Routing Strategies for IP Networks

Transcription

1 - 1 - Routing Stratgis for IP Ntworks Authors : W. Bn-Amur, N. Michl, B. Liau Contributors : J. Gffard, E. Gourdin Franc Tlcom R&D ru du Général Lclrc F Issy-Ls-Moulinaux Cdx 9 (walid.bnamur,jrom.gffard,ric.gourdin,nicolas.michl,brnard.liau)@franctlcom.com Abstract This work addrsss th problm of static routing complxity and prformanc for bst ffort traffic in a data ntwork and mor spcifically an Intrnt ntwork running an IGP (Intrior Gatway protocol), and MPLS if ncssary. W first giv a short prsntation of th various routing stratgis (singl-path and multi-path) and thir possibl ralization in an IP intra domain ntwork. W thn brifly introduc th problm of th prformanc masurmnt of a routing pattrn. W also dfin th complxity of a routing pattrn as th numbr of MPLS tunnls ndd for its ralization. W show how th numbr of MPLS tunnls that ar ndd to nhanc an IGP routing stratgy can b minimizd. W compar diffrnt routing stratgis in IP ntworks from th two points of viw: complxity and prformanc. W thn propos two off-lin Traffic Enginring mthodologis for IP intra-domain ntwork: th first on is basd on an IGP/MPLS architctur; th scond on is basd only on th IGP routing using an optimizd load balancing schm. Th algorithms usd to comput th IGP mtric and to optimiz th routing pattrns ar also brifly dscribd. Kywords Intrnt Ntworks, Routing Stratgis, Routing Prformanc, Administrativ Mtric, Traffic Enginring, IGP, MPLS, Algorithms.

2 - 2-1 Introduction Traffic routing within a tlcommunication ntwork dfins how th traffic matrix is mappd on th ntwork topology. Routing mchanisms ar thus idntifid as an ssntial fatur in th control of th ntwork prformanc [Awduch_1]. Th routing mchanisms involvd allow to assign th ntwork capacitis, mor or lss fficintly, to th dmands. Th routing choic has a dirct impact on th xistnc and location of congstion within th ntwork. A high lvl of congstion may dcras th grad of srvic (call blocking, incrasd dlays, packt losss, tc). Routing mchanisms within an IP ntwork may induc som rstrictions on th path choic rlatd to th path slction algorithm. Th problm occurs mor spcifically in th cas of a IP ntworks running an IGP (Intrior Gatway Protocol) routing protocol. In this cas, th routs driv from vry simpl routing algorithms (shortst path calculations) which offr only limitd control ovr th routing paths. This oftn lads to a sub-optimal utilization of th ntwork rsourcs. Today svral nw mchanisms ar proposd to incras th routing control and to optimiz th ntwork prformanc, and among thm MPLS. Howvr such mchanisms also introduc som complxity in th ntwork managmnt. W try to analyz th compromis btwn routing prformanc and complxity. W propos two off-lin Traffic Enginring mthodologis: th first on is basd on an IGP/MPLS architctur; th scond on is basd only on th IGP routing using an optimizd load balancing schm. 2 Organization of th papr W introduc various (static) routing stratgis (singl-path and multi-path routing stratgis) and dscrib how thy can b spcifically ralizd in an IP intra domain ntwork (Sction 3). W thn prsnt som of th routing prformanc critria that can b optimizd (Sction 4). W also introduc th complxity of an IP routing stratgy as th numbr of MPLS tunnls ndd. Th prformanc and complxity of various IP routing stratgis ar thn compard according to th most havily loadd link critrion (Sction 5). Som classs of fficint routings stratgis ar slctd from ths comparisons and two off-lin Traffic Enginring mthodologis ar drivd (Sction 6). Sction 7 is dvotd to th algorithms usd in th contxt of prformanc optimization. 3 Som static routing pattrns W first nd th following dfinitions: Ntwork topology: w assum that w can rprsnt th ntwork topology as a simpl non orintd graph that is rprsntd by its nods and dgs. Multipl paralll links ar rprsntd by a uniqu dg btwn th nods. Not that in MPLS Traffic Enginring although n paralll links can b announcd as a singl bundld link [Komplla], in ordr to us all links capacity, n paralll LSPs must b stlishd (unlss a solution basd on LSP hirarchy is usd [Komplla_2]). For IGP routing s ECMP blow. Routing pattrn: for a givn ntwork topology, w dfin a routing pattrn as a st of (possibly multipl) dirctd routs btwn pairs of nods in th ntwork. If thr is at last on rout in ach dirction btwn ach pair of nods, th routing pattrn is fully mshd.

3 - 3 - Various static routing pattrns ar introducd hr with thir possibl ralization in an IP intradomain ntwork. W also focus on som spcific IP routing stratgis basd on th modification of th IGP routing with ER-LSP (Explicit Routd Ll Switchd Path) cratd with MPLS. In th squl th trms ER-LSP, tunnl, and MPLS tunnl ar indiffrntly usd. 3.1 Singl-path routing pattrns In a singl-path routing pattrn thr is at most on rout btwn ach pair of nods. W can distinguish symmtric singl-path routing pattrns if th paths btwn A and B and B and A us th sam dgs for all pair of nods (A,B). Singl-path routing pattrns may b dividd in th following intrsting sub-classs: Shortst path routings pattrns: if thr xists a mtric (a st of pairs of valus, on for ach dirction, on th dgs of th ntwork) such that all paths of th routing pattrn ar a shortst path btwn th nd-points according to that mtric. A spcial cas is whn all shortst paths ar also uniqu (uniqu shortst path). Classical intra domain routing protocols (OSPF, IS-IS) ar basd on such shortst path calculations. Administrativ mtric valus ar rlatd to th systm intrfacs: btwn two routrs a diffrnt mtric valu can b affctd to ach intrfac of a sam link. Rsulting routing pattrns can thus b symmtric or not. Routing pattrn satisfying Routing pattrn not satisfying th sub-optimality condition th sub-optimality condition Figur 1 : Th sub-optimality condition Routing pattrns satisfying a sub-optimality (SO) proprty: two givn paths having two points in common satisfy th sub-optimality condition if thy shar th sam sub-path btwn ths two points (Figur 1). Not that this sub-optimality condition xcluds traffic load balancing and load distribution which aims to divid at an intrmdiat nod th traffic toward th sam dstination on svral distinct paths. Not also that routing pattrns satisfying th SO condition ar ncssarily symmtric. Routing pattrns basd on uniqu shortst paths satisfy th sub-optimality condition whn th mtric valus ar th sam on th two intrfacs of a link. Th contrary is fals [Bn- Amur&Gourdin_1]. Dstination-basd singl-path routing: any packt is forwardd through th ntwork using th dstination addrss. Obviously, shortst path routing and sub-optimal routing ar also basd on dstination. Howvr, this class of routing pattrns is largr. In fact, this is quivalnt to stlishing a spanning tr for ach dstination. Th dstination trs can b compltly indpndnt. Gnral singl-path routing pattrns without constraints: th whol traffic dmand btwn an origin-dstination pair is routd through a singl path without any additional constraint.

