1. CSci5221: Intra-Domain Traffic Engineering 1 Intra-Domain Traffic Engineering Traffic Engineering (TE) – MPLS and traffic engineering (will go over very briefly) – traffic engineering as network-wide optimization problem – TE through link weight assignments Traffic Matrix Estimation (only briefly) – challenges and issues Readings: do the required readings.

2. 2 Traffic Engineering Goal: configure routes to meet traffic demands –balanced load, low latency, service agreements operates at coarse timescales –Not to adapt to short-term sudden traffic changes –May take potential failures into consideration Input to traffic engineering: –Topology: connectivity & capacity of routers & links –Traffic matrix: offered load between points in the network Traffic Engineering: network-wide optimization –Subject to protocol mechanisms, configurable parameters and other practical constraints, …. CSci5221: Intra-Domain Traffic Engineering

3. 3 Traffic Engineering Framework Basic Requirements –Knowledge of Topology Connectivity and capacities of routers/links of a network –Traffic Matrix (average) traffic demand between difference ingress/egress points of a network Instrumentation –Topology: monitoring of the routing protocols –Traffic matrix: “fine-grained” traffic measurement and inference, for example, via SNMP edge measurements + routing tables network tomography packet sampling CSci5221: Intra-Domain Traffic Engineering

4. 4 Traffic Engineering Framework (cont’d) Traffic Engineering as Network-Wide Optimization Network-wide models –Network topology: graph (V,E), c ij : capacity of link (i,j) –Traffic Matrix: K set of (ingress/egress) source-destination pair demands –k  K, d k – demand, s k – source, t k – destination Optimization criteria, e.g., –minimize maximum utilization, –minimize sum of link utilization –keep utilizations below 60% CSci5221: Intra-Domain Traffic Engineering

5. 5 Traffic Engineering as a Global Optimization Problem topology G = (V,E) c ij – capacity of link K – set of origin-destination flows (demands) – F k ij : traffic load of O-D flow k routed on link (i,j) CSci5221: Intra-Domain Traffic Engineering

6. 6 More Cost Functions works for rich set of cost functions example: where  ij are piecewise linear CSci5221: Intra-Domain Traffic Engineering

7. 7 Traffic Engineering as a Global Optimization Problem (cont’d)  Objective function: minimize  Constraints: -- flow conservation: total outflow vs. total inflow -- capacity and (non-negative load) constraints CSci5221: Intra-Domain Traffic Engineering

8. 8 Traffic Engineering Example: minimize maximum link utilization Minimize Multi-commodity flow problem –There exists polynomial time solutions to the problem Equivalent linear programming formulation – CSci5221: Intra-Domain Traffic Engineering

9. 9 Traffic Engineering: LP Formulation CSci5221: Intra-Domain Traffic Engineering

10. 10 Traffic Engineering w/ MPLS We can set up label-switched paths (LSPs) between origin-destination pairs to realize the optimal TE traffic load distributions Let {X *k ij } be the optimal solutions –If for a given k (corresponding to a given O-D pair), X *k ij = 0 or 1, then we set up one LSP (or tunnels) for the O-D pair –Otherwise, traffic load for flow (demand) k is carried over multiple paths, we need to set up multiple LSPs (or tunnels) for the given O-D pair In general, traffic split among multiple LSPs are not equal! worst-case complexity: –O(N^2E) LSPs/tunnels needed CSci5221: Intra-Domain Traffic Engineering

11. 11 Traffic Engineering w/o MPLS Can we perform traffic engineering without MPLS? –we need to use “shortest path” routing –But shortest paths are defined based on link weights TE becomes link weight assignment problem! Other constraints we need to take into account –destination-based routing: not pair-based! –multiple shortest paths (“equal-cost” paths, ECPs) may exist and can be used for load-balancing But typical equal splitting is used to split traffic among ECPs for a given destination prefix On the other hand, multiple destination prefixes are mapped to the same egress point of a network! CSci5221: Intra-Domain Traffic Engineering

12. 12 Traffic Engineering under Shortest Path Routing: Tuning Link Weights Problem: congestion along the blue path –Second or third link on the path is overloaded Solution: move some traffic to bottom path –E.g., by decreasing the weight of the second link 3 2 2 1 1 3 1 4 5 3 3 CSci5221: Intra-Domain Traffic Engineering

13. 13 Effect of link weights (see [FRT02]) unit link weights local change to congested link global optimization –to balance link utilizations CSci5221: Intra-Domain Traffic Engineering

14. 14 Shortest Path Routing and Link Weight Assignment Problem Key Problem: how to assign