Restorable Dynamic Quality of Service Routing

Transcription

1 QOS ROUTING Resorable Dynamic Qualiy of Service Rouing Murali Kodialam and T. V. Lakshman, Lucen Technologies ABSTRACT The focus of qualiy-of-service rouing has been on he rouing of a single pah saisfying specified QoS consrains. Upon failure of a node or link on he pah, a new pah saisfying he consrains has o be esablished. However, resources needed o saisfy he QoS requiremens are no guaraneed o be available a he rerouing insan, so QoS is no guaraneed upon failure. Resorable QoS rouing, where acive and backup pahs mus be simulaneously se up, has only recenly been sudied. This is mosly moivaed by he incorporaion of mechanisms o esablish QoS guaraneed pahs wih failure proecion in muliproocol label swiching neworks. This aricle describes some recenly developed algorihms for dynamic rouing of resorable QoS guaraneed pahs. INTRODUCTION The objecive of qualiy of service (QoS) rouing has been o selec a single pah ha saisfies he specified QoS requiremens and opimizes nework usage. This opic has been exensively sudied [1 4]. Pah selecion algorihms such as wides shores pah and minimum inerference rouing are examples. In hese schemes, failure resilience is no an objecive, and if a link or node fails, all pahs ha raverse he failed link or node have o be re-roued. Since seing aside resources for failure rerouing was no an objecive of he iniial rouing, here is no guaranee ha rerouing can be successfully done, so he iniially roued pahs are no faul-oleran or resorable. In circuiswiched neworks, resorable rouing is commonly used (e.g., seing up pahs wih or 1:1 proecion). In proecion, wo disjoin pahs are used and daa is sen on boh pahs. The receiver picks he beer pah o use and discards daa from he oher. In 1:1 proecion, wo disjoin pahs also exis, bu daa is sen only on one acive pah. The backup pah is acivaed by signaling only if he acive pah fails. In he conex of packe neworks, recenly here has been much ineres in seing up QoS guaraneed pahs ha are resilien o fauls. This ineres sems from he incorporaion of mechanisms o suppor resoraion in he pah seup signaling for muliproocol label swiching (MPLS) neworks. This aricle discusses recenly developed schemes for resorable rouing wih QoS guaranees. We firs describe he differen nework resource informaion models perinen o resorable rouing wih resource reservaions. We hen describe differen resoraion schemes and he algorihms ha can be used. We also describe aspecs of signaling relevan o resorable QoS rouing. The descripion of schemes is only for he case where he QoS guaranees are bandwidh guaranees, and he wo are used synonymously in he res of he aricle. We describe he schemes using he erminology of MPLS neworks since he described schemes are mos likely o be used in MPLS neworks. A he ingress poins of an MPLS nework, incoming packes are encapsulaed wih labels ha are used o forward he packes along label swiched pahs (LSPs). These LSPs can be hough of as virual raffic runks and are se up using signaling proocols such as Resource Reservaion Proocol wih Traffic Engineering (RSVP-TE) or consrain roued label disribuion proocol (CR-LDP) [5]. One of he goals in seing up LSPs is o permi service providers o raffic engineer heir neworks, and o dynamically provision QoS or bandwidh guaraneed pahs ha can be made failure-resilien [6]. Failure resilience is achieved by resoraion mechanisms ha allow backup pahs ono which raffic can be quickly redireced upon failure deecion, o be se up simulaneously wih he acive pah. This necessiaes exensions o rouing and signaling proocols, and he developmen of new pah selecion algorihms. RESTORABLE QOSROUTING We assume ha all demands (LSP seup requess) are no known a priori. Hence, we are only ineresed in online (or dynamic) rouing ha roues LSP requess ha arrive one by one. The main issues are he mode of resoraion (local vs. end-o-end resoraion), he failure modes we proec agains, and he informaion abou he nework ha can be made available o pah selecion algorihms /02/$ IEEE IEEE Communicaions Magazine June 2002

2 RESTORATION MODEL Backup for connecions in a nework can be buil so ha here is eiher pah resoraion or local resoraion. In pah (or end-o-end) resoraion, he idea is o provide a backup pah from he source o he desinaion for each acive LSP. This backup pah is (link or node) disjoin from he acive pah. However, he drawback wih his approach is ha when here is a link or node failure, his failure informaion has o propagae back o he source, which in urn swiches raffic from he acive o he backup pah. This has o be done for all he LSPs ha use his link on heir acive pahs. Noe ha he link failure informaion has o be poenially propagaed o all nodes in he nework. Pah resoraion along wih he informaion ransfer on failure is illusraed in Figs. 1 and 2. The ime aken for his informaion propagaion o he source may no be accepable for many applicaions. This necessiaes he use of a local resoraion scheme. In local resoraion, he backup pahs are se up for every node or link. Therefore, upon failure he firs upsream node can locally direc raffic ono he backup pah bypassing he failure. These wo differen backup mehods are explained in deail laer. FAILURE MODES We consider wo differen failure modes agains which we proec. The firs is agains single link failures. In his case, we have o proec he acive pah agains all single link failures. The second is single elemen (node or link) failures. The amoun of resources needed o provide backup for he second mode will be greaer. In erms of deecing