4 - 4 - In an IP ntwork running a classical IGP routing protocol, only shortst path routing pattrns can b ralizd. Othr singl-path routing pattrns can b ralizd with th xplicit routing functionality nld by MPLS (strict ER-LSP). As an ER-LSP is always unidirctional, symmtric or dirctional routing pattrns can b ralizd. Whn th routing pattrn is fully mshd, th total numbr of ER-LSP to crat is qual to n*(n-1) whr n is th numbr of nods. In th squl, for th sak of simplicity of th study, w focus our attntion on symmtric singl-path routing pattrns only. Not that for oprational rasons this proprty is oftn rquird by ntwork oprators. On rason is to limit th complxity of managmnt of th ntwork. Anothr rason is to prvnt to hav a routing path up in on dirction whil th rturn routing path is down du to a link failur. With symmtric routing pattrns, routing paths in both dirctions ar simultanously up or down in cas of link failur. 3.2 Multi-path routing pattrns In a multi-path routing pattrn, traffic btwn two nods can b forwardd among svral distinct paths. In IP ntworks, load sharing can b achivd at an intrmdiat nod in multipl ways: on a packt pr packt basis, or with a hashing function valuatd from th information rad in th packt hadr, tc. A hashing function basd on th origin and dstination can achiv sufficint granularity in a cor ntwork. An IGP routing protocol can provid multipl qual cost paths btwn which load sharing can b implmntd. Bcaus thr is no information in currnt IGP routing protocols out traffic loading on distant links, tchniqus hav bn utilizd to divid traffic somwhat vnly among th availl paths. Thos tchniqus ar rfrrd to as Equal Cost MultiPath (ECMP). A classical utilization of ECMP is to assign th sam mtric to paralll links btwn two routrs so that all thos links will b usd to forward traffic. This is thus quivalnt to singl-path routing in our topology modl whr w considr multipl paralll links as a uniqu (aggrgatd) link. Anothr tchniqu, Optimizd MultiPath (OMP) [OSPF-OMP], tris to adjust th load balancing paramtrs at ach nod in function of th ntwork load. This rquirs significant chang to th IGP bcaus dynamic information is ndd in ach routr out link loads in th ntwork. This proposition was nvr implmntd; E C D 1 3 B F G A Load Balancing paramtrs at nod B for dstination A: - Dst=A,Intrfac=E,60% -Dst=A,Intrfac=F,30% -Dst=A,Intrfac=G,10% H Figur 2: Gnral ECMP Gnral ECMP: instad of splitting th traffic vnly btwn th shortst paths, w can split it in any arbitrary way. In fact, it is vry asy to s that whn no particular routing constraints ar addd (numbr of hops for xampl), th link loads of any multi-path routing pattrn can b

5 - 5 - rproducd by a routing stratgy whr forwarding is basd only on dstination. That is to say, a nod B who hav to rout a packt to A, will randomly choos a path (an intrfac) using only th dstination addrss. In othr trms, if a crtain proportion of th traffic dmands from C to A and from D to A, us B as an intrmdiat nod, thn this traffic will b split in th sam way btwn B and A whatvr th origin (C or D) (Figur 2). W will show in Sction 7 how a multi-path routing can b transformd into a shortst path routing. With MPLS, svral tunnls can b opnd btwn a pair of nods and traffic can b arbitrarily shard among thm; 3.3 Spcific routing pattrns in IP ntworks Th ralization of th routing pattrns mntiond ov is basd ithr on th IGP routing or on administrativly configurd TE tunnls. Both mchanisms can b intgratd : th IGP routing can b modifid to tak into account TE tunnls. Thr diffrnt modls can b idntifid: in th first two modls, only th path slction procss of th IGP in a nod is modifid taking into account th TE tunnls originating at this nod, in th third modl TE tunnls ar advrtisd by th IGP protocol. «Basic IGP Shortcut : if a packt arrivs in a routr whr originats a tunnl with rmot xtrmity th dstination of th packt, thn th packt is forwardd to th dstination. Othrwis th packt follows th classical IGP routing; «IGP Shortcut» : in this modl proposd at th IETF [Smit], th shortst path calculation in th routrs rmains unchangd but th dtrmination of th nxt hop is modifid in th following way: if a tunnl originats in th routr with its xtrmity blonging to th shortst path, thn th packt will b forwardd in this tunnl; Advrtis tunnls into th IGP : in this modl implmntd by som manufacturrs, tunnls ar advrtisd in th IGP and usd in th shortst path calculations as virtual intrfacs. Dpnding on implmntation dtails and in particular on th tunnls mtric assignmnt, many diffrnt options ar possibl in th path slction procss. Thy giv mor flxibility to th currnt IGP routing protocols: th rsulting routing pattrns will not ncssarily b shortst paths, nor satisfy th SO condition nor vn b dstination basd. 4 Routing prformanc critria for bst ffort IP traffic W considr static routing pattrns and bst ffort traffic controlld by TCP. Th prformanc of routing pattrns can b viwd from th usr s point of viw or from th ntwork s point of viw. This distinction is introducd in [Awduch_2] whr traffic orintd prformanc and rsourc orintd prformanc objctivs ar dfind: Traffic orintd prformanc: th quality of srvic prcivd by nd usrs is mainly dtrmind by th (random) duration of a documnt transfr (Wb pag, -mail, FTP fil, tc). Sinc th sourc traffic rats ar ractiv to th ntwork load (TCP bhavior), th quality of srvic will dpnd on th link loads across th path; Rsourc orintd prformanc: from th oprator s point of viw, th objctiv is to minimiz rsourc utilization (link capacity). Anothr objctiv can b th robustnss of th traffic rpartition against traffic fluctuations. Th first objctiv implis that a routing pattrn must b found such that anothr routing cannot b found with a lowr load on ach link and with a strictly lowr load for at last on link. Such a routing pattrn is said to b non dominatd Th scond objctiv can b partially addrssd by looking for a routing pattrn that minimizs th maximum

