Intra-Doman Traffc Engneerng Traffc Engneerng (TE) MPLS and traffc engneerng (wll go over very brefly) traffc engneerng as networ-wde optmzaton problem TE through ln weght assgnments Traffc Matrx Estmaton (only brefly) challenges and ssues Readngs: do the requred readngs. 1
Traffc Engneerng Goal: confgure routes to meet traffc demands balanced load low latency servce agreements operates at coarse tmescales Not to adapt to short-term sudden traffc changes May tae potental falures nto consderaton Input to traffc engneerng: Topology: connectvty & capacty of routers & lns Traffc matrx: offered load between ponts n the networ Traffc Engneerng: networ-wde optmzaton Subject to protocol mechansms confgurable parameters and other practcal constrants. 2
Traffc Engneerng Framewor Basc Requrements Knowledge of Topology Connectvty and capactes of routers/lns of a networ Traffc Matrx (average) traffc demand between dfference ngress/egress ponts of a networ Instrumentaton Topology: montorng of the routng protocols Traffc matrx: fne-graned traffc measurement and nference for example va SNMP edge measurements + routng tables networ tomography pacet samplng 3
Traffc Engneerng Framewor (cont d) Traffc Engneerng as Networ-Wde Optmzaton Networ-wde models Networ topology: graph (VE) c : capacty of ln (j) Traffc Matrx: K set of (ngress/egress) source-destnaton par demands K d demand s source t destnaton Optmzaton crtera e.g. mnmze maxmum utlzaton mnmze sum of ln utlzaton eep utlzatons below 60% 4
Traffc Engneerng as a Global Optmzaton Problem topology G = (VE) c capacty of ln ( j) E K set of orgn-destnaton flows (demands) K d demand s source t destnaton F : traffc load of O-D flow routed on ln (j) F := ( ) on ln ( j) F : total load of all demands Optmzaton objectve functon: Φ({F c }) e.g. Φ({F c }) := max {( j )E} {F / c } or Φ({F c }) := {F / c } {( j )E } 5
More Cost Functons wors for rch set of cost functons example: Φ= Φ ( j) E ( dx) where F are pecewse lnear 6
7 Traffc Engneerng as a Global Optmzaton Problem (cont d) Objectve functon: mnmze Constrants: -- flow conservaton: total outflow vs. total nflow = = = K t s d K t s d K t s F F E j j j E j j 0 ) :( ) :( -- capacty and (non-negatve load) constrants 0 ) ( K F E j c F Φ({F c })
Traffc Engneerng Example: mnmze maxmum ln utlzaton Mnmze Mult-commodty flow problem There exsts polynomal tme solutons to the problem Equvalent lnear programmng formulaton α -- maxmum ln utlzaton Let X := F / d Φ({F c }) := max {( j )E} {F / c } X denotes fracton of demand on ln ( j) X [01] 8
mn Traffc Engneerng: LP Formulaton α 0 s t K st.. X 1 j:( j) E X j:( j ) E j = s K 1 t K K 0 X 1 dx cα ( ) E 9
Traffc Engneerng w/ MPLS We can set up label-swtched paths (LSPs) between orgn-destnaton pars to realze the optmal TE traffc load dstrbutons Let {X * } be the optmal solutons If for a gven (correspondng to a gven O-D par) X * = 0 or 1 then we set up one LSP (or tunnels) for the O-D par Otherwse traffc load for flow (demand) s carred over multple paths we need to set up multple LSPs (or tunnels) for the gven O-D par In general traffc splt among multple LSPs are not equal! worst-case complexty: O(N^2E) LSPs/tunnels needed 10
Traffc Engneerng w/o MPLS Can we perform traffc engneerng wthout MPLS? we need to use shortest path routng But shortest paths are defned based on ln weghts TE becomes ln weght assgnment problem! Other constrants we need to tae nto account destnaton-based routng: not <src dst> par-based! multple shortest paths ( equal-cost paths ECPs) may exst and can be used for load-balancng But typcal equal splttng s used to splt traffc among ECPs for a gven destnaton prefx On the other hand multple destnaton prefxes are mapped to the same egress pont of a networ! 11
Traffc Engneerng under Shortest Path Routng: Tunng Ln Weghts Problem: congeston along the blue path Second or thrd ln on the path s overloaded Soluton: move some traffc to bottom path E.g. by decreasng the weght of the second ln 3 2 31 1 2 5 3 1 4 3 12
Effect of ln weghts (see [FRT02]) unt ln weghts local change to congested ln global optmzaton to balance ln utlzatons 13
Shortest Path Routng and Ln Weght Assgnment Problem Key Problem: how to assgn ln weghts to optmze TE objectves under conventonal ln-state (shortest path) routng paradgm? Key Insght: traffc engneerng optmzaton s closely related to optmal ln weght assgnment usng shortest path routng (wth some caveats!) The relatonshp comes from dualty propertes of lnear programmng optmal ln weght assgnment problem s a dual problem to the optmal traffc engneerng problem! For materals n sldes 53-62 see [WWZ01] 14
Dualty of Lnear Programmng Prmal maxmze c T x subject to Ax = b x 0 Dual mnmze y T b subject to y T A c T Y s are Lagrange multplers for equalty constrants Ax=b; z 0 Lagrange multplers for nequalty constrants x 0 Lagrange functon: L(x yz) := c T x y T (Ax b) + z T x c T x f x s a feasble soluton Lagrange dual: g(yz) := nf x 0 L(x yz) c T x * (x * optmal soluton) g(yz) = y T b f c T y T A + z T 0 or y T A c T as z T 0 15
Complementary Slacness. Let x and y be feasble solutons. A necessary and suffcent condton for them to be optmal s that for all 1. x > 0 è y T A = c 2. x = 0 ç y T A < c Here A s -th column of A 16
Example: Prmal (P-SP) topology G = (VE) ln weghts {w : ( j) E } mn ( j) E w ( X ) s. t. j:( j) E X j:( j ) E X j = 0 s t j:( s j) E X j:( j s ) E X j = 1 j:( t j) E X j:( j t ) E X j = 1 X 0 17
18 Example: Dual (D-SP) K U E j K w U U s t U s j K t = 0 ) (.. max
Dual Soluton Interpretaton s. t. max U U K j s U = 0 U t w K ( j) E K { } U optmal soluton to dual problem X > 0 U j U = w U j length of shortest path from s to j U t length of shortest path from s to t 19
Dualty (More General Form) Prmal maxmze c T x subject to Ax = b 1 A'x b 2 Dual mnmze y T b + y T b 1 1 2 2 subject to y T A + y T A' c T 1 2 y 0 2 x 0 y 1 : Lagrange multplers for equalty constrants Ax=b 1 ; y 2 0 : Lagrange multplers for nequalty constrants A x b 2 Lagrange dual: g(y 1 y 2 ) :=nf x 0 {c T x +y T 1 (b 1 -Ax) +yt 2 (b 2 -A x)} 20
21 Load Balancng Optmzaton Problem 1 0 ) ( 1 1 0.. mn ) :( ) :( = K E j j j E j j E (j) K X E j c X d K t K s K t s X X s t X d
Re-formulatng the Problem Let {X * } be optmal solutons then d X* load of demand (flow) placed on ln (j) Defne C * := * d X s the -- total load of all demands on ln (j); C * b C Prmal Problem: mn ( j) E K 0 s t K st.. X 1 j:( j) E X j:( j ) E j s K = 1 t K K 0 X 1 dx c ( ) E dx 22
Dual Formulaton dual varables { U } { W } max t ( j) E st.. U U W + 1 K( j) E W U s 0 = 0 K du j cw 23
Propertes of Prmal-Dual Solutons optmal soluton to prmal problem f X can thn of dual problem > j U j 0 then U U = W + 1 as shortest path dstance from s to j when ln weghts are { X } { U }{ W } { W +1} Therfore: soluton to TE problem s also soluton to shortest path problem wth w W = +1 24
Ln Weght Assgnment: Generalzaton wors for rch set of cost functons example: Φ = ( j) E Φ ( ) d X K where F are pecewse lnear 25
Issues solutons are flow specfc - need destnaton specfc solutons not a bg deal can reformulate to account for ths solutons may not support equal splt rule of OSPF accountng for ths yelds NP-hard problem modfy IP routng 26
One approach to overcome the splttng problem current routng tables have thousands of routng prefxes nstead of routng each prefx on all equal cost paths selectvely assgn next hops to (each) prefx.e. remove some equal cost next hops assgned to prefxes goal: to approxmate optmal ln load see [FT00] [FRT02] and [SDG05] 27
Example : EQUAL-SUBSET-SPLIT 9 j Prefxes: D C 5 + 4 = 9 Prefx A : 5 Prefx B : 1 Prefx C : 8 Prefx D : 10 3 12 Prefxes: A B 2.5 + 0.5 = 3 Prefx A: Hops l Prefx B : Hops l Prefx C: Hops jl Prefx D: Hops jl l Prefxes: D C B A 5 + 4 + 2.5 + 0.5 = 12 28
Advantages requres no change n data path can leverage exstng routng protocols current routers have 10000s of routes n routng tables provdes large degree of flexblty n next hop allocaton to match optmal allocaton 29
Performance CSc5221: Intra-Doman Routng and TE 30
Traffc Engneerng Summary can use OSPF/ISIS to support traffc engneerng objectves performance objectves ln weghts Further consderatons: Ln weght assgnment under multple traffc matrces and/or under multple topologes (under ln falures) equal splttng rule complcates problem heurstcs provde good performance small changes to IP routng provde n better performance MPLS suffers none of these problems but protocol more complex! 31
Traffc Demands & Traffc Matrces How to measure and model the traffc demands? Know where the traffc s comng from and gong to Why do we care about traffc demands? Traffc engneerng utlzes traffc demand matrces n balancng traffc loads and managng networ congeston Support what-f questons about topology and routng changes Handle the large fracton of traffc crossng multple domans Understandng traffc demand matrces are crtcal nputs to networ desgn capacty plannng and busness plannng! How to populate the demand model? Typcal measurements show only the mpact of traffc demands Actve probng of delay loss and throughput between hosts Passve montorng of ln utlzaton and pacet loss Need networ-wde drect measurements of traffc demands How to characterze the traffc dynamcs? User behavor tme-of-day effects and new applcatons Topology and routng changes wthn or outsde your networ 32
Traffc Demands Bg Internet Web Ste User Ste 33
Traffc Demands Interdoman Traffc Web Ste AS 2 AS 3 U AS 3 U AS 3 U User Ste AS 1 AS 4 AS 3 U AS 4 AS 3 U What path wll be taen between AS s to get to the User ste? Next: What path wll be taen wthn an AS to get to the User ste? 34
Traffc Demands Zoom n on one AS OUT 1 25 110 110 Web Ste 200 300 300 75 OUT 2 User Ste IN 110 10 50 110 OUT 3 Change n nternal routng confguraton changes flow ext pont! 35
Defnng Traffc Demand Matrces Granularty and tme scale: Source/destnaton networ prefx pars source/ destnaton AS pars ngress/egress routers or ngress/egress PoP pars? Fner granularty: traffc demands lely unstable or fluctuate too wdely! 36 36
Traffc Matrx (TM) Pont-to-Pont Model: T: = [T j ] where T j from an ngress pont to an egress pont j over a gven tme nterval ngress/egress ponts: routers or PoPs an ngress-egress par s often referred to as an O-D par Pont-to-Multpont Model: Sometmes t may be dffcult to determne egress ponts due to uncertanty n routng or route changes Defnton: V(n {out} t) Entry ln (n) Set of possble ext lns ({out}) Tme perod (t) Volume of traffc (V(n{out}t)) 37
(Ideal) Measurement Methodology Measure traffc where t enters the networ Input ln destnaton address # bytes and tme Determne where traffc can leave the networ Set of egress lns assocated wth each networ address (forwardng tables) Compute traffc demands Assocate each measurement wth a set of egress lns Even at PoP-level drect measurement can be too expensve! We ether need to tap all ngress/egress lns or collect netflow records at all ngress/egress routers May lead to reduced performance at routers large amount of data: lmted router ds space export Netflow records consumes bandwdth! Ether pacet-level or flow-level data need to map to ngress/ egress ponts and a lot of processng to generate TM! In practce: a combnaton of sampled flow measurements ln loads & estmaton/nference technques 38 38