Improving Survivability through Traffic Engineering in MPLS Networks

Transcription

1 Improvig Survivabiiy hrough Traffic Egieerig i MPLS Neworks Mia Ami, Ki-Ho Ho, George Pavou, ad Michae Howarh Cere for Commuicaio Sysems Research, Uiversiy of Surrey, UK Emai:{M.Ami, K.Ho, G.Pavou, M.Howarh}@eim.surrey.ac.uk Absrac The voume of higher prioriy Iere appicaios is icreasig as he Iere coiues o evove. Cusomers require Quaiy of Service (QoS) guaraees wih o oy guaraeed badwidh ad deay bu aso wih high avaiabiiy. Our objecive is for each esimaed raffic fow o fid a primary pah wih improved avaiabiiy ad miimum faiure impac whie saisfyig badwidh cosrais ad aso miimizig ework resource cosumpio. We devise a heurisic agorihm wih four differe cos fucios o achieve our objecive. Our approach ca ehace avaiabiiy of primary pahs, reduce he effec of faiure ad aso reduce he oa resource cosumpio for boh primary ad backup pahs.. Iroducio The seady growh i he use of compuer eworks for higher prioriy Iere appicaios ecourages service providers o offer ew services ha deped o a commied Quaiy of Service (QoS); hese services require coiuous ework avaiabiiy i he presece of various faiure scearios. Hece, ework survivabiiy, which refers o he abiiy of a ework o maiai uierruped service regardess of he scae, magiude, duraio ad ype of faiures, is a impora issue. We ivesigae survivabiiy i Mui- Prooco Labe Swichig (MPLS) eworks. May MPLS survivabiiy mehods have bee proposed [-2]. A fudamea cosideraio i he desig of a MPLS survivabe ework is he creaio of backup pahs o proec he primary pahs from faiure whie preservig he required QoS as has bee cosidered i proposas [-2]. However, oher exisig MPLS-based survivabiiy mehods [3] ake io cosideraio aspecs such as avaiabiiy of ework compoes ad faiure impac parameers durig he compuaio of he primary pah. Poor rouig of primary pahs migh roue raffic hrough ow avaiabiiy iks, eadig o higher probabiiy of faiure occurrece ad as a resu more faiure cosequeces such as recovery ime ad packe oss. Therefore, we address a Offie Traffic Egieerig Survivabiiy Desig (OTESD) probem ha akes io accou he ework compoe avaiabiiy ad faiure impac parameers i order o provisio a survivabe ework. Our goa is summarised as foows: give a physica opoogy, aggregae esimaed raffic fows ad esimaed ik avaiabiiy, for each raffic fow fid a primary pah wih ehaced avaiabiiy ad miimum faiure impac whie preservig he fow s badwidh requireme ad opimisig he use of ework resources. To sove he OTESD probem, we adop a dua approach i which we firs fid primary pahs wih improved avaiabiiy ad ow faiure impac. We subsequey provide backup pahs for hose raffic fows where a sufficiey high avaiabiiy primary pah cao be foud. Therefore our approach is a kid of proecio scheme. Our work is moivaed by he survivabiiy mehod proposed i [3], however [3] is based o oie rouig whie we cosider offie Traffic Egieerig (TE) for ework provisioig i order o achieve cosiderabe improveme i survivabiiy performace ad beer resource uiizaio. Buidig a survivabe ework hrough offie TE has aso bee ivesigaed i [7], i which a agorihm o se ik weighs was proposed for IP backboe eworks so as o miigae he effecs of faiure. However, he OTESD probem has o ye bee addressed i MPLS eworks ad is herefore he subjec of his paper. We beieve o previous work has ake io accou avaiabiiy parameers whe sovig survivabiiy desig probem hrough offie TE. 2. Backgroud Survivabiiy mehods [-2] ca be divided io wo basic approaches. The firs approach, caed proecio, is a pre-deermied faiure recovery scheme i which a he same ime as he primary pah is roued bewee he source ad he desiaio, he backup pah is aso provisioed o forward he raffic if he primary pah fais. I he secod approach, caed resoraio, firs a primary pah is se-up bewee he source ad he Proceedigs of he 0h IEEE Symposium o Compuers ad Commuicaios (ISCC 2005) /05 $ IEEE