6 - 6 - link load: such a routing pattrn will b l to cop with th maximal traffic incras (with th assumption of a homognous traffic incras across all origin-dstination dmands) For th sak of computational tractility, a simpl prformanc critrium is rquird: it should b only rlatd to th dg loads and capacitis, but indpndnt on th ntwork topology and on th ffctivly usd routing paths. Notations: W considr a ntwork dfind by its st of dgs L and a givn static routing pattrn. Lt C l b th capacity of dg l and A l b th avrag traffic load carrid through this dg (this load ffctivly dpnds on th routs within th ntwork). Th avrag load of dg l is dfind as ρ l = Al Cl. A routing pattrn is said to b fasibl if ρl 1 for any dg. Critria basd on th dg loads: It sms natural to try to maximiz a concav dcrasing functions of th dg loads as for instanc: 1 ( 1 ) 1 α ρl, α 0, α 1 (1) 1 α l L This function was proposd and studid in [Mo&Warland] and [Bonald&Massoulié]. L l. 1 α Whn α is clos to 1, th function (1) is quivalnt to + log( 1 ρ ) Thrfor, for 1 α =, critrion (1) can b xtndd and rplacd by log ( 1 ρ ) l L l. A routing is said to b optimal if it is l to carry th whol traffic flow minimizing critrion (1). An intrprtation can b proposd for som valus of α : α = 0 minimizs th avrag dg load. This is a simpl critrion but w wouldn t rcommnd it bcaus it is unl to diffrntiat two links with rspctiv loads of 0% and 100% and two links 50 % loadd (contrarily to th cas α > 0, th function is not strictly concav); α = 1 maximizs log ( 1 ρl ), quivalntly th gomtric man of ( 1 ρ l ); α = 2 minimizs 1 ( 1 ρl ), quivalntly th harmonic man of ( 1 ρ l ); α = corrsponds to a «min-max» critrion. On is succssivly intrstd in minimizing first th maximum load, thn th scond maximum load, and so on. Th highr th valu of α is, th mor attntion is paid to th most havily loadd dg. Critria basd on th dg rsidual capacitis: It is also possibl to rplac in (1) th dg load by th rsidual capacity C ( 1 ρ ) functions of th following typ can thus b considrd: 1 ( ( 1 )) 1 α C 1, 0, 1 l ρl α α (2) α l L l Objctiv l

7 - 7 - Intrprtations similar as for critria (1) can b proposd. Th highr th valu of α is, th mor attntion is paid to th dg with th lowst rsidual capacity. Not that a routing pattrn achiving th optimum valu for on of th critria dscribd ov is a non-dominatd solution. Th choic of a prformanc objctiv can b drivn by th natur of th studid ntwork, backbon or accss ntwork. Considring a backbon ntwork, th customr bit rat is gnrally boundd by th accss rat (or th rat of th Wb srvr) which is small compard to th dg capacitis. Th traffic orintd prformanc critria ar thus lss crucial than th ntwork orintd prformanc ons. A critria rlatd to th most havily loadd dg sms rlvant in th cas of static routing whn th ntwork is unl to adapt itslf automatically to traffic fluctuations. Th most havily loadd dg critrion is on of th most oftn usd critria to valuat th prformanc of backbon ntworks. 5 Comparison of static routing pattrns Th following static routing stratgis ar compard (listd in a dcrasing ordr of flxibility): Multi-path symmtric routing; Singl-path symmtric routing; Singl-path symmtric routing with constraint of sub-optimality; Uniqu symmtric shortst path routing; Minimum hop (symmtric) routing. In th squl, it is implicit that all routing pattrns considrd ar symmtric. W bliv som of th rsults can b xtndd to asymmtric routing pattrns but this is lft for furthr study. Rmind that for any multi-path routing pattrn, it is possibl to find a dstination basd multipath routing schm that achivs th sam load links (s Sction 3.2). This routing schm can b implmntd using a gnralizd ECMP tchniqu. Dfinitions : 1) for a givn routing stratgy and a givn ntwork topology, w call routing st of a routing stratgy th st of all routing pattrns that can b achivd with this routing stratgy; 2) for a givn routing stratgy, a givn ntwork topology, and a givn prformanc critrion, w call prformanc of a routing stratgy th bst prformanc of all routing pattrns that can b achivd with this routing stratgy. W first dfin th notion of complxity of a routing stratgy in an IP ntwork. W thn try to analyz th various routing pattrns that can b achivd with th ov routing stratgis and th associatd complxity. Finally w compar th prformanc of ths routing stratgis. 5.1 Complxity of th ralization of a routing pattrn in IP ntworks Th IGP routing protocol has som advantags: its simplicity, scalility, automatd and distributd implmntation. Morovr IGP routing has alrady provn its robustnss and rsilinc. A disadvantag of using MPLS xplicit routs is th administrativ burdn and potntial for human inducd rrors from using this approach on a larg scal [Michl&al]. Ntwork oprators thus might want to minimiz th total numbr of MPLS tunnls cratd in th ntwork. W dfin th complxity of a routing pattrn as th numbr of tunnls that ar ndd for its ralization in an IP ntwork.

8 Scnarios Svral scnarios (topology and traffic matrix) hav bn slctd in ordr to compar th diffrnt routing stratgis. Som of thm hav bn studid by C. Villamizar [Villamizar_1, Villamizar_2] in th valuation of OMP approachs and th othrs hav bn xtractd from ral cas world ntworks. Th scnarios usd by Curtis Villamizar ar availl on his Wb sit along with th rsults of his simulations [Villamizar_2]. Nods Edgs Msh dgr Dmands OMP_10_ OMP_20_ OMP_50_ Ths scnarios ar dfind by a ntwork topology (obtaind by random gnration) along with capacity on th dgs and a traffic matrix. Edgs ar symmtric but may hav a diffrnt capacity in ach dirction. Th traffic matrix is orintd. Th two following scnarios xtractd from ral cas ntworks hav also bn studid: Scnario FT_1 : 9 nods 20 dgs and 35 symmtric dmands; Scnario FT_2 : 26 nods 39 dgs and 154 symmtric dmands. 5.3 Comparison of routing sts: siz and complxity In what follows, w try to answr th following qustions: what is th rlativ siz of th routing sts of ach routing stratgy? What is th complxity of ralization of th corrsponding routing pattrns in an IP ntwork? Shortst path routing W first introduc som dfinitions: 1) A singl path and a mtric ar compatibl if th path is a uniqu shortst path according to th mtric. A mtric is compatibl with a singl-path routing pattrn if all paths ar compatibl with th mtric. In Sction 7, w addrss th cas whr th constraint of uniqunss of a shortst path is rlaxd; 2) A routing pattrn is compatibl if thr xists a mtric compatibl with all paths in th routing pattrn; 3) For a givn singl-path routing pattrn th numbr of compatibl paths is dfind as th maximal numbr of paths of a compatibl sub-routing pattrn (a subst of paths of th routing pattrn). A first stp in this routing stratgy analysis is to masur th difficulty to find compatibl mtrics for a givn routing pattrn.. For diffrnt ntwork topologis, w hav randomly gnratd 100 fully mshd singl-path routing pattrns and 100 fully mshd singl-path routing pattrns satisfying th suboptimality condition. In ach cas a compatibl mtric has bn sarchd using a linar programming mthod dscribd in [Bn-Amur&Gourdin_1] and [Bn-Amur&Liau] (s Sction7).

