). Th wlk us for th prottion n n ritrry squn of ths no ourrns of th irulr list stisfying th prviously mntion onitions. Evntul rturns to som nos in th yl prmit iffrnt n mor flxil (ut mor omplit) prottion of th nirl rnhing no. In th following, w prsnt spil s s on prtiulr non-simpl yl. This xmpl lso illustrts th prottion pilitis of th non-simpl yls. A prtiulr prottion shm n propos whn non-simpl NEC is ompos using two firs (on in oth irtions) twn th onnt no pirs in th yl. Figur 9 shows suh n NEC n its propos utiliztion for th filur rovry. Thr r multipl MI nos in th yl, ut MC n MI typ nos ltrnt whih prmit th prottion using th prsnt NEC in prtiulr mnnr. In th following proposition, w suppos tht th links longing to p-yl n us ritrrily for th prottion. Tht is, n ritrry onnt sust of th links (n not only pth or wlk) n srv th prottion. roposition 3. Lt non-simpl NEC systmtilly ompos from two firs twn th onrn (nighor) nos. It n prott ginst th filur of th nirl no if it ontins pth ovring th no st S of nighors suh tht th pth os not ontin squn of thr sussiv intrnl MI nos longing to S. roof. Eh no s in S hs t lst on su tr T s root in s whih must r-onnt to th sour ftr th filur rovry. Trivilly, if s is n MI no, it hs only on su tr in th originl multist tr. Morovr, h no ourrn of n MI no n hv gr 2 in th rovry strutur. Contrrily, th MC nos n rnhing nos ftr th rovry. 15

17 f f Fig. 9. A prtiulr non-simpl NEC n its usg for th prottion ginst th filur of th rnhing no using prtiulr wlk on th NEC Th pitis in th mntion NEC n llot to th filur rovry s follows. From th sour, th visit MC nos longing to S r rnhing nos. Lt us suppos tht n intrnl MI typ no s is rly no in th NEC. Rmmr tht th uniqu su tr T s n not onnt to th kup strutur y this no ourrn of s. To this, th kup strutur must rturn to s from n othr visit no. If ontins thr sussiv intrnl MI nos longing to S, n thr is no MC no twn thm, th rturn to th mil MI no in S is not possil using th yl. Lt s 1, s 2 n s 3 th thr sussiv MI nos in th yl (f. Figur 10). In th st s, th su trs of s 1 n s 3 r onnt to th rovry strutur using inoming links (l 01 n l 43 ) s it is illustrt. Morovr, pth from s 1 to s 3 must us to onnt th two prts of th multist routs. Sin s 1, s 2 n s 3 r MI nos, th mil no s 2 n rly no in this pth ut n not rnhing no. Its su tr n not onnt to th multist rout using th in-yl links. If thr is t lst on MC no (nm t) ithr from s i to th nxt MI no in S or for s i, thn this no t oms rnhing no n th not yt us pth from t to s i n onnt th su tr of s i to th kup strutur. Figur 11 illustrts two yls: on with fsil n nothr with not fsil squn of nos. 16

18 l 01 l 12 l 23 l 34 l 10 s 1 l 21 S2 l 32 S3 l 43 su tr su tr su tr Fig.10. Th su tr of th mil MI no n not onnt to th rovry strutur Th prtiulrity of this prottion is tht it uss not only pth or wlk in th yl ut lso othr rlt links whih r onnt to th si pth. So, th onfigurtion of th prottion onrns not only th onfigurtion of th nos following th wlk or th pth shm ut it is omplt with som itionl onfigurtions. Th otin kup strutur is light hirrhy using th pitis of iffrnt in-yl links. f g f g?? Fig.11. A fsil n not fsil squn of nos in n NEC using kup hirrhy on th yl 6 rsptivs In this stuy, w prsnt th onitions how NEC n us to prott light trs ginst rnhing no filurs in ll optil WDM ntworks. Th most importnt ontriution of this work is simpl: th kup multist rout must orrspon to th wll known optil onstrints. W nlyz th onstrint impos y spr splitting pitis in th ntwork. Th rnhing nos of th kup rout must MC nos. 17

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