2 desiaio; ad he, afer faiure occurs, a backup pah is discovered dyamicay o resore he raffic. I his paper we use proecio o achieve our objecive. Backup pah ypes deped o which rouer aog he primary pah akes he rerouig decisio, ad his is caed recovery scope [2]. I he goba scope, he igress ode aways akes resposibiiy for fau recovery whe a Fau Idicaio Siga (FIS) arrives (ay message se o idicae ha faiure has occurred is caed a FIS). The advaages of his scope are firsy ha he backup pah ca be seeced from iks aywhere i he eire ework, so he ework spare resources are used efficiey, ad secody ha oy oe backup pah eeds o be se up per primary pah. However, sice a FIS has o be propagaed a he way back o he igress ode, his mehod has high recovery ime ad packe oss. I he oca scope, he Labe Swich Rouer (LSR) a he head of he faied ik swiches he raffic from he broke ik o he backup pah. Sice a FIS is o eeded, his scope has a faser recovery ime ad reduced packe oss i compariso o goba scope. O he oher had, creaio ad maieace of muipe backup segmes is required, resuig i iefficie uiizaio of resources ad icreased compexiy [3]. The effecs of ework faiure ca be evauaed i erms of recovery ime ad packe oss. The recovery ime (T REC ) is defied as he period of ime bewee fau deecio ad he raffic resoraio o he correspodig backup pah. Recovery ime cosiss of a umber of phases as foows [3]. a) Deecio Time: he ime required for fau deecio. b) Hod off ime: he waiig ime before riggerig he fau recovery process i case ower ayers ca overcome he fau faser. c) Noificaio Time: he ime required o covey fau iformaio o he ode resposibe for rerouig he raffic (for exampe, by rasmiig a FIS). d) Swichover Time: he ime required o redirec he raffic from he primary pah o he backup pah. A hese phases are foowed by a goba scope proecio scheme; a oca scope scheme does o have a oificaio phase. Packe oss (P LS ) is defied as he oa umber of packes os durig T REC. Sice packe oss depeds o he recovery ime, a oger recovery ime eads o more packe oss. Hece, i order o reduce he faiure impac, we oy eed o reduce he recovery ime. Survivabiiy provisioig by esabishig backup pahs has a umber of imiaios. Firsy, i may overuse ework resources for esabishig hese pahs if he ework is o we provisioed. Secody, i requires sigaig overhead for backup pah esabishme, faiure deecio ad oificaio. Fiay, i requires raffic swichig from primary pah o backup pah ad he from backup pah o primary pah, which may cause ework osciaio. These survivabiiy mehods hus ead o high overa overhead. Our dua approach, described beow, aemps o miimize he aforemeioed imiaios. 3. Nework avaiabiiy aaysis The avaiabiiy of a compoe i (A i ) is he fracio of ime he compoe is operaioa ( up ) durig he eire service ime [4]. A ework compoe s avaiabiiy is a reaivey saic vaue. Typica daa o ework compoes (rasmier, receiver, fiber ik) faiure rae ad repair imes ca be foud i [9]. I addiio, he avaiabiiy of a compoe ca be cacuaed by reiabiiy predicio modes such as Tecordia [8]. If he raffic fow is carried by a sige pah, is avaiabiiy, deoed byα, is equa o he avaiabiiy of he pah he fow raverses. If we deoe pah avaiabiiy by A pah, we have: α = Apah () A pah ca be cacuaed based o he kow avaiabiiies of he ework compoes aog is roue [4]. Suppose he pah is composed of iks, he he ed-o-ed pah avaiabiiy is cacuaed as foows: pah 2... = A = A A A = A (2) where A is he avaiabiiy of ik. 4. The OTESD probem Defiiio : We disiguish bewee ow ad high avaiabiiy iks. I his paper, we defie ow avaiabiiy iks as A < ad high avaiabiiy iks as A Defiiio 2: we defie he Lik Proecio Requireme (LPR) as a biary vaue for each ik o idicae wheher he ik shoud be proeced or o. For ow avaiabiiy iks we se LPR= ad for high avaiabiiy iks LPR=0. Defiiio 3: We disiguish bewee ow ad high avaiabiiy pahs. I his paper, we defie ow avaiabiiy pah as A pah < ad high avaiabiiy pah as Apah respecivey. 4.. Dua approach Our approach cosiss of wo phases: () a preveive phase, ad (2) a impac miimisaio phase. I he preveive phase, TE is used o map he esimaed raffic fows oo he exisig physica Proceedigs of he 0h IEEE Symposium o Compuers ad Commuicaios (ISCC 2005) /05 $ IEEE