9 - 9 - W rmind that a routing pattrn that is not satisfying th sub-optimality condition is nvr compatibl [Bn-Amur&Gourdin_1]. Numbr of compatibl routing pattrns Gnral singlpath routing pattrn sub-optimality compliant routing pattrn Prcntag of compatibl paths (in cas of non compatibl routing pattrn) Gnral singlpath routing pattrn sub-optimality compliant routing pattrn OMP_10_29 0 % 51 % 35 % 95 % OMP_20_51 0 % 2 % 29 % 88 % OMP_50_101 0 % 0 % 33 % 69 % Although a limitd numbr of topologis has bn tstd, w can draw th following trnds from ths rsults: Gnral singl-path routing pattrns: it sms difficult to find a compatibl mtric for gnral singl-path routing pattrns (not a singl cas in our tsts). Th routing st of singl-path routing stratgy is thus much largr than th routing st of th uniqu shortst path routing stratgy. Howvr it is possibl to find a mtric compatibl with at last a significant sub-routing pattrn: in avrag 30 % of th paths whatvr th siz of th ntwork; Sub-optimality compliant routing pattrns: in a significant numbr of cass it is possibl to find a compatibl mtric. Th siz of th routing st of th sub-optimality compliant routing stratgy sms to b vry clos to th siz of th routing st of th uniqu shortst path routing stratgy for (vry) small ntworks (scnario OMP_10_29). As th siz of th ntwork incrass (a fw dozn of nods), th siz of th routing st of th sub-optimality compliant routing stratgy sms to b again much biggr than th siz of th routing st of th uniqu shortst path routing stratgy (scnario OMP_20_51 and OMP_50_101). Howvr th prcntag of compatibl routing paths is highr than for th gnral routing pattrns (mor than 70 %) although it sms to dcras with th siz of th ntwork. Ths rsults dpnd on th studid topologis. For xampl, for a ring ntwork th routing st of th sub-optimality compliant routing stratgy is qual to th routing st of th uniqu shortst path routing stratgy [Bn-Amur&Gourdin_1]. It is likly that th rsults dpnd on th dgr of connctivity of th ntwork. Othr rlvant topologis for IP ntworks ar undr study Singl-path routing with mtrics and tunnls W hav sn that a gnral singl-path routing pattrn is not oftn compatibl. It is possibl to raliz such routing pattrns in an IP ntwork using strict xplicit routing, for xampl by crating two ER-LPS pr path, on in ach dirction. This rquirs n*(n-1) MPLS tunnls in th ntwork (if th routing pattrn is fully mshd). Th routing complxity is thus dirctly rlatd to th numbr of dmands.

10 Howvr in th cas of sub-optimality compliant routing pattrns, it is oftn possibl to find a mtric compatibl with a larg prcntag of th paths in th routing pattrn. Th qustion is now th following : is it possibl to rproduc th rmaining non-compatibl paths with th IGP routing modifid with a limitd numbr of MPLS tunnls? W considr th IGP Shortcut modl of intgration of th IGP routing with th MPLS tunnls (Sction 3.3). For ach rmaining path not compatibl with th mtric, th two corrsponding ER-LSP ar cratd (on in ach dirction). Th modifid IGP routing will thus rout th traffic along th corrct paths for ths routing paths not compatibl with th mtric. Howvr thos tunnls can modify th routs found by th modifid IGP for th paths that ar compatibl with th mtric. It is asy to show th following rsult : if th initial routing pattrn satisfis th sub-optimality condition, thn th tunnls cratd as dscribd ov do not modify th IGP routing for th paths that wr compatibl with th mtric. Thus, in th cas whr th routing pattrn satisfis th sub-optimality condition, it can b ralizd by an IGP routing protocol modifid by som tunnls. Th numbr of pairs of tunnls (on in ach dirction) ndd is qual to th numbr of paths in th routing pattrn minus th numbr of compatibl paths. Howvr in som cass, it may b possibl to crat lss tunnls bcaus a pair of tunnls may modify mor than on shortst path into th corrct routing path (s Sction 7.1.2) Complxity of th routing pattrns W considr all routing pattrns (including singl-path and multi-path routing pattrns) and thir ralization in IP ntworks. Som of thm can b rproducd without any MPLS tunnls (i.. using only th IGP routing), som othrs rquir th cration of a limitd numbr of MPLS tunnls (IGP routing modifid with som MPLS tunnls) and th last routing pattrns rquir a larg numbr of MPLS tunnls (in th ordr of th numbr of paths in th routing pattrn). Basd on th rsults ov, w can rprsnt on Figur 3 a comparison of th complxity of diffrnt routing pattrns. Figur 3: Complxity of various routing pattrns W can s that a larg numbr of routing pattrns (much largr than th numbr of routing pattrns that can b achivd with th IGP routing only) can b achivd with a rasonl complxity

