ualiy-of-service Class Specific Traffic Marices in IP/MPLS Neworks Sefan Schnier Deusche Telekom, T-Sysems D-4 Darmsad +4 sefan.schnier@-sysems.com Franz Harleb Deusche Telekom, T-Sysems D-4 Darmsad +4 franz.harleb@-sysems.com Marin Horneffer Deusche Telekom, T-Com Hammer Sr. - D-4 Münser +4 0 ABSTRACT In his paper we consider he problem of deermining raffic marices for end-o-end demands in an IP/MPLS nework ha suppors muliple qualiy of service (os) classes. More precisely, we wan o deermine he se of raffic marices T i for each os class i separaely. T i conains average bandwidh levels for os class i for every pair of rouers wihin he nework. We propose a new mehod for obaining os class specific raffic marices ha combines esimaion and measuremen mehods: We ake advanage of he fac ha he oal raffic marix can be measured precisely in MPLS neworks using eiher he LDP or RSVP-TE proocol. These measuremens can hen be used in a mahemaical model o improve esimaion mehods known as nework omography ha esimae os class specific raffic marices from os class specific link uilizaions. In addiion o he mahemaical model, we presen resuls of he proposed mehod from is applicaion in Deusche Telekom s global IP/MPLS backbone nework and we show ha he esimaion accuracy (mean relaive error) is improved by a facor of. compared o resuls from nework omograviy. We invesigae he srucure of he esimaed raffic marices for he differen os classes and moivae in his paper why os class specific raffic marices will be essenial for efficien nework planning and nework engineering in he fuure. Caegories and Subjec Descripors C.4 [Performance of Sysems]: Measuremen echniques, Modeling echniques. C.. [Compuer-Communicaion Neworks]: Nework Operaions. General Terms: Algorihms, Measuremen. Keywords: Traffic Marices, MPLS, LDP, os.. INTRODUCTION Traffic marices or origin-desinaion (o-d) marices conain end o end raffic demands beween each pair of nodes in a given IP nework. In his paper we are ineresed in minues average raffic demands beween rouers. For an ISP, here are muliple reasons why he availabiliy of good qualiy raffic Permission o make digial or hard copies of all or par of his work for personal or classroom use is graned wihou fee provided ha copies are no made or disribued for profi or commercial advanage and ha copies bear his noice and he full ciaion on he firs page. To copy oherwise, or republish, o pos on servers or o redisribue o liss, requires prior specific permission and/or a fee. IMC0, Ocober 4-, 00, San Diego, California, USA. Copyrigh 00 ACM ---0-/0/000...$.00. marices is essenial: Imporan asks for an ISP ha require raffic marices include nework planning and raffic engineering. They are needed o perform simulaions of failure scenarios and nework exension scenarios as well as for (IGP) rouing opimizaion. For some asks especially in nework planning raffic marices are needed on he level of PoPs bu hey can generally be obained by aggregaing rouer level raffic marices. Already he ask of raffic marix generaion is difficul for he oal raffic wihin a nework and may require esimaion mehods or complex measuremen infrasrucures. Bu as rue muli-service neworks become realiy and raffic classes wih differen service requiremens exis, he need for raffic marices per class-of-service (CoS) is geing sronger: In order o plan and operae a muli-service IP/MPLS nework economically, an ISP needs o incorporae os class specific raffic marices ino is planning and engineering asks. Possible scenarios include: Differen service level agreemens for he os classes require a differen bandwidh dimensioning. For each os class he acual raffic mus never exceed he bandwidh guaraneed o ha class by he scheduler. Only he bes effor class can be allowed o use up o he physical link bandwidh wihou violaing given service level agreemens. The use of links wih low delay (e.g. direc links from Europe o Asia no via America) only for raffic from cerain os classes. Failure simulaions in order o validae cerain os conceps (e.g. o make sure ha non-bes-effor raffic remains below a cerain link uilizaion hreshold) While applicaions wih high os requiremens such as IPTV or VoIP are growing o a significan conribuion o he overall raffic demand, a service provider needs o incorporae os class specific raffic daa ino is planning and engineering processes. In his paper we consider only unicas raffic marices. Mulicas raffic will generally be divided ino differen os classes, oo, and has o be measured separaely. For disribuion plaforms wih fixed raffic sources and sinks (e.g. IPTV wihin he backbone nework) his may be possible from he knowledge of he source raffic and he mulicas ree. For (unicas) raffic marices, a variey of mehods have already been invesigaed, boh for raffic marix esimaion and for raffic marix measuremen. One mehod ha is widely deployed for raffic marix measuremen based on IP flow level measuremens is Cisco s Neflow []. Bu he implemenaion is raher complex and issues ha arise in pracice include:
Neflow availabiliy and performance depend on he line card ypes in use in a service provider s nework here is usually a large number of differen hardware ypes in use. Thus only a parial measuremen migh be possible. IP flow measuremens generally use packe sampling, so here is a radeoff o make beween he measuremen accuracy (low sampling raes) and performance (high sampling raes). Some rouer ypes are no even able o provide anyhing han very high sampling raes. Large effor for aggregaion of he flows ha are expored by he rouers. Well-esablished esimaions mehods for raffic marices are graviy esimaion [0], where a raffic demand from s o is se proporional o he oal ougoing raffic of s and he oal incoming raffic of or nework omography, where end-o-end demands are esimaed from link uilizaions see []. The combinaion of hose wo esimaion mehods is commonly referred o as nework omograviy see [] for a survey and comparison of differen esimaion mehods. I is obvious ha hose esimaion mehods can also be used o esimae os class specific raffic marices if he necessary inpu daa (mosly link uilizaions) are available per os class. In neworks ha use muli-proocol label swiching - MPLS [] o forward packes here are addiional mehods o measure he oal raffic marix. If RSVP-TE [] is used, a full mesh of unnels can be deployed and couners for hose unnels exis o measure he raffic marix. If LDP [4] is used o disribue he label informaion in a nework, LDP saisics of he rouers can be used o compue raffic marices on a rouer level see [], []. The LDP mehod resuls in a very high measuremen accuracy (for example, here is no sampling involved) while he measuremen complexiy is very low: The measuremen is based on aggregaed forwarding equivalence classes (FEC) ha are inroduced in MPLS/LDP and is no based on he IP flow level. However, he LDP mehod can only be used for he nework s oal raffic marix and no per os class. For Deusche Telekom s IP/MPLS backbone nework he LDP mehod is currenly used o compue oal raffic marices o suppor IGP meric opimizaion (see [] for a heoreical survey or [] for a discussion on he pracical implemenaion) and nework planning. Dependen on he exising measuremen infrasrucure, he nework opology or he deployed proocols, i may be easier o obain raffic marices for he oal raffic wihin he nework han os class specific raffic marices. This is why we propose a model for os class specific raffic marices ha combines esimaion mehods wih oal raffic marix measuremens. This paper is organized as follows: Secion describes he mahemaical model used o esimae os class specific raffic marices and secion gives numerical resuls from he applicaion of his model o a par of Deusche Telekom s global IP/MPLS backbone nework.. OS TRAFFIC MATRIX MODEL. Noaions for Tomograviy Model If our nework has n nodes and m links we denoe by x he vecor of link uilizaion and he vecor represenaion of he raffic marix, i.e. i j (i,j=,,n) conains he raffic from node i o node j. From he nework opology and he IGP merics in use, we can consruc he nework s rouing marix A. The enry a k, i j [0,] (i,j=,,n; k=,,m) of A conains he par of he demand i j on link k. The rouing marix A resuls from a shores-pah calculaion wih respec o he given IGP merics if he nework makes no use of equal cos pah spliing (ECMP) a k, i j {0,} holds. The relaion beween raffic marix, link uilizaions and rouing marix is hen described by he following equaion: (R) A = x. The omography esimaion of he raffic marix can be consruced by solving he following sysem of equaions for a given rouing marix A, a given vecor of measured link uilizaions x and a given iniial esimae E for he raffic marix: A x min (TG) s.. E min The soluion of (TG) is given by ~ = E + A ( x A E ) where ~ T A = V S U denoes he Moore-Penrose-Inverse (also pseudo inverse) of he rouing marix A and is consruced wih a singular value decomposiion (SVD) of A: A = U S V We use he SVD rouines conained in LAPACK [4] for his purpose ieraive mehods for large scale SVD compuaions are also available see []. If a graviy esimaion is used as an iniial esimae E, (TG) is referred o as omograviy mehod. The soluion of (TG) can be inerpreed as a (orhogonal) projecion of he iniial soluion E ono he subspace of all raffic marices ha saisfy he link uilizaion resricions (R), i.e. we calculae ha admissible raffic marix ha is closes o E. For omograviy esimaion mehods a graviy esimae is chosen for E one possibiliy o improve he graviy esimae is he use of a generalized graviy model as given in [] which akes ino accoun he knowledge of where peering raffic eners he nework. The assumpion ha here is no ransi peering raffic in he nework hen resrics he number of possible raffic demand combinaions and hereby improves he esimae. One mehod o improve he numerical sabiliy of he soluion of he sysem (TG) is o remove parallel links from he nework opology. Service providers ofen use parallel links in heir neworks o increase capaciy before hey move o a echnology wih higher capaciy (e.g. wo or hree.gbi/s links before insalling on 0Gbi/s link). Those parallel links have he same IGP meric so ha hey are uilized equally when using ECMP. In pracice, he raffic is no shared enirely equal depending on which hashing algorihm he rouers use for load sharing ha means ha here are differences in he corresponding componens of he uilizaion vecor x. On he oher hand he rouing marix A inroduces heoreical load sharing properies T 4
and equaion (R) canno be fulfilled exacly. We herefore combine parallel links o one link wih he sum of he parallel links capaciies and heir average uilizaion.. Inegraed Model wih os class raffic In his secion we exend (TG) o a sysem ha can be used o esimae raffic marices per os class. Unlike in he previous secion we now assume ha he full raffic marix is given. In Deusche Telekom s IP/MPLS backbone nework we use he LDP mehod o obain - oher mehods as discussed in he inroducion (RSVP-TE unnel couners or Neflow measuremens) could also be used. If we inend o apply (TG) for differen os classes, os class specific link uilizaions are a prerequisie. Bu here may no be os class specific link uilizaions available for all links in he nework: For example in case of Cisco rouers os-class specific link uilizaions require he use of he Modular os CLI (MC) whose availabiliy depends on he IOS sofware release and he hardware (line card ypes) in use. For a os-class raffic marix esimaion mehod ha can be implemened in pracice i is reasonable o assume os-class link uilizaions are available for a subse of all links and End-o-End loads are available for he sum of all os classes (l) If here are q os classes in he nework and we denoe by and x ˆ l he raffic marix and he link uilizaion vecor for he os class l (l =,,q), and by  he rouing marix reduced o subse of links whose os-class specific link uilizaions are available, he following se of equaion holds analog o (R): Aˆ () () x 0 ˆ () O M = ( q) 0 Aˆ M xˆ 44 L q I I 4 A x (R) Using he model (R) we can now apply he same esimaion mehod as in secion II.A analog o (TG) o solve (R): The esimaion accuracy of (TG) will depend highly on he size of he subse of links ha have os specific link uilizaions available. Also i should be noed ha (TG) can resul in raffic marix esimaions wih negaive enries since (TG) has no condiion for being nonnegaive. We apply a simple ieraion scheme o assure posiive soluions whose convergence is discussed in he following secion. Compared o an applicaion of he omograviy mehod (TG) for each os class separaely (TG) inroduces furher resricions: he sum of he os class specific raffic demands mus equal he oal raffic for he respecive raffic relaion. These addiional resricions should improve he esimaion qualiy of he mehod. Secion invesigaes he improvemen of he esimaion qualiy for a concree example wih realisic daa. Model (R) applies he same rouing for all os classes bu i can be easily exended o os specific rouing schemes if we replace  by os specific rouing marices ˆ l A (l =,,q).. NUMERICAL RESULTS The os-omography model (TG) is applied o an example nework wih nodes and 0 edges (Figure ). We assume four os classes: voice, low loss, low delay, and bes effor. In he following secion, we discuss wo problems: esimaion convergence and esimaion accuracy. The hird example shows esimaion resuls based on os link uilizaion measuremens from our backbone nework. The numerical resuls focus on he differences in he demand srucures of he os class specific raffic marices. Therefore raffic marices for one given (- minue) ime inerval are compared. Anoher difference ha is no covered wihin his paper is he difference in he ime dependen variance of he raffic volume: Differen os classes will have differen daily peak hours. As an example Figure shows his difference in he daily link uilizaion char for one backbone link. The ime dependen behavior of raffic marices is paricularly imporan for he choice of he raffic marix ha is acually used for raffic engineering or nework planning: For non-bes-effor raffic classes he raffic profile migh follow business hours and a raffic marix from a differen ime inerval has o be used for nework planning or raffic engineering purposes. (TG) A s.. x E min min The iniial esimae for he os class specific raffic marix E is consruced from he oal raffic demand beween he nodes ha is divided proporionally o os class specific link uilizaions, more precisely: where ( l) ( ) E i j = i j q r= X E l X r = ( ( q) E, K, E ) m ( r), l =,, q and X r = xˆ k. k = Figure : Daily profiles for differen os classes for one backbone link (normalized diagrams)
. Esimaion accuracy For analyzing he esimaion accuracy we assume given raffic marix values for all os classes. This given vecor of raffic marices is denoed by. We use a random number generaor o se he values in he range beween 0 and 00000. In a simulaion, he raffic of he four os classes is roued according o he IGP merics of our backbone nework. From he roued raffic we can hen calculae he link uilizaions x ˆ l k for each link k and os class l. The raffic marix of he oal raffic is calculaed from he sum over he given os raffic marices. Finally, is esimaed from and x as a soluion of (TG) and we calculae he relaive error E as measure for he esimaion accuracy. = qn E i i i i Figure : Example nework opology.. Esimaion convergence Dependen on he iniial esimae vecor E, problem (TG) may resul in negaive values for individual raffic marix enries. In his case we apply an ieraive procedure where he negaive elemens per origin-desinaion (o-d) relaion are se o 0 and he negaive volume is added o he values of he posiive enries. Afer his modificaion, he sum over he os classes per o-d relaion is unchanged and all enries of he raffic marix are non negaive. This resul is used as a new sar vecor E for he nex ieraion wih equaion (TG). The diagram in Figure shows ha he ieraion scheme converges: The percenage of he negaive raffic marix volume is reduced from % o 0.0 % afer only 0 ieraions. Negaive raffic volume [%]. 0. 0 0 0 0 Ieraion Figure : Esimaion convergence If we ake ino consideraion all elemens of he raffic marices, he mean relaive error is dominaed by he small elemens. As he conribuion of hese elemens o he overall raffic volume is very small, we focus on he mean relaive error E α of hose elemens ha are larger han he (-α) quanile of he raffic marix elemen disribuion funcion. Figure 4 we compare E α from he (TG) mehod (normal lines) wih resuls from a omography model wih a sar vecor from he graviy model (TG model: dashed lines, same color). The omography model (TG) is applied o each os class separaely. The resuls show ha he mean relaive error is reduced by a facor of. compared o resuls from he (TG) esimaion. Neverheless, a mean relaive error in he range beween 0 % and 00 % indicae ha furher improvemens are needed. Mean relaive error [%] 00 0 00 0 00 0 0 TG: os TG: os TG: os TG: os TG: os TG: os4 TG: os TG: os4 0. 0. 0. 0. α Figure 4: Esimaion accuracy.
One applicaion of os class specific raffic marices is os dependen rouing - especially if he srucure of he os raffic marices differs from class o class. The esimaion resul is useful only, if he srucures are idenified accuraely by he esimaion mehod. The following accuracy es analyzes his problem. We assume wo differen os classes. Class raffic originaes a nodes o, class raffic originaes a nodes o. Each source sends 00000 raffic unis o each oher node of our nework. Nodes o and nodes o respecively are no in a close opological region. The nodes are sored by name alphabeically and numbered from o. The esimaion resul for he os class specific raffic marices is shown in Figure and Figure. The marix elemens are colored as follows: green: less han 000 raffic unis, yellow: beween 000 and 0000 raffic unis, red: more han 0000 raffic unis. Therefore, a perfec mach is achieved, if he firs rows of he os marix are red and he ohers are green and vice versa for os. The srucures of he os raffic marices are accuraely idenified in he esimaion. The mean relaive error E is 4. % for os class and. % for class. If we calculae he E α, only he posiive elemens of he raffic marices are considered. In ha case, he mean relaive error E α is. % for class and. % for class. 4 0 4 0 4 4 ### 0 0 4 0 4 Figure : Esimaion of os raffic. 4 0 4 0 4 4 0 4 0 4 Figure : Esimaion of os raffic.. Esimaion resuls wih real nework daa In he following secion he os class specific raffic marix esimaion (TG) is applied o daa from our backbone nework. The oal raffic marix is calculaed by means of he LDP mehod. In he considered nework opology only of he backbone rouers could measure he link uilizaion saisics per os class. Therefore, we expec more accurae resuls when all he rouers are upgraded o an OS version ha allows measuremens per os class. Firs we show he relaion of he amoun of raffic beween he four os classes ( Figure ). Obviously, he oal raffic volume is dominaed by he bes effor raffic (os4) and he srucure of he os4 marix agrees wih he srucure of he oal raffic marix (Figure ). The srucures of he os, os and os raffic marices are differen o he srucure of he oal raffic marix. This is mainly caused by specific applicaion archiecures (e.g. posiion of voice gaeway rouers), or locaions of specific cusomers wih relaively high os demands. From he os raffic marix in Figure (voice raffic), we can see ha a lo of raffic is desined o node and node, he locaion of voice gaeways. Main sources are he nodes o node 4. Traffic.E+0.E+0.E+0.E+00.E-0 os os os os4 os classes Figure : Disribuion over os classes.
4 0 4 0 4 4 0 4 0 4 4 0 4 0 4 Figure : Overall raffic marix. 4 0 4 0 4 Figure : os raffic marix. 4. CONCLUSION We have presened a new model and numerical resuls from a real world nework for os class specific raffic marices. We demonsraed ha his mehod can significanly improve he esimaion qualiy. The numerical resuls show he differences in he demand srucure for differen os classes. Thereby we moivae why he availabiliy of good qualiy os class specific raffic marices is imporan for efficien nework planning and raffic engineering. The absolue size of he esimaion errors is sill quie high for he inended use of he os class specific raffic marices. On he oher hand a good esimaion of he demand srucure of he raffic marices could already be achieved and he need for os class specific raffic marices will only grow wih he raffic growh in non-bes-effor raffic classes. Figure shows ha here is sill some ime o improve he esimaion qualiy. Fuure improvemens of our mehod include he usage of saeof-he-ar mehods from numerical linear algebra (e.g. sparse marix SVD). This would allow us o invesigae larger nework opologies. Furhermore, we aim o incorporae a larger number of os class specific link uilizaions no only from links wihin he backbone nework bu also from ingress links ino he nework - o improve he esimaion qualiy.. REFERENCES [] Neflow Aggregaion, Cisco IOS release.0()t. [] E. Rosen, A.Viswanahan, R. Callon: Muliproocol Label Swiching Archiecure, IETF RFC 0, Jan 00 [] D. Awduche, L. Berger, D. Gan, T. Li, V. Srinivasan, G.Swallow: RSVP-TE: Exensions o RSVP for LSP Tunnels, IETF RFC 0, Dec 00 [4] L. Anderson, P. Doolan, N. Feldman, A. Fredee, B. Thomas: LDP Specificaion, IETF RFC 0, Jan 00 [] S. Schnier, M. Horneffer, Traffic Marices for MPLS Neworks wih LDP Saisics, Proc Neworks004, VDE- Verlag, Vienna, 004. [] S. Schnier, T. Morsein and M. Horneffer, Combining LDP Measuremens and Esimaion Mehods for Traffic Marices in IP/MPLS Neworks, Proc. Neworks00, VDE-Verlag, New Delhi, 00. [] S. Schnier, G. Haßlinger, Heurisic Soluions o he LSP- Design for MPLS Traffic Engineering, Proc. Neworks00, VDE-Verlag, Munich, 00. [] M Horneffer, IGP uning in an MPLS nework, NANOG, Las Vegas, 00. [] B. Forz, M. Thorup, Inerne Traffic Engineering by Opimizing OSPF Weighs, Proc. IEEE INFOCOM 000, 000. [0] J. Kowalski, B. Warfield, Modeling raffic demand beween nodes in a elecommunicaions nework, Proc. ATNAC,. [] J. Cao, D. Drew, S. Wiel, B. Yu, Time-Varying Nework Tomography: Rouer Link Daa, Bell Labs Tech. Memo, 000. [] Y. Zhang, M. Roughan, N. Duffield, A. Greenberg, Fas Accurae Compuaions of Large-Scale IP Traffic Marices from Link Loads, Proc. SIGMETRICS 0, San Diego, 00. [] A. Gunnar, M. Johansson, T. Telkamp, Traffic Marix Esimaion on a Large IP Backbone A Comparison on Real Daa, Proc. IMC 04, Taormina, 004. [4] E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Croz, A. Greenbaum, S. Hammarling, A. McKenny, D. Sorense, LAPACK User s Guide, SIAM,. [] M. Berry, Large Scale Singular Value Compuaions, Inernaional Journal of Supercompuer Applicaions, :, pp. -4,