3 ework opoogy i he mos effecive way o improve ework survivabiiy whie opimisig resource uiizaio. I order o improve he avaiabiiy of he primary pah our TE roues he raffic mosy hrough he high avaiabiiy iks by akig io accou he ik avaiabiiy parameer durig he compuaio of primary roues. This objecive is achieved by usig he ik avaiabiiy parameer i differe ways i he cos fucio of he Shores Disace rouig agorihm [5] as expaied i secio 5. However, i is o aways possibe o avoid usig he ow avaiabiiy iks. I fac, i some cases raffic may be roued hrough primary pahs wih ow avaiabiiy iks. I his case, we perform he impac miimizaio phase. Recovery ime is miimized by reducig he ime eeded for each phase of he recovery as foows. Deecio ad swichover ime deped o he echoogy used ad cao be easiy modified. Hod off ime depeds o he ower ayers recovery scheme ad ca be se up bewee (0-50ms). Therefore, he oificaio ime seems o be he key facor for miimizig he recovery ime. The oificaio ime depeds o he propagaio ime of a FIS per ik ad o he Noificaio Disace (ND) [3]. ND is defied as he umber of iks bewee he ode ha deecs he faiure ad he ode ha reroues he raffic. Sice he propagaio ime depeds oy o he ik rasmissio rae, oificaio ime ca oy be decreased by reducig he ND. I oca scope he disace is zero, so i is he opima case. Bu as we discussed i secio 2, he goba scope is more efficie ad more scaabe. However, i he goba scope he disace is o kow i advace because obviousy i is o kow which ik wi fai. Therefore i he impac miimizaio phase, we use he ik avaiabiiy parameer o esimae he disace i a probabiisic maer. Moreover, if we cao fid a sufficiey high avaiabiiy primary pah for he raffic fow, we provide a goba ik-disjoi backup pah for he correspodig primary pah The OTESD Probem Formuaio We formuae he OTESD probem as a muiobjecive opimisaio probem. A souio of OTESD compues a primary pah for each raffic fow, which yieds he bes vaue for oe or more objecive fucios. The foowig assumpios are give:. G=(V,E,A,C), he physica ework opoogy where V is he se of odes, E is he se of iks, A: E (0,) is he avaiabiiy of each ik (where (0,) deoes he se of rea umbers bewee 0 ad ), C: E Z + specifies he oa physica capaciy o each ik. 2. T = ( = s, d, B ), he raffic marix, which is a se of esimaed raffic fows, where s is he source, d is he desiaio, ad B is he Badwidh requireme of he raffic fow. We assume ha aggregae esimaed raffic fows have a cosa bi rae paer due o saisica muipexig. The raffic marix ca be measured or esimaed. We cosider he foowig objecives: () Improve he primary pahs avaiabiiy, (2) Miimise faiure impac ad (3) Miimise he oa Resource Cosumpio. These objecives are opimised subjec o he souio saisfyig he ik capaciy cosrais A heurisic agorihm To impeme our approach, we use he foowig heurisic agorihm. Primary pah provisioig procedure: Sep : sor he raffic fows i descedig order based o heir badwidh requiremes ad choose oe a a ime i ha order. Sep 2: remove he iks wih he residua badwidh ess ha he raffic fow badwidh requireme o esure ha he remaiig iks ca guaraee he badwidh requireme. Sep 3: compue he primary pah, usig he cos fucios proposed i secio 5. Sep 4: oce he primary pah is foud, aocae he requesed badwidh o he pah. Sep 5: cosider he ex raffic fow ad repea sep 2 o 5 ui a he raffic fows have bee cosidered. Backup pah provisioig procedure: Sep is he same as sep of he primary pah provisioig procedure. Sep 2: compue he primary pah avaiabiiy of he correspodig raffic fow accordig o equaio (2), if i is a ow avaiabiiy primary pah go o he ex sep, oherwise go o sep 5. Sep 3: remove he iks wih he residua badwidh ess ha he raffic fow badwidh requireme. Sep 4: compue a goba ik disjoi backup pah accordig o he Shores Disace cos fucio (3) by usig he Dijksra rouig agorihm ad aocae he requesed badwidh o he pah. Sep 5: cosider he ex raffic fow ad repea sep 2 o 5 ui a raffic fows have bee cosidered. 5. Proposed cos fucios The Shores Disace (SD) agorihm is a shorespah agorihm wih he cos fucio defied as: C( p) = c = (3) = = R Where c is he ik cos ad R is he residua badwidh of ik ( ). The shores pah ca be Proceedigs of he 0h IEEE Symposium o Compuers ad Commuicaios (ISCC 2005) /05 $ IEEE