11 (with a limitd numbr of tunnls). Th natural qustion that ariss is th following: what lvl of prformanc can b achivd with ach lvl of complxity? 5.4 Comparison of prformanc Th prformanc critria considrd in this Sction concrns th ntwork ility to support traffic incrass. It is masurd by th maximum dg load (Sction 4) Optimization A diffrnt optimization problm has to b solvd for ach routing stratgy. Som of thm ar NP-hard and cannot b solvd xactly: in ths cass a huristic has bn usd. As a consqunc, th comparison of th routing stratgy prformanc may b affctd by th accuracy of ths huristics. Th routing optimization procdurs w hav usd ar dscribd blow: Multi-path routings: a linar programming (xact solution); Singl-path routings: a huristic (a branch and cut algorithm) basd on linar programming which also provids an uppr bound on th optimal solution [Gffard]. Only symmtric problms can b solvd with this tool (consquntly not th Villamizar scnarios 1 ); Singl-path with constraint of sub-optimality: an xact solution (basd on a linar programming) is undr study [Bn-Amur&Gourdin_2]. Uniqu shortst path: a simulatd annaling huristic [Bn-Amur&al]. Mor dtails out ths optimization algorithms ar givn in Sction Rsults Tl 1 summarizs th main rsults of our tsts. In ordr to undrstand this tl, not that : A rsult markd with a * mans that th solution valu is optimal; Rsults in bold charactrs wr obtaind by Villamizar and ar dirctly rportd from his Wb sit [Villamizar_2]: rsults for MPLS-OMP ar usd for th multi-path routing stratgy and th singl-path routing stratgy (rsults ar obtaind with a simpl grdy huristic). Rsults Multi-path Singl-path Minimum Hop Routing Uniqu Shortst Path OMP_10_ (MPLS-OMP) OMP_20_ (MPLS-OMP) OMP_50_ (MPLS-OMP) FT_9 0.78* 0.79* FT_ * 0.66* Tl 1 : Prformanc of diffrnt routing stratgis Th following commnts can b drivd : 1 Rsults for th Villamizar scnarios ar dirctly rportd from his Wb sit [Villamizar_2].

12 Singl-path vrsus multi-path routing: in th cas of scnarios FT_9 and FT_26, th proposd solution is optimal and th prformanc of both routing stratgis is vry clos. Th rsult is quit diffrnt in th cas of Villamizar scnarios. Th singl path constraint dcrass th prformanc (out 30 %). Not that in th lattr cas th optimization huristic usd is vry simpl and w hav no guaranty on th quality of th solution. Rsults sm to dpnd highly on th ntwork topology and on th traffic matrix. Not that it is asy to build scnarios for which th prformanc of th singl-path routing stratgy is arbitrarily wors than th prformanc of th multi-path routing stratgy (blow is an xampl of a topology on which a singl-path routing stratgy will prform vry badly compard to a multi path routing stratgy bcaus it is not possibl to balanc th traffic from O to D on th n paralll paths). Howvr in an oprational prspctiv, th worst cas is not rlvant, only th avrag cas ovr ralistic topologis; D n I n*1 Shortst path routing vrsus minimum hop routing: th comparison btwn uniqu shortst path routing and minimum hop routing stratgis illustrats th significant impact of a wis slction of th mtric valus. Th choic of a dfault valu (in th minimum hop routing stratgy, th dg mtric valu is systmatically st to on) may induc a vry poor prformanc compard to th prformanc achivl with an optimizd mtric (in th studid scnarios, th rlativ prformanc drop from 25 % up to 200 %); Singl-path routing vrsus uniqu shortst path routing: Not that for th Villamizar scnarios, th prformanc achivd with uniqu shortst path stratgy is somtims bttr than with a lss constraind singl-path routing stratgy. It only mans that, in th cas of singl-path routing optimization, th huristic is not accurat nough to rach a valu clos to th optimum. This may b of som importanc, bcaus such huristics ar quit oftn usd, vn in oprational ntwork configuration tools; In th cas of FT_9 and FT_26 scnarios, th optimal prformanc of th singl-path routing stratgy is found. For th smallr ntwork (FT_9), th prformanc that can b achivd with th uniqu shortst path stratgy is vry clos to this valu. Howvr for scnario FT_26, th bst prformanc that can b achivd with th uniqu shortst path stratgy is 30 % worst than this valu. Furthr tsts ar ndd to invstigat whthr th gap incrass with th siz of th ntwork (numbr of dgs) Prformanc improvmnt with MPLS tunnls Th siz of th routing st for th uniqu shortst path routing stratgy modifid with a fw MPLS tunnls if much largr than th siz of th routing st for th uniqu shortst path routing stratgy. A natural qustion thn follows : is it possibl to significantly improv th prformanc of uniqu shortst path routing by adding a fw MPLS tunnls? O

13 W suppos that th IGP routing is modifid by th MPLS tunnls according to th «IGP Shortcut» intgration modl (Sction 3.3). For xampl, if w considr scnario OMP_10_29, th bst prformanc achivd with th uniqu shortst path routing stratgy is By looking at th routing paths, w not that 3 links hav th maximum load of 85 %. W hav idntifid 3 pairs of MPLS tunnls that lad to a modifid routing pattrn whr th most havily loadd link hav a load of 77 %. By crating a fw MPLS tunnls, it is in som cass possibl to raliz a nw routing pattrn with a significantly improvd prformanc. An important point to mntion hr is that th rsulting routing pattrn dos not ncssarily satisfy th sub-optimality condition. This mans that it is possibl to achiv som kind of load distribution whr two dmands may b routd on two paths with two nods in common but using a distinct path btwn th 2 nods (Figur 4). A RAG D A D C G RAG C G TAG B RBG E F B RBG E F Figur 4 : shortst path routing pattrn modifid by a TE tunnl thrby achiving load balancing Finally, not that it is not clar which of th thr diffrnt modls of intgration of th IGP routing with MPLS tunnls is th most intrsting. Th first on, howvr, may add mor complxity bcaus on tunnl can b usd by only a limitd numbr of dmands. 6 «Off-lin» Traffic Enginring mthodologis Basd on th rsults of Sction 5, w can propos off-lin «Traffic Enginring» mthodologis. Th objctiv is to improv th prformanc of th ntwork in trms of rsourc utilization. Two diffrnt mthodologis ar dscribd: th first on using MPLS, th othr on rlying on th IGP routing only but and using a gnralizd ECMP tchniqu. In both cass, a singl class of (bst ffort) traffic is considrd. It is also assumd that a rprsntativ nd-to-nd traffic matrix btwn th ntwork nods can b masurd or stimatd. 6.1 An MPLS basd off-lin Traffic Enginring mthodology Th following assumptions ar mad: MPLS is dployd in th ntwork and it is possibl to crat xplicitly routd MPLS tunnls (ER-LSP); Th IGP routing is modifid to tak into account th MPLS tunnls in th dtrmination of th nxt hop according to th IGP Shortcut modl (Sction 3.3).