failures, we assume he following: In he single link failure model, when a link fails, he wo nodes ha are a he endpoin of he link know ha he link has failed, and immediaely swich all he demands ha go on his link o he alernae pah. In he single elemen failure model, when a node fails we assume ha all he link inerfaces a ha node fail, and herefore all links ha are inciden on he node fail. This is deeced as in he link failure case, and he LSPs are roued across he failed node. Noe ha in he case of single elemen failures, here has o be a backup pah for all node failures. We do no provide a backup if he source or desinaion of he raffic fails. Taking care of single node failures almos handles all link failures also excep for he las link on he acive pah. This is illusraed in Fig. 3. Therefore, for he single elemen failure case we proec agains all single node failures and he failure of he las link. BACKUP PATHS For pah resoraion, he backup pah has o be link disjoin wih he acive pah when we are proecing agains link failures. The node failure case can be ransformed o he link failure case, as shown laer. For local resoraion o be possible wih single link failures, he backup bypass pah for a link (i, j) can be any pah connecing nodes i and j ha does no include link (i, j). This backup pah for link (i, j) can include any link, including any links on he acive pah for he curren LSP Figure 1. Pah resoraion: acive and backup pahs. s s Flow seup on backup pah Primary pah Backup pah Figure 2. Informaion ransfer on link failure. Backup pah for he failure of node a and links l and m s l m a (apar from link (i, j)), as well as any links ha are used in he backup pah for oher links on he acive pah for his LSP. For he single elemen failure case, he backup pah for he failure of node k involves doing he following: Firs deermine he links (j, k) and (k, l) in he acive pah. If node k fails, i will resul in he failure of all links inciden on node k, in paricular link (j, k). Therefore, he failure will be deeced a node j, and if here is an alernae pah from node j o node l (or some oher node beween l and he desinaion ), node j can diver raffic along his backup pah. Noe ha he backup pah for he failure of node k has o avoid all links inciden on node k. SHARING BACKUP LINKS Capaciy on he acive pah canno be shared. Capaciy on he backup pah can be shared a wo levels. Inerdemand sharing is he case where he backup reservaion belonging o differen LSPs ha do no share links in he acive pah can be shared. For example, if wo LSPs wih equal Failure Informaion ransfer back o source Figure 3. A backup pah for single elemen failure. p Backup pah for he failure of link p IEEE Communicaions Magazine June

3 5 s 2 6 Primary arc s Figure 4. Acive and backup pahs for single link failure. 3 8 Backup pah s Failure Informaion flow 9 bandwidh demands beween a given source and desinaion do no have any links in common on heir acive pahs, he backup pah for hese wo LSPs can be shared compleely. This is an exreme case. However, even if he wo LSPs acive pahs have some links in common, i may sill be possible o share capaciy on he backup pah. The second case is inrademand sharing. We use Fig. 4 o illusrae inrademand sharing. In Fig. 4 noe ha link (8, 4) is used o backup links (2, 3) and (3, 4). This in urn means ha backup capaciy is shared on his link. The algorihms we ouline exploi boh iner- and inrademand sharing in order o minimize he amoun of bandwidh consumed. Figure 5 illusraes sharing backup in he case of single elemen failure. THE INFORMATION MODEL The amoun of sharing ha is possible depends on he kind of link usage informaion made available o he pah selecion algorihm. There are hree cases of ineres. The firs is wha we call he no informaion case. Here, he only informaion made available abou he nework is he oal bandwidh ha has been reserved on each link. This informaion is obainable from rouing proocol exensions. Since he link capaciies are all known, he residual bandwidh on all links can be inferred. Noe ha no informaion abou backup resource usage is available since he amoun of bandwidh uilized separaely by he acive and backup pahs on a link is no known. Nex is he case where here is complee informaion; ha is, he pah selecion algorihm knows he roues for he acive and backup pahs of all LSPs currenly in progress. This informaion is obainable if pah selecion is done in a cenralized manner. The very large amoun of informaion ha needs o be sen makes i impracical o disseminae his complee informaion o all nodes using link sae flooding mechanisms. In he hird parial informaion case, he informaion available o he rouing algorihm is slighly more han ha in he no informaion case. The addiional informaion is ha for each link, insead of knowing only he oal (or equivalenly residual) bandwidh usage, we now separaely know he oal bandwidh used by acive pahs and he oal bandwidh used by backup pahs. This incremenal informaion is very useful. I is possible o disseminae i in a disribued manner by incremenal addiions o proposed raffic engineering exensions o rouing proocols. In he firs no informaion scenario, i is no possible o do any inerdemand sharing of he backup pahs since he relevan informaion on backup bandwidh usage is no available. Inrademand sharing is sill possible since he source node has he backup bandwidh usage informaion for he curren demand. The second complee informaion scenario permis he bes sharing bu is no always pracical, so i is mainly useful only for comparison purposes. The hird parial informaion scenario is fairly modes in