4 foud by he Dijksra rouig agorihm usig he correspodig cos fucio. The shores pah is he pah wih miimum pah cos deoed by C(p). The above cos fucio baaces he objecives of miimisig resource cosumpio ad improvig oad baacig. However, he SD cos fucio does o cosider he objecive of improvig pah avaiabiiy. Hece, i may resu i usig ow avaiabiiy primary pahs. Hece, we propose severa exesios of he SD cos fucio o achieve our dua approach objecives. Our proposas use he ik avaiabiiy parameer i he foowig wo ways. A. Usig ik avaiabiiy as a hreshod: ) Avaiabiiy Threshod (AT): The cos fucio (3) is modified by icudig a hop cou peay, 2, for he ow avaiabiiy iks. For he high avaiabiiy iks he cos fucio remais he same as SD (3). (We experimeed he hop cou peay wih vaues oher ha 2 ad we observed o sigifica chages i he resus). I his approach, higher coss are assiged o ow avaiabiiy iks ha he high avaiabiiy oes. Moreover, he ow avaiabiiy iks which are far away from he igress ode are peaized more i order o reduce he faiure impac as expaied i secio 4.. I his way he faiure oificaio disace (ND) is decreased which resus i reduced recovery ime (T REC ) ad, herefore, reduced packe oss (P LS ). Our AT cos fucio is defied as: C ( p) = = R 2 R if A oherwise (4) 2) Avaiabiiy Threshod 2 (AT2): Our secod cos fucio, AT2, is defied as foows. C ( p) = = 2 R 2 R β if A oherwise (5) I compariso o SD (3), a hop cou peay, 2, is appied boh o high avaiabiiy ad ow avaiabiiy iks i order o assig higher cos o he iks ocaed far from he igress ode. This gives ower coss o shorer pahs. A cosa, β, is associaed wih he residua badwidh of high avaiabiiy iks. We se β o 2, which experimes show ha has sufficie impac o he cos fucio. By squarig he residua badwidh of he high avaiabiiy iks ess cos is assiged o hem i compariso o he ow avaiabiiy oes. B. Usig ik avaiabiiy i he cos fucio: ) K-SD-AD: Firs of a, K-Shores-Disace (K- SD) pahs are compued by modifyig he agorihm proposed i [6] ad usig cos fucio (3). The amog he K pahs, he pah wih he miimum cos fucio accordig o (6) is seeced as he fia pah. We associae a hop cou peay, 2, wih each ik i addiio o is ik avaiabiiy fucio. Low avaiabiiy iks ocaed far away from he igress ode are herefore peaized more. As a resu, his cos fucio combies he objecives of improvig primary pah avaiabiiy wih miimisig faiure impac. C( p) = 2 ( og A ) (6) = Accordig o he order of he cos fucios used i his case, he pah seeced here firs opimises he resource cosumpio ad oad baacig objecives ad he opimises he pah avaiabiiy ad faiure impac objecives. 2) K-AD-SD: Firs of a, K-shores (K-AD) pahs are compued by modifyig he agorihm proposed i [6] ad usig cos fucio (6). The amog he K pahs, he pah wih miimum cos fucio accordig o (3) is seeced as he fia pah. I fac, he cos fucio used i his approach is he same as K-SD-AD bu i he opposie order. Hece, he pah seeced i his case opimizes he objecives i he opposie order. 6. Performace evauaio We evauae our heurisic agorihm wih he four proposed cos fucios hrough simuaio usig he foowig four performace merics.. Nework Proecio Degree (NPD): ( B ) T NPD = (7) B T where T is he oa umber of raffic fows, badwidh is deoed by B ad = i his paper. If a cos fucio resus i a high NPD vaue i impies ha he cos fucio performs beer regardig improvig he primary pah avaiabiiy which is he firs objecive. 2. Faiure Impac Degree (FID): ( B ND > ) T FID = (8) B T If a cos fucio resus i a ow FID vaue i impies ha i performs beer regardig miimisig he effecs of faiure which is he secod objecive. 3. Number of Liks o be Proeced (NLP): NLP = T p = = ( LPR x ) T (9) Proceedigs of he 0h IEEE Symposium o Compuers ad Commuicaios (ISCC 2005) /05 $ IEEE