14 - 14 -? Routing Pattrn SO compliant Find wights (Linar program) Optimiz prformanc with SO Optimiz prformanc with USP Othr linar constraints (x: wights that cannot b changd) {wights} {Routs satisfid} {Routs not satisfid} {ER-LSP} 1 Gnrat ER_LSP Long/Mdium Trm Improv Prformanc (Huristic) {ER-LSP} 2 Numbr max of ER- LSP Mdium/Short Trm Figur 4: Off lin Traffic Enginring mthodology Th mthodology is dpictd on Figur 4. It involvs th following stps: Stp 1) First optimiz in an off-lin procdur th routing pattrn according to th prformanc critria chosn (for xampl, try to minimiz th load of th havist loadd link) allowing ithr all sub-optimality compliant singl-path routing pattrns or uniqu shortst paths routing pattrns only. Th output is a singl-path routing pattrn satisfying th sub-optimality condition; Stp 2) Sarch a mtric compatibl with a numbr of paths in this routing pattrn qual to th numbr of compatibl paths of th routing pattrn. This stp can also includ som xtra constraints providd that thy can b xprssd using a linar formulation (for xampl, qualitis or inqualitis vrifid by th mtric valus, minimizing th valu changs from an xisting mtric st); Stp 3) If th mtric obtaind in Stp 2) is not compatibl with th ntir routing pattrn obtaind in Stp 1), crat th ncssary MPLS tunnls (ER-LSP) in ordr to rproduc compltly th routing pattrn obtaind in Stp 1) (Sction 5.3.2); Stp 4) Thn try to improv th routing prformanc of th solution obtaind in Stp 3) by adding a fw MPLS tunnls : it is ncssary in this stp to find a tradoff btwn th numbr of tunnls cratd and th gain in prformanc. W can idntify two diffrnt parts in this mthodology. Th first on (Stps 1 through 3) implis th modification of administrativ mtric valus of th IGP in th ntwork. This opration is not dsirl too oftn. This typ of action can b considrd in a mdium or long trm basis. Th scond part of th mthodology only attmpts to crat (or modify) MPLS tunnls in ordr to improv th routing prformanc. Th tunnl cration and th rsulting modification of th routing pattrn (calculatd by th modifid IGP) ar simpl and fast oprations (compard to th IGP convrgnc). This can b considrd as a short trm action. On of th advantags of this TE mthodology is to rly as much as possibl on th IGP routing which has alrady provn its scalility, rliility and which is automatd. Th administrativ mtric valus ar changd whn ndd in ordr to optimiz th routing prformanc of th nominal routing pattrn. Th us of MPLS tunnls nls th ntwork oprator to significantly improv th routing

15 prformanc in rspons to vnts in th ntwork (transint chang of traffic profil tc.) whil limiting th numbr of MPLS tunnls which limits th complxity of managmnt. 6.2 An ECMP basd off-lin Traffic Enginring mthodology W assum that th routrs ar l to split th traffic through diffrnt qual cost paths (s Sction 3.2). Th load splitting paramtrs hav to b administrativly configurd. Th mthodology involvs th following stps: Stp 1) First comput off-lin a multi-path routing pattrn optimizing th prformanc critria chosn (for xampl, try to minimiz th load of th havist loadd link). This is gnrally asy to achiv (s Sction 7.2); Stp 2) Dtrmin th dstination basd multi-path routing pattrn that achivs th sam load links. In othr words, dtrmin th adquat load balancing paramtrs at ach intrmdiat nod and for ach dstination so that th rsulting hop-by-hop routing achivs th sam link loads (s Sction3.2); Stp 3) Comput a mtric compatibl with this routing pattrn (s Sction 7.1.3). W not that with this mthodology, both IGP mtrics and load balancing paramtrs must b administrativly configurd. Th opration of modification of administrativ mtric valus of th IGP in th ntwork can b considrd in a mdium or long trm basis. Th opration of modifying load balancing paramtrs howvr dos not hav any convrgnc consqunc. This could b don on a mor frqunt basis in rspons to vnts in th ntwork (transint chang of traffic profil tc.). 7 Algorithms for traffic nginring In this Sction w brifly prsnt som of th algorithms usd to addrss th problms that aris in th contxt of traffic nginring as dscribd ov. Du to spac limitation, it is not possibl to giv in this papr ithr th proofs or th whol dtails of th algorithms. Howvr, this Sction is slfcontaind and can b undrstood asily. 7.1 Compatibl mtrics This Sction is dvotd to mthods usd to comput a st of dg mtrics compatibl with a st of routing paths Uniqu Shortst Paths First lt us focus on th cas of uniqu shortst paths. As said in Sction 3, th sub-optimality condition (Figur 1) of th routing paths is a ncssary condition to find a st of compatibl mtrics. Lt G=(V,E) b th graph associatd with th ntwork. Th st of nod pairs of G for which a routing path R is givn is dnotd by K. In othr trms, w assum that a path R(a,b) is givn for ach (, ) K. If c and d ar such that c R( a, b) and d R( c, b), thn R(c,d) is assumd to b th subpath of R(a,b) linking c to d (by sub-optimality). S(a,b) is dfind as th st of paths btwn a and b which ar diffrnt to R(a,b). Th mtric is dnotd by( m ). A gnral linar modl that can b usd to find mtrics is th following: E

16 Find ( m ) E Subjct to: LP1 m = y ; ( a, b) K R ( a, b ) m 1 + y ; ( a, b ) K, p S ( a, b ) p m 0; E ( ) This linar program can b solvd by gnralizd linar programming. An quivalnt polynomial formulation can also b givn [Bn-Amur&Gourdin_1][Bn-Amur&Liau]. If a solution is found, th mtric givn by LP 1 is compatibl with th routing paths: vry path R(a,b) is a uniqu shortst path, according to this mtric, btwn a and b. Not that many particular constraints can b addd to LP 1 : - All th mtric valus must b largr than 1; - W may also want som links to hav qual mtrics; - Th routing paths usd during failurs ar also givn in advanc (thy must b shortst paths in th rsulting graph obtaind aftr th failur); - Th mtrics may b rquird to b intgr. LP1 can also b solvd considring various kinds of objctiv functions: minimiz th maximum mtric, th sum of mtrics, or any linar function of th varils tc. Not that LP 1 dos not always hav a solution. Said anothr way, th sub-optimality condition is a ncssary but not always a sufficint condition to find a mtric. Som othr ncssary conditions ar proposd in [Bn-Amur&Gourdin_1]. Howvr, w showd that th sub-optimality is sufficint for som graphs such as cycls, cactus tc. In th cas whr thr is no fasibl solution, an intrsting particular formulation of LP 1 is th on maximizing th numbr of dmands whos routing paths ar uniqu shortst paths (or quivalntly that maximizs th numbr of compatibl paths): ( LP ) 2 Maximiz ε (a,b) K Subjct to: m = y ; ( a, b) K R ( a, b ) m ε + y ; ( a, b) K, p S ( a, b) p m 0; E 0 ε 1; ( a, b) K LP 2 always has a solution. It is also asy to show that th varilsε, obtaind by solving LP 2, will b qual to 1 and 0. Said anothr way, LP 2 givs xactly th dmands that can b satisfid (in trms of uniqu shortst path constraint). Th objctiv function of LP 2 can also b mor gnral.