erms of he amoun of informaion o be mainained. Because only aggregae informaion is needed and no per-lsp informaion, i is easy o mainain and use his informaion in a disribued fashion. Therefore, online rouing of bandwidh guaraneed acive and backup pahs for resoraion under he parial informaion model is he main case of ineres. Furhermore, as discussed laer, even hough he parial informaion case only provides aggregae (and no per-demand) link usage informaion, i is sill possible o make exac backup bandwidh reservaions a each link. This makes he performance of he parial informaion case very close o ha of he ideal complee informaion case. NOTATION AND DEFINITIONS We consider a nework of n nodes (swiches/rouers) and m links. All he links are assumed o be direcional. We consider he seup reques for LSP k o be defined by a riple (o k, k, b k ). The firs field, o k, specifies he ingress rouer, he second, k, specifies he egress rouer, and he hird, b k, specifies he amoun of bandwidh required for LSP k. For each LSP seup reques, an acive pah and a backup pah have o be se up. In he single link failure case, resoraion is guaraneed for any single link failure in he nework. In he single elemen failure case, resoraion is guaraneed for eiher a single link or single node failure. If we deermine ha here is insufficien bandwidh in he nework o se up eiher he acive pah or he backup pah for he curren reques, his reques is rejeced. Requess are assumed o come one a a ime. For ease of noaion, assume ha he curren reques is for b unis of bandwidh beween source node s and desinaion node. If his reques is acceped, we noe ha all links on is acive pah will reserve b unis of bandwidh for his reques. Le A ij represen he se of LSP acive pahs ha use link (i, j) and B ij represen he se of LSPs ha use link (i, j) as a backup. Le F ij represen he oal amoun of bandwidh reserved for he LSPs ha use link (i, j) on he acive pah. Le G ij represen he oal amoun of bandwidh reserved by LSPs ha use link (i, j) on is backup pah. 74 IEEE Communicaions Magazine June 2002

4 and  Fij = kœ A ij bk Gij =  bk. kœb ij Le R ij = C ij F ij G ij represen he residual bandwidh of link (i, j). In he complee informaion case we assume ha each node knows he ses A ij and B ij for all links (i, j) in he nework. In he parial informaion case we assume ha each node knows he value of F ij, G ij, and R ij for all links (i, j) in he nework. Since we do no have any knowledge of he requess ha will arrive in he fuure, he objecive of he rouing algorihm is o deermine he acive and backup pahs for he curren reques so as o opimize use of he nework infrasrucure. A reasonable objecive hen is o minimize he sum of he bandwidhs used by he acive and backup pahs. In he case where no resoraion is needed (i.e., we jus have o deermine one pah), his objecive leads o min-hop rouing. PATH RESTORATION We firs consider pah resoraion for single link failures under he hree informaion scenarios. For all he cases, we need o se up an acive pah and a link disjoin backup pah. The bandwidh reserved on he acive pah is b. The backup bandwidh reservaion can be less han b due o he possibiliy of backup sharing. The amoun of sharing achieved depends on he informaion model. The objecive used in finding he pahs is ha he oal bandwidh used by he wo pahs be minimized. NO INFORMATION Since no informaion is known oher han R ij, he pah selecion algorihm does no know he backup bandwidh currenly used on he differen links. Hence, i canno deermine wheher sharing of backup bandwidh is possible, and mus assume ha no sharing is possible. Thus, bandwidhs of b unis have o be reserved on each link in he acive as well as he backup pah. Clearly, if R ij < bfor link (i, j), ha link canno be used for he acive or backup pah for he curren reques. Wih he objecive of minimizing he oal amoun of bandwidh consumed by boh he acive and backup pahs, we have o deermine wo link disjoin pahs. Since he bandwidh consumed on each link is b unis, he objecive of minimizing he oal amoun of bandwidh consumed is equivalen o deermining a pair of link disjoin pahs, where he oal number of links is minimum. This problem can be formulaed as a sandard nework flow problem where each link has uni cos and uni capaciy. There is a supply of wo unis a node s and a demand for wo unis a d. Any minimum cos flow algorihm can be used o solve his problem. A very fas algorihm for solving his problem is given in [7] and involves solving wo shores pah problems. An alernaive would be o roue wo disjoin pahs using he minimum inerference objecive. s 2 3 Failure Figure 5. Acive and backup pahs for single elemen failure. The minimum inerference objecive and an algorihm for dynamic rouing of nonresorable bandwidh guaraneed pahs using his objecive are described in [2]. An algorihm for dynamic rouing of resorable bandwidh guaraneed pahs using he minimum inerference objecive is developed in [8]. The no informaion model gives an upper bound on he bandwidh consumed for he parial informaion model. COMPLETE INFORMATION The complee informaion model, alhough pracical only in a cenralized implemenaion, is neverheless useful for comparison purposes since i gives a lower bound on bandwidh used in he parial informaion model. Rouing under complee informaion can be formulaed as an ineger linear programming problem [9]. In his scenario, he ses A ij and B ij are known for all links (i, j). Since we are assuming robusness under single link failures, i is possible o share backup pahs beween requess whose acive pahs do no share he same link. To formulae his problem, we firs define he quaniy q u ij u for each link pair (i, j) and (u, u). This quaniy q u ij u is he cos (bandwidh usage) of using link (u, u) on he backup pah if link (i, j) is used in he acive pah. To compue he value of q u ij u we firs define he se f u ij u = A ij «B. This is he se of demands ha use link (i, j) on he acive pah and link (u, u) on he backup pah. Le he sum of all he demand values in he se f u ij u be represened by d u ij u =  kœij. Recall ha he curren demand is for b unis of bandwidh beween nodes s and d. Now q u ij u is defined as follows: Ï 0 qij = Ìd ij + b -G Ó Informaion flow if dij + b G if dij + b > G and R dij + b -G oherwise. Node 2 Node 3 Node 4 Link Backup pah s IEEE Communicaions Magazine June

5 The complee informaion model, alhough pracical only in a cenralized implemenaion, is neverheless useful for comparison purposes since i gives a lower bound on bandwidh used in he parial informaion model. The moivaion for he above is as follows: Since links (i, j) and (u, u) canno be on boh he acive and backup pahs, he value of q ij is se o infiniy if (i, j) = (u, u). The quaniy d ij represens he amoun of backup capaciy on link (u, u) ha canno be used o back up he curren demand, if link (i, j) is used in he acive pah. This is because d ij is he amoun of bandwidh needed on link u u o backup he acive pahs currenly raversing link ij. Therefore, aking he curren reques ino accoun as well, a oal of d ij + b unis of backup bandwidh are needed on link u u if he curren reques were o raverse link ij and use link for backup. Recall ha G is he amoun of backup (and hence shareable) bandwidh usage currenly on link. Then he curren reques can be backed up on link (u, u) wihou reserving any addiional bandwidh if d ij + b G. Since only G unis of bandwidh is shareable, if d ij + b > G, an addiional reservaion of d ij + b G unis is necessary. If his bandwidh is no available, his backup pah is no feasible, so for his reques he backup cos of link is se o infiniy. Le vecor x represen he flow on he acive pah, where x ij is se o 1 if link (i, j) is used in he acive pah. Le vecor y represen he flow on he backup pah, where y ij is se o 1 if link (i, j) is used on he backup pah. The rouing wih full informaion can be formulaed as he following ineger programming problem wih quadraic consrain:  minb xij + z (,) ij ŒE ( u, u) ŒE Ï 0 if i π s, Âxij - Âxij = Ì 1 if i = s j j - i Ó 1 if = Ï 0 if i π s,  yij -  yij = Ì 1 if i = s j j - i Ó 1 if = z qij xij y "(,) i j "( u, u) xij yij Œ{ 01, } The firs se of consrains (x-variables) gives he flow balance for he acive pah; he second se of consrains (y-variables) gives he flow balance for he backup pah. The variable z represens he amoun of backup bandwidh reserved on link (u, u). The firs erm in he objecive funcion is he bandwidh consumed by he acive pah; he second erm is he bandwidh consumed by he backup pah. Noe ha he amoun of backup bandwidh consumed on link (u, u) is he larges value of q u ij u for any link (i, j) on he acive pah. Noe ha if he ineger program is infeasible, here is no feasible soluion o he rouing problem and he curren reques is dropped. We can inroduce an addiional consrain x ij + y ij 1 o explicily ake care of he fac ha he acive and backup pahs are disjoin. This is curren implicily handled by seing q u ij u = if (i, j) = (u, u): As oulined in [10], he quadraic consrain can be linearized.  PARTIAL INFORMATION This is he mos pracical case. The informaion available is he aggregae bandwidh used on each link by acive pahs denoed by F ij, he aggregae bandwidh used on each link by backup pahs denoed by G ij, and he link residual bandwidhs R ij. Noe ha since we are only mainaining aggregae informaion on bandwidh usage, he amoun of informaion being disribued o all nodes is independen of he number of LSPs ha are currenly using he nework. Whereas he complee informaion scenario requires per-lsp informaion o be mainained, he parial informaion scenario requires informaion o be mainained only for wo classes of LSPs: acive and backup LSPs. This is only slighly more informaion han he no informaion model, which keeps rack of only he oal aggregae bandwidh usage. As we shall see laer, using he developed rouing algorihms, he small amoun of exra informaion in he parial informaion scenario in comparison o he no informaion scenario can be used o obain big gains in nework performance fairly close o he complee informaion scenario when he performance meric is he number of rejeced requess. Firs noe ha some sharing of he backup pahs is possible even hough only minimal informaion is mainained. Le AP represen he acive pah and BP represen he backup pah for he curren demand. Le us assume for he momen ha AP has been seleced already. Le M represen he larges value of F ij for some link (i, j) in he acive pah, ha is, M = arg max F ( i, j) ŒAP ij. For a poenial link (u, u) on he backup pah, if M + b G, no addiional bandwidh needs o be reserved on he backup pah because any link failing on he acive pah generaes a bandwidh need of a mos M + b on he links of he backup pah. Recall ha G is he amoun of bandwidh in use by backups on link. If M + b > G u u, since G u u unis of bandwidh is shareable, only an addiional reservaion of M + b G unis is necessary. If his bandwidh is no available, his backup pah is no feasible. We can capure hese sharing noions in a formulaion similar o he complee informaion formulaion. For parial informaion, we se he value of q u ij u as follows: Ï 0 qij = ÌFij + b -G Ó This is based on he observaion ha dij Fij "(,) i j "( u, u). if Fij + b G if Fij + b > G and R Fij + b -G oherwise. 76 IEEE Communicaions Magazine June 2002

6 One can solve he ineger linear programming problem wih he new values for q u ij u. However, a faser algorihm is needed for online rouing in large neworks. This is paricularly so if he algorihm is o run on edge nodes wih limied compuaional resources. Le us assume ha AP has been deermined already; hence, he value of M is known. In his case he cos c of using a link (u, u) on he backup pah is given by Ï0 if M + b G if M + b > G c = ÌM + b -G and R M + b -G Ó oherwise. One can solve a shores pah problem wih he cos c on link (u, u). This will resul in he opimal backup pah provided he acive pah has somehow been independenly seleced. Of course, he amoun of sharing possible on he backup pah influences he choice of acive pah, so he acive pah canno be independenly chosen a he ouse. Le M = max (i,j) F ij, represen he maximum acive bandwidh ha can be reserved on any link. Below, we give a high-level view of an algorihm solving he pah selecion problem under parial informaion. I assumes here is a subrouine DISJOINT PATH () ha reurns he opimal soluion o he problem of finding wo link disjoin pahs beween nodes s and d in he nework where he cos of he firs pah is given by he sum of he a ij for all links (i, j) on he firs pah, and he cos of he second pah is given by he sum of c ij for all links (i, j) on he second pah. We define his problem more formally and give a soluion procedure laer in his secion. Assuming ha DISJOINT PATH () exiss, he pah selecion algorihm is he following: STEP 1: Le M = 0.If BEST =. STEP 2: If M > M hen exi else compue he cos a ij for using link (i, j) on he acive pah as Ï b if Fij M aij = Ì Ó oherwise. Also compue c ij, he cos o use link (i, j) on he backup pah, as Ï0 if M + b Gij if M + b > Gij cij = ÌM + b -Gij and Rij M + b -Gij Ó oherwise. STEP 3: Solve DISJOINT PATH (). If he opimal soluion o his problem is OPT and he value of OPT < BEST hen se BEST = OPT. Incremen M and go o STEP 2. Therefore, he feasibiliy of his approach o solving for he parial informaion case depends on he abiliy o solve DISJOINT PATH (). This problem can be saed more formally as follows: Given a direced graph and wo coss a ij and c ij on link (i, j), find a pair of link disjoin pahs beween a given pair of nodes s and wih minimum oal cos, where he cos of he firs pah will be he sum of he a ij for all links (i, j) on he firs pah and he cos of he second pah sum of he c ij for all links (i, j) on he second pah. Unlike he disjoin pah problem considered in he no informaion scenario where he link coss are he same for boh pah compuaions, his problem wih is differen link coss a ij and c ij is NP-hard. The proof is in [11]. This aricle also gives an algorihm for his problem wih a worscase guaranee. However, he wors-case guaranee is oo weak for our purposes. A more suiable dual-based algorihm is given in [12]. The basic idea in solving he overall problem is ha once M is fixed, he problem becomes ha of compuing DISJOINT PATH (). Since we don know he bes choice of M, we ry all values of M and ake he leas cos soluion. The number of feasible M values is upper bounded by he number of nework links, so rying all values of M is no very expensive. This algorihm execues very fas even on large-sized neworks and usually obains soluions wihin 5 percen of he opimal soluion. Several ricks can be used o speed up he algorihm even furher. For example, insead of ieraing from M = 0 o M = M, i is enough only o do he compuaion for values of M = f ij for some link (i, j). Therefore, we have o call DISJOINT PATH () a mos m imes, where m is he number of links in he nework. Of course, if differen links have he same f ij values, we need o do he experimen only once for all hose links. NODE FAILURES To exend he algorihm o work for node failures, we merely change he represenaion of nodes by spliing each node ino an ingress subnode where all he incoming links erminae and an egress subnode where all he ougoing links erminae. The wo subnodes are conneced wih a link, and he failure of his link is equivalen o a node failure. PARTIAL INFORMATION WITH EXACT RESERVATIONS Noe ha he use of aggregaed (parial) informaion as described above causes he pah compuaion algorihm o be conservaive in is esimae of he amoun of flow ha will occur on a link in he backup pah when a link in he acive pah fails. This is because he algorihm canno deermine which link in he acive pah will fail and hence has o assume he wors case, ha is, he flow on a link in he backup pah is aken o be he maximum of all he curren acive flows on links in he acive pah. This conservaive value is used in compuing he link coss for each link in he backup pah (as explained above), and hence in deermining he acive and backup pahs. Once he pahs are deermined, LSP seup is done using signaling. We assume ha he se of links in he acive pah is conveyed o every link in he backup pah during he signaling phase. The moivaion for doing his is he following: In he complee informaion model he values of q u ij u depend only on knowing he se f u ij u = A ij «B. We do no need o know he ses A ij and B To exend he algorihm o work for node failures, we merely change he represenaion of nodes by spliing each node ino an ingress subnode where all he incoming links erminae and an egress subnode where all he ougoing links erminae. IEEE Communicaions Magazine June

7 BACKUP COST COMPUTATION USING SHORTEST PATH ITERATIONS s k Figure 6. Compuing backup cos. j Las permanenly labeled node l individually. Therefore, when he links belonging o he acive pahs are passed along he backup pah, any link (u, u) on he backup pah can updae he se f u ij u for any link (i, j) in he acive pah. Noe ha his se changes only when link (i, j) is in he acive pah and link (u, u) is on he backup pah. This means ha link (u, u) on he backup pah can compue he value of q u ij u (as in an earlier secion), and can hen make he exac reservaion insead of he more conservaive value used by he parial informaion model. The value of f u ij u is only known o he link (u, u); hence, he pah compuaion a he source is sill done using parial informaion. The se f u ij u and hence he value of q u ij u changes when an LSP is removed from he nework. Since here has o be signaling along boh he acive and backup pahs o ear down he connecion, each link on he backup pah can updae he value of q u ij u for all links (i, j) on he acive pah ha is currenly being orn down. Observe ha in order o do all he compuaion above, a link (u, u) only needs o know abou he LSPs ha use ha link on he backup pah. I does no need o have knowledge of any oher LSP in he nework. This lends iself well o he signaling proocols. NO INFORMATION WITH EXACT RESERVATION This is very similar o he seup described in he las secion, excep ha parial informaion is no available o all he nodes in he nework. In his case, he source node compues he shores pair of disjoin pahs, as in he no informaion case. One of hese pahs is designaed he acive pah and he oher he backup pah. This informaion is signaled o he acive and backup pahs. In paricular, he links in he acive pah are known o he backup pah. Exac reservaions are made by he backup pah links as in he previous secion. LOCAL RESTORATION In his secion we ouline an algorihm for rouing wih local resoraion. Insead of giving he deails of he algorihm, we ouline he key ideas involved in he design of he algorihm. m Poenial backup pahs for link (k,l) Links in he curren shores pah ree Firs we consider he single link failure case, ignoring he inrademand sharing of backup bandwidh, under he parial and complee informaion models. Analyzing his case leads o an overall design of he algorihm. If link (i, j) is used in he acive pah, here has o be a backup pah bypassing link (i, j) so as o back up any failure of his link. Noe ha he backup pah has o sar a node i bu can erminae a any node beween node j and he desinaion on he acive pah. For now we ignore his, and consider he case where he backup pah for link (i, j) has o sar a i and erminae a node j. In his case, he overall bandwidh needed when link (i, j) is used in he acive pah is he sum of he bandwidh for using i in he acive pah and he bandwidh used for backing up he link. The bandwidh needed if link (i, j) is used on he acive pah is b. The bandwidh needed o back up link (i, j) can be compued as he shores pah from node i o node j afer removing link (i, j). We firs consider robusness o single link failures. The cos of using link (u, u) on he backup pah if link (i, j) is used in he acive pah, denoed by q u ij u, is he same as in he pah resoraion case, and depends on he informaion model used. Afer q u ij u is compued, we can deermine he oal cos of using link (i, j) in he acive pah. This oal cos is he sum of he acive pah cos of link (i, j) and he cos of is bypass pah. To deermine he cos of bypassing link (i, j), we compue he shores pah from i o j (excluding link (i, j)) where he cos of each link (u, u) in he pah is given by q u ij u. Le he lengh of his shores pah beween i and j be f ij. Then he cos of using link (i, j) on he acive pah is b + f ij, ha is, he sum of he bandwidh usage on link (i, j) and bandwidh usage for bypass of link (i, j). Once usage coss are associaed wih each link in he nework (using a oal of m shores pah compuaions), we now compue he shores pah beween s and using b + f ij as he cos of link (i, j). This gives he minimum amoun of bandwidh wihou inrademand sharing aken ino accoun. Therefore, we oally solve m + 1 shores pah problems. This leads o he firs design idea: The cos of backup pahs can be deermined by solving shores pah problems, one for each link in he nework. REVERSE SHORTEST PATH COMPUTATION In he above discussion, we ignored he fac ha he backup pah for link (i, j) sars a i bu can end a any node on he pah from j o (including j and ). Handling his case is faciliaed by execuing he shores pah algorihm backward from he desinaion o he source. This faciliaion is illusraed by Fig. 6, which shows a sep in he backward execuion of he algorihm. The dark lines in he graph represen he shores pah ree when Dijksra s algorihm is execued backward from he desinaion. For every node ha is permanenly labeled in he shores pah ree here is a unique pah from ha node o he sink. Consider a node k ha is permanenly labeled when we are consrucing he shores pah ree from he sink. Associaed 78 IEEE Communicaions Magazine June 2002

8 wih node k is he pah P(k) = {l, m, } along he shores pah ree from node k o he desinaion. Consider link (k, j) in he nework. The cos of using link (k, j) in he acive pah is he sum of bandwidh currenly being roued and he cos of backing up link (k, j). The doed lines in Fig. 6 illusrae hree differen pahs o backup link (k, j). Previously, he cos of backing up link (k, j) was compued as he shores pah from k o j wih qkj u u as he cos of link (u, u). Now insead of compuing he shores pah from j o k we compue insead he shores pah from k o any node in P(k). This can be done easily by running Dijksra s algorihm from j using quvjk on link (u, u), and erminaing he algorihm when any node in he se P(k) is permanenly labeled by he algorihm. This example illusraes he reasoning leading o he second design principle: I is necessary o execue he shores pah (Dijksra s) algorihm backward saring a he sink. INTRADEMAND SHARING USING STATE INFORMATION To derive he nex key idea, we consider he single link failure case where we also ake ino accoun inrademand sharing of backup bandwidh. Inrademand sharing of bandwidh occurs when link (i, j) uses link (u, u) for a backup and reserves a bandwidh of w on link (u, u). When some oher link (k, l) on he acive pah wans o use link (u, u) for is backup, in addiion o any inerdemand sharing i can use he already reserved bandwidh of w for free. Recall ha he shores pah algorihm is o be run backward from he desinaion. In order o keep rack of how much bandwidh is reserved a each link, we inroduce an m-vecor l u corresponding o node u in he nework. (Recall ha he number of links in he nework is m.) l u ij represens he amoun of bandwidh reserved by he curren demand for all he backup pahs for all he links leading from node u o desinaion. This bandwidh reservaion for he curren demand can be used o save bandwidh, by inrademand sharing, when backing up he links from u o he source s ha are ye o be deermined. Consider he case where he backup pah for link (k, j) is being deermined. Assume ha he shores pah is being deermined in he backward direcion from node j o node k. The m-vecor l j represens he reservaion made for his demand for all he backup pah from node j o he sink. This pah is known since here is a unique pah from node j o he sink in he shores pah ree. Consider a link (m, n) in he nework. Define k mn = F kj + b B mn lmn. j Then he cos of link (m, n) when deermining he shores backup pah is given by Ï0 if k mn 0 if 0 kmn < band Rmn kmn and lmn = Ìd mn ( mn, ) π ( k, j) Ó oherwise. The cos in he case of he complee informaion case can also be modified similarly. Therefore, he above procedure gives us a mehod for accouning for he inra-demand sharing. This gives he hird design principle: Mainaining he m-vecor a each node ha gives us he amoun of bandwidh reserved for he curren demand for backing up all links from he given node o he desinaion can be used o accoun for inra-demand sharing. ADAPTING ALGORITHM FOR NODE FAILURES To ge node bypass pahs, he procedure is almos he same as he edge bypass pah case. There are wo main differences. The firs is ha when we wan o deermine he cos of including link (i, j) in he acive pah, we have o deermine he cos of finding a backup from node i o he successor of node j wihou using any of he links inciden on node j. Of course, when he algorihm is run backward from he sink, he successors of all he nodes ha are permanenly labeled by Dijksra s algorihm are already known since a pah has been esablished from ha node o he desinaion. The second imporan difference is ha when a node fails, all he links inciden on he node fail. Therefore, he cos of he backup has o accoun for all he links failing simulaneously. We only consider he ougoing links from he node. For example, when compuing he cos of using link (i, j) in he acive pah, we have o consider he cos of backing up demands ha use link (j, l) for l Œ V. Therefore, he cos of all links (wihou considering inrademand savings) have o be modified as follows: Ï 0  dij q jk E ij = (, ) Œ Ì + b -Gu u Ó Cos of using link (u, u) for parial informaion case: Ï 0 Â( jk, ) ŒE qij = Ì Fjk + b -Gu u Ó if dij + b ( jk, ) ŒE Gu u and (, i j) π ( u, u) if  d jk E ij + b > (, ) Œ G, R  d ( jk, ) ŒE ij + b -Gu uand (, ij) π ( u, u) oherwise. if Fjk + b G ( jk, ) ŒE if  F jk E jk + b > G (, ) Œ and R Fij + b -G oherwise. The nex algorihm design idea is hen he following: Modifying he cos of he links in he compuaion of he backup coss can be used o accoun for node failures. The descripion of he complee algorihm using hese ideas is in [12]. ILLUSTRATIVE EXPERIMENTAL RESULT This secion gives an example experimenal resul illusraing he sharing efficiency and performance obained in he differen informaion   Mainaining he m-vecor a each node ha gives us he amoun of bandwidh reserved for he curren demand for backing up all links from he given node o he desinaion can be used o accoun for inra-demand sharing. IEEE Communicaions Magazine June

9 Complee Informaion (CI) Parial Informaion (PI) No Informaion (NI) Parial Informaion-Exac Reservaion (PI- ER) No Informaion-Exac Reservaion (NI-ER) Local Resoraion o proec agains single link failures (LOC) The resuls are shown in Fig. 8. Noe ha exac reservaion modes perform much beer han he case where reservaions are no exac. Furhermore, among he pah resoraion algorihms, Parial Informaion wih Exac Reservaion performs he bes and is fairly close o complee informaion. Parial informaion (wih nonexac reservaion) performed beer han no informaion wih exac reservaion. This perhaps is a funcion of he opology. We expec NI-ER o be reasonably good bu inferior o PI-ER. The performance of LOC also looks very compeiive. Figure 7. The 15-node es nework. Number of rejecs ou of 100 requess CI PI NI PI-ER NI-ER LOC Experimen number Figure 8. Number of rejeced requess for 5 random experimens in he 15- node es nework. scenarios. We show ha making exac reservaions leads o very good performance, making he case of parial informaion wih exac reservaions boh pracical and efficien. The experimenal seup is as follows. We performed experimens on a nework wih 15 nodes and 56 links. The 15-node nework is shown in Fig. 7. Each undireced link in he figure represens wo direced links. The capaciy of each of he hin links is 60 unis and of each hick link is 240 unis. In each experimen LSPs wih bandwidh requess uniformly disribued in he range [6, 9] arrive ino he nework. The source and desinaion of he LSPs are chosen a random. The objecive of he experimens was o deermine he number of rejeced requess ou of he 100 requess ha arrive in he nework. We performed five experimens. There were six algorihms run on he same daa: SIGNALING AND ROUTING PROTOCOL EXTENSIONS As discussed before, he informaion in he PI model is only an incremenal addiion o he NI model. In he NI model a link sae rouing proocol wih raffic engineering exensions is used o indicae he bandwidh on each link ha has been reserved by (acive) pahs already se up. The only addiional informaion needed for he PI model is o include he bandwidh reserved on each link by backup pahs ha have already been se up. This can easily be accomplished by modifying he OSPF opaque LSA used o convey raffic engineering capabiliies so ha i now has a subype indicaing he link bandwidh allocaed for backup. In MPLS neworks, a proocol like RSVP-TE or CR-LDP is used for LSP seup. In addiion o he capabiliies already incorporaed in a proocol like RSVP-TE, he main addiional informaion needed is ha he acive pah informaion (conveyed by he explici roue objec, ERO) be sen during backup pah seup o links on he backup pah. This permis links on he backup pah o make exac reservaions for backup when using only he PI model. CONCLUDING REMARKS QoS rouing research has been mosly focused on he rouing of a single pah wihou any faul olerance requiremens. Due o poenial applicaions in MPLS neworks, rouing of QoS guaraneed resorable pahs has become an issue of recen research ineres. This aricle discussed some recenly developed algorihms for resorable rouing of bandwidh guaraneed pahs. Also, he possible informaion models for link usage, and incremenal addiions o signaling and rouing proocols were discussed. A mehod for rouing wih parial or aggregae informaion bu wih exac reservaions of shared backup bandwidh was proposed as being boh feasible and efficien for he rouing of resorable bandwidh guaraneed pahs. This scheme can be exended o handle he case of failures associaed wih shared risk link groups. 80 IEEE Communicaions Magazine June 2002

10 REFERENCES [1] R. Guerin, D. Williams, A. Orda, QoS Rouing Mechanisms and OSPF Exensions, Proc. GLOBECOM [2] K. Kar, M. Kodialam, and T. V. Lakshman, Minimum Inerference Rouing of Bandwidh Guaraneed Tunnels wih Applicaions o MPLS Traffic Engineering, IEEE JSAC, Special Issue on Qualiy of Service in he Inerne, Dec [3] S. Plokin, Compeiive Rouing of Virual Circuis in ATM Neworks, IEEE JSAC, 1995, Special Issue on Advances in he Fundamenals of Neworking, pp [4] I. Maa and A. Besavros, A Load Profiling Approach o Rouing Guaraneed Bandwidh Flows, Proc. IEEE INFOCOM, Apr [5] B. Davie and Y. Rekher, MPLS Technology and Applicaions, Morgan Kaufman, [6] V. Sharma e al., Framework for MPLS based Recovery, Inerne draf, draf-ief-mpls-recovery-frmwrk- 04.x, July [7] J. W. Srballe and R. E. Tarjan, A Quick Mehod for Finding Shores Pairs of Disjoin Pahs, Neworks, vol. 14, 1984, pp [8] K. Kar, M. Kodialam, and T. V. Lakshman, Minimum Inerference Rouing for Resorable Bandwidh Guaraneed Connecions, Proc. INFOCOM 02, June [9] M. Kodialam and T. V. Lakshman, Dynamic Rouing of Bandwidh Guaraneed Tunnels wih Resoraion, Proc. INFOCOM 2000, Apr [10] H. D. Sherali and W. P. Adams, A Reformulaion-Linearizaion Technique for Solving Discree and Coninuous Non-convex Problems, Kluwer, [11] C. Li, S. T. McCormick, and D. Simchi-Levi, Finding Disjoin Pahs wih Differen Pah Coss: Complexiy and Algorihms, Ne., vol. 22., 1992, pp [12] M. Kodialam and T. V. Lakshman, Dynamic Rouing of Locally Resorable Bandwidh Guaraneed Tunnels using Aggregaed Link Usage Informaion, Proc. INFO- COM 2001, Apr BIOGRAPHIES MURALI KODIALAM [M] (muralik@bell-labs.com) obained a Ph.D. in operaions research from Massachuses Insiue of Technology in He has worked a Bell Laboraories since Ocober He is currenly in he High Speed Neworks Research Deparmen, working on resource allocaion and performance of communicaion sysems including rouing in MPLS sysems, opology consrucion and rouing in ad hoc wireless neworks, and reliable rouing in opical neworks. He is a member of INFORMS. T. V. LAKSHMAN (lakshman@research.bell-labs.com) received his Ph.D degree in compuer science from he Universiy of Maryland, College Park. Prior o ha he received a Maser s degree from he Deparmen of Physics, Indian Insiue of Science, Bangalore. He is currenly a direcor in he Neworking Research Laboraory a Bell Laboraories. Previously, he was a Bellcore (now Telcordia) where he was mos recenly a senior research scienis and echnical projec manager in he Informaion Neworking Research Laboraory. His recen research has been in issues relaed o raffic characerizaion and provision of qualiy of service, archiecures and algorihms for gigabi IP rouers, end-oend flow conrol in high-speed neworks, raffic shaping and policing, swich scheduling, and rouing in MPLS and opical neworks. He is a co-recipien of he 1995 ACM Sigmerics/Performance Conference Ousanding Paper Award, and he IEEE Communicaions Sociey 1999 Fred. W. Ellersick Prize Paper Award. QoS rouing research has been mosly focused on he rouing of a single pah wihou any faul-olerance requiremens. Due o poenial applicaions in MPLS neworks, rouing of QoS guaraneed resorable pahs has become an issue of recen research ineres. IEEE Communicaions Magazine June