5 where x = if raffic fow has bee assiged o ik ; oherwise x =0. Aso, p is he umber of iks o he primary pah ad LPR is he parameer defied i defiiio 2 (i secio 4). If a cos fucio resus i a ow NLP vaue, i reduces resource cosumpio by oy esabishig oca backup pahs for ow avaiabiiy iks, which is he hird objecive. 4. Resource Cosumpio (RC): T RC = B (0) = where is he umber of iks o he raffic fow s pah ad B is he badwidh required for each raffic fow. We compue he RC for wo cases. I he firs case, we oy compue he resources cosumed by he primary pahs. Therefore, if we deoe he umber of iks o a sige raffic fow s primary pah by p, he for his firs case = p. I he secod case, we provide a pre-esabished, pre-aocaed goba ik-disjoi backup pah for each ow avaiabiiy primary pah o aemp o maximize avaiabiiy for 00% of he raffic fows. We assume ha he required badwidh is dedicaed o each backup ik ad o resource sharig is cosidered. I his way we ca evauae he oa RC (cosisig of high ad ow avaiabiiy primary pahs ad backup pahs for ow avaiabiiy primary pahs). Therefore, if we deoe by b he umber of iks o he raffic fow s backup pah provided for he ow avaiabiiy primary pahs, he for he secod case = p + b. If a cos fucio provides ow oa RC vaue i performs beer regardig miimisig he oa RC by esabishig goba backup pahs (if ecessary) for proecig he ow avaiabiiy primary pahs, which is he hird objecive. 6.. Simuaio resus Simuaio resus are based o he ework opoogy used i [3]. I he opoogy, 7 odes are ideified as raffic igress ad egress odes (odes, 2, 4,5, 9, 3 ad 5). The capaciy of he iks is 200 (orma ies) ad 4800 (bod ies) uis, ad each ik is bidirecioa. The avaiabiiy of each ik is a preassiged vaue radomy geeraed bewee ad. Each poi i he simuaio graphs is he average of 0 idepede rias. Each ria uses a idepede se of raffic fows. The badwidh of each fow is uiformy disribued bewee 70 ad 25 (uiess) ad radomy assiged o igress-egress ode pairs. Noe ha, i our simuaio we cosider K=5 for K-SD-AD ad K-AD-SD, sice his vaue is adequae for his sma ework. Figures (a)-(c) prese he NPD, FID ad NLP performace of he heurisic agorihm wih he proposed cos fucios as a fucio of oa umber of raffic fows. I hese hree figures we se he oa perceage of ow avaiabiiy iks o 30%. Figure (a) shows ha AT2 has he bes NPD. This is due o he fac ha for AT2, i mos of he cases he coss associaed o he high avaiabiiy iks are ess ha he ow avaiabiiy iks. The oher cos fucios have ower NPD vaues bu are si sigificay beer ha SD which does o cosider he ik avaiabiiy vaues a a ad has he owes NPD vaues. Figure (b) shows ha K-AD-SD has he bes FID. This is due o he fac ha i K-AD-SD, peaizig he ow avaiabiiy iks which are far away from he igress rouer is cosidered direcy as is firs objecive i he cos fucio. The oher cos fucios have higher FID vaues bu are si sigificay beer ha SD, which does o cosider he faiure impac a a. Figure (c) shows ha AT2 has he bes NLP which meas ha fewer iks eeded o be proeced ad as a resu ess resources eed be cosumed by oca backup pahs for he same reasos as described for figure (a). Oher cos fucios have higher NLP vaues bu are si sigificay beer ha SD. Figures (a)-(c) show ha amog he four proposed cos fucios K-SD-AD has he worse performace regardig NPD,FID,NLP. The reaso is ha his approach firs fids K umber of shores pahs accordig SD cos fucio ad he as is secod objecive cosiders he avaiabiiy ad faiure impac parameers o choose he fia pah. Hece, is avaiabiiy performace is ess ha oher proposed cos fucios bu si performs beer ha SD. Figure 2(a) shows he primary pah resource cosumpio of he proposed cos fucios. The resus show ha i a of he proposed cos fucios, he resources cosumed by primary pahs are more ha hose by SD. I fac, here is a rade off bewee he avaiabiiy performace of he proposed cos fucios ad heir primary pah resource cosumpio. For exampe, sice AT2 has he bes avaiabiiy performace regardig NPD ad NLP, i cosumes 54% more resources ha he SD o average. I compariso, K-SD-AD cosumes oy 6% more resources o average i compariso o ha of SD sice i provides he eas avaiabiiy amog he four proposed cos fucios. However, he resource cosumpio figures are markedy differe whe we icude backup pah resources, as show i Figure 2(b). This shows ha SD cosumes he mos resources i compariso o a he oher proposed cos fucios. This is due o he fac ha mos of is primary pahs have ow avaiabiiy ad backup pahs eed o be provisioed for hem. However, our proposed cos Proceedigs of he 0h IEEE Symposium o Compuers ad Commuicaios (ISCC 2005) /05 $ IEEE

6 fucios require fewer backup pahs o achieve overa pah avaiabiiy. Sice our approach improves ework pah avaiabiiy whie reducig oa ework resource cosumpio, i ca be a aeraive o he exisig approaches o achieve high avaiabiiy ad miimum cos ework provisioig. We summarise he performace of he proposed cos fucios as foows. AT has he bes performace regardig oa resource cosumpio. AT2 has he bes performace regardig NPD ad NLP. K-SD-AD has he bes performace regardig primary pah RC afer SD. K-AD-SD has he bes performace regardig FID. Nework Proecio Degree NLP per LSP Faiure Impac Degree 00 (a) (b) (c) Figure. Effecs of umber of raffic fows o (a) NPD, (b) FID ad (c) NLP 7. Cocusio SD AT AT2 K SD AD K AD SD Number of Traffic Requess SD AT AT2 K SD AD K AD SD Number of Traffic Requess SD AT AT2 K SD AD K AD SD Number of Traffic Requess We have formuaed he offie TE survivabiiy desig (OTESD) probem. The objecive is o fid for each raffic fow a primary pah wih improved avaiabiiy ad miimum faiure impac ha saisfies he badwidh requireme whie opimisig resource cosumpio. We have proposed a heurisic agorihm wih four various cos fucios o sove he probem. Primary Pah Resource Cosumpio SD K SD AD AT K AD SD AT2 Cos Fucios 2(a) 2(b) Figure 2. Resource cosumpio for (a) Primary pahs ad (b) Toa pahs Simuaio resus show ha our proposed heurisic agorihm icreases he ework proecio, which meas high avaiabiiy primary pahs ca be provided for mos of he raffic fows ad so ess faiure deecio, oificaio ad raffic swichig are required. Aso, i decreases resource cosumpio for esabishig oca backup pahs (if ecessary). Fiay, i ca improve he resource efficiecy by savig some amou of resources. I summary, his work aows ISPs o appy beer TE ad QoS rouig sraegies o icrease service avaiabiiy for heir cusomers. 8. Refereces AT K SD AD K AD SD AT2 SD Cos Fucios [] C. Huag e a., Buidig Reiabe MPLS Neworks usig a pah proecio mechaism, IEEE Commuicaio Magazie, vo. 40, o. 3, March [2] J.L. Marzo e a., Addig QoS Proecio i order o Ehace MPLS QoS Rouig, IEEE Ieraioa Coferece o Commuicaios, vo. 3, 2003, pp [3] E. Cae e a., Proecio Performace Compoes i MPLS Neworks, Compuer Commuicaios Joura, vo. 27, o. 2, Juy 2004, pp [4] J. Zhag e a., A New Provisioig Framework o Provide Avaiabiiy-Guaraeed Service i WDM Mesh Neworks, IEEE Ieraioa Coferece o Commuicaios, vo. 2, 2003, pp [5] Q. Ma e a., O Pah Seecio for Traffic wih Badwidh Guaraees, IEEE Ieraioa Coferece o Nework Proocos, 997, pp [6] D. Eppsei, Fidig he k Shores Pahs, 35h IEEE Symposium o Foudaios of Compuer Sciece, 994, pp [7] A. Nucci e a., IGP Lik Weigh Assigme for Trasi Lik Faiures, Esevier ITC8 2003, Beri, Germay. [8] Tecordia docume Reiabiiy Predicio Procedure for Eecroic Equipme (docume umber SR-332, Issue ), AT&T Be Labs 999. [9] M. To e a., Uavaiabiiy aaysis of og-hau eworks, IEEE Joura o Seeced Areas i Commuicaios, vo. 2, 994, pp Toa Resource Cosumpio Proceedigs of he 0h IEEE Symposium o Compuers ad Commuicaios (ISCC 2005) /05 $ IEEE