17 Singl-path routing with mtrics and tunnls Whn a compatibl mtric cannot b found (bcaus th routing pattrn is not compatibl or bcaus xtra constraints hav bn addd to th linar program), th routing pattrn can b rproducd by introducing a fw tunnls in ordr to modify th IGP routing according to th IGP Shortcut modl (Sction 5.3.2). In ordr to minimiz th numbr of MPLS tunnls that nd to b addd a linar formulation slightly diffrnt from LP 2 can b usd. Instad of considring all th paths of S(a,b), w considr only th st N(a,b) of paths that ar nod disjoint with R(a,b). Th program solvd is th following. ( MIP ) 3 M inimiz th numbr of tunnls = t (a,b) K Subjct to: m = y ; ( a, b) K R ( a, b ) m 1 ε + y ; ( a, b) K, p N ( a, b) p 0 m M ; E ε 0; ( a, b) K ε t ; ( a, b) K 1 + R ( a, b) M t { 0,1 }; ( a, b) K W assum in MIP 3 that th mtric valus ar boundd by a maximum valu M. W also us R(a,b) to dnot th numbr of hop of rout R(a,b). Th varil t indicats if it is ncssary to crat a tunnl btwn a and b. Not that a tunnl is cratd only if thr is a path disjoint with R(a,b) having a cost lss or qual to th cost of R(a,b). In th othr cass, vn if R(a,b) is not a uniqu shortst path, w do not nd a tunnl btwn a and b bcaus som othr intrmdiat tunnls will b cratd and usd by th dmand (a,b) ( IGP Shortcut modl). MIP 3 can b rplacd by othr asir linar programs that giv a good approximation of th numbr of tunnls (without th uppr bound M): ( LP ) 4 M inimiz ε (a,b) K Subjct to: m = y ; ( a, b) K R ( a, b ) m 1 ε + y ; ( a, b) K, p N ( a, b) p 0 m ; E 0 0 ε 1; ( a, b) K

18 Multi-path routing pattrn W assum that a st of paths R 1 (a,b), R 2 (a,b),,is givn btwn ach pair of vrtics (, ) K. W would lik to comput a mtric such that all ths paths ar shortst paths. Lt C(a,b) b th st of paths btwn a and b diffrnt from th givn routing paths R 1 (a,b), R 2 (a,b),. Obviously, a null mtric is a solution of th problm. Howvr, for practical rasons, w want to minimiz th numbr of links with a null mtric valu. This is formulatd blow: ( LP ) 5 Minimiz ε E Subjct to: m = y; (, ) K, Ri(, ) Ri ( a, b) m y; ( a, b) K, p C( a, b) p m 1 ε ; E 0 ε 1; E Th optimal solution of LP 5 is ncssarily intgr: varils ε will b qual to 0 or 1. Rcall that any optimal multi-path routing without particular routing constaints (such as lngth constraints), can b sn as an optimal routing basd only on dstination. As LP 5 provids a mtric which is compatibl with any multi-path routing, w can dduc that it is possibl to optimiz th ntwork prformanc only by using a modifid ECMP mchanism (Sction 3.2). Said anothr way, first w hav to comput an optimal multiflow optimizing th prformanc critrion (for xampl th maximum load). Thn, w can dtrmin th load balanc cofficints by vry simpl calculations and transform th multiflow into a multi-path routing basd only on dstinations. Finally, w comput th dg mtrics solving LP 5 (or any othr variation of LP 5 ). 7.2 Optimization algorithms Routing prformanc optimization is oftn a non trivial problm. Adquat modls and mthods hav to b dvlopd to addrss ach spcific problm. Oftn an xact rsolution will not b possibl in a rasonl computational tim bcaus som problms ar NP-hard. In such cass fficint huristics hav to b found. Not that th difficulty of th optimization problm associatd with a givn routing stratgy can b a dcision critrion for an oprational application. W prsnt brifly in this Sction th diffrnt problms and how thy can b addrssd Multi-path routing stratgis Whn multi-path routing is considrd, th problm may b asy to solv. For xampl, if th optimization critrion is th maximum load or any linar function dpnding on dg loads, thn th problm is polynomial (classical multiflow problm). Morovr, it is asy to intgrat som additional constraints. For xampl on can rstrict th problm to paths with limitd numbr hops tc. Multiflow problms ar vry classical. Howvr, som simpl and important rsults ar not vry known. Suppos for xampl that w would lik to minimiz th maximum load. It is vry asy o show that w can find an optimal solution such that th numbr of usd paths is lowr than th numbr of

19 dmands plus th numbr of dgs. This mans that many dmands in an optimal solution will b singlpath routd Singl-path routing stratgis For gnral singl-path optimization problms, w us th tool dscribd in [Gffard]. This tool is basd on a branch&cut algorithm. Th singl-path routing with sub-optimality condition was studid in [Bn-Amur&Gourdin_2]. Th algorithm usd to comput a mtric satisfying th sub-optimality condition is basd on a cutting plan algorithm. To impos th sub-optimality condition, w dfin two nw sts of 0-1varils: r k E and r k v for ach traffic dmand k, ach vrtx v and ach dg. Th sub-optimality condition can b writtn in th following way: r r + r 1,, ac, c Many valid inqualitis hav bn introducd to acclrat th algorithm of [Bn- Amur&Gourdin_2]. Finally, th optimization problms corrsponding to shortst path routing stratgis hav bn solvd using som local sarch algorithms (s [Bn-Amur&al] and [Michl&al]). Th advantags of this mthod ar, first its flxibility: it can b usd for diffrnt kinds of optimization critrion and can intgrat various constraints rlatd to quality of srvic. Scond it can solv larg siz problms. Th main principl of ths algorithms consists in changing th mtric of som dgs and r-computing th routing paths at ach itration. Som survivility constraints and th multi-hour bhavior of th traffic hav bn considrd in [Bn-Amur]. Othr huristics hav bn proposd in [Pioro&al] and [Thorup&al]. 8 Conclusion To summariz, w dscrib nw intra-domain routing mchanisms in IP ntwork and how thy can improv routing flxibility and prformanc in IP ntworks. Basd on som numrical rsults, w thn propos two diffrnt off-lin Traffic Enginring mthodologis that illustrat two possibl volutions of IP routing in intra-domain ntworks. Ncssary algorithms to implmnt thos mthodologis ar also shortly prsntd. A) MPLS BASED TRAFFIC ENGINEERING METHODOLOGY A nw mchanism lik MPLS tunnls xplicit routing givs mor control ovr routing in IP ntworks. Various routing stratgis for bst ffort traffic using this nw functionality can b considrd and all possibl routing pattrns can b ralizd in IP intra domain ntwork. Ths routing stratgis giv mor or lss flxibl control ovr th routing of th traffic but should also b compard in trms of complxity, scalility and robustnss. Th comparison of th prformanc of ths diffrnt routing stratgis with th critria of th havist loadd link shows that : Th diffrnc in trms of routing prformanc of th diffrnt routing stratgy sms to strongly dpnd on th siz and topology of th studid ntworks (which is not vry surprising). It is thus important to focus on rlvant topologis for IP ntworks;

20 Whatvr th routing stratgy considrd, optimization has an important consqunc on th routing prformanc. This is spcially tru for th stratgy of uniqu shortst path routing according to an administrativ mtric: a wis choic of th mtric can significantly improv th routing prformanc; A routing stratgy that prmits to raliz much mor various routing pattrns can not ncssarily achiv a significantly bttr prformanc. A uniqu shortst path routing stratgy prforms vry wll in gnral and somtims clos to th optimum achivl with singl-path or vn multi-path routing stratgis; Th us of xplicitly routd MPLS tunnls can improv th prformanc of routing. W show howvr that it is not ncssary to rly only on xplicit routing (which rquirs a larg numbr of tunnls), but that mixd routing stratgis basd on IGP routing and MPLS tunnls can produc vry intrsting routing pattrns in trms of prformanc. W giv an algorithm minimizing th numbr of MPLS tunnls that nd to b addd to rproduc a givn singl-path routing pattrn; Basd on thos rsults, an off-lin Traffic Enginring mthodology is proposd. It is basd on an optimization of th IGP routing (by a wis choic of th administrativ mtrics) nhancd by th us of a limitd numbr of xplicitly routd MPLS tunnls. Advantags of such a Traffic Enginring systm would b to bnfit from th highly provn robustnss of th IGP routing whil improving th prformanc and ractivity of th routing control in trms of rsourc utilization with a limitd addd oprational complxity. B) ECMP BASED TRAFFIC ENGINEERING METHODOLOGY W assum that routrs ar l to split th traffic towards on dstination on multipl paths according to som administrativly dfind load balancing paramtrs. It is thn possibl to rproduc th sam (optimal) link loads in th ntwork as thos rsulting from any givn (optimal) multi-path routing pattrn. This dos not rquir any MPLS tunnls. Howvr MPLS can intgrat various typs of routing constraints allowing to implmnt spcific routing stratgis and QoS policis. 9 Rfrncs [Awduch_1] A framwork for Intrnt Traffic Enginring, draft-itf-twg-framwork-02.txt, D. Awduch t al., July [Awduch_2] MPLS and Traffic Enginring in IP Ntworks, D. Awduch (UUNET), IEEE Communications Magazin, Dcmbr [Bn-Amur&al] Dsigning Intrnt ntworks, W. Bn Amur, E. Gourdin, B. Liau and N. Michl, in Proc. DRCN 2000, "Rlil Ntworks for th Information Ag", pp 56-61, Munich, April 2000 [Bn-Amur&Gourdin_1] Intrnt routing and rlatd topology issus, W. Bn Amur, E. Gourdin, submittd to SIAM journal of discrt mathmatics (2000). [Bn-Amur&Gourdin_2] An xact mthod to optimiz IP ntworks. W. Bn-Amur and E. Gourdin, submittd (2000). [Bn-Amur&Liau] Computing Intrnt routing mtrics, W. Bn Amur and B. Liau, Annals of tlcommunications, Mars/April N56, pag , [Bn-Amur] Multi-hour dsign of survivl Intrnt ntworks, W. Bn-Amur, Submittd to Tlcommunications Systms, 2000

21 [Gffard] A 0-1 modl for singly routd traffic in tlcommunication ntworks. J. Gffard. Annals of Tlcommunications. March/April N56, pags , [Komplla] Link bundling in MPLS Traffic Enginring, draft-komplla-mpls-bundl-04.txt, K. Komplla, Y. Rkhtr, L. Brgr, Mai 2000 [Komplla_2] LSP hirarchy with MPLS TE, draft-komplla-lsp-hirarchy-00.txt, K. Komplla, Y. Rkhtr, Dcmbr 2000 [Li] MPLS and th Evolving Intrnt Architctur, Tony Li, IEEE Communications Magazin, Dcmbr [MATE] MATE : MPLS Adaptiv Traffic Enginring, draft-widjaja-mpls-mat-01.txt, I. Widjaja, A. Elwalid, Octobr [Michl&al] Optimizing administrativ wights for fficint singl-path routing, W. Bn-Amur, E. Gourdin, B. Liau and N. Michl, In Proc of Ntworks [ [Mo&Walrand] Fair End-to-End Window-Basd Congstion Control, J. Mo and J. Walrand, IEEE/ACM Transactions on Ntworking, Vol. 8, NO. 5, OCTOBER [OSPF-OMP] OSPF Optimizd Multipath (OSPF-OMP), C. Villamizar (UUNET), draft-itf-ospfomp-00.txt, March [Pioro&al] On OSPF rlatd ntwork optimisation problms, M. Pioro, A. Harmatos, J. Juttnr, P. Gajowniczk and S. Kozdrowski, IFIP ATM IP 2000, Ilkly, July 2000 [Smit] Calculating IGP routs ovr Traffic Enginring tunnls, draft-hsmit-mpls-igp-spf-00.txt, Naiming Shn, Hnk Smit, Jun [Thorup&al] Intrnt Traffic Enginring by Optimizing OSPF Wights, Brnard Fortz, Mikkl Thorup, INFOCOMM [Villamizar_1] MPLS Optimizd Multipath, C. Villamizar (UUNET), draft-villamizar-mpls-omp- 01.txt, Fbruary [Villamizar_2] C. Villamizar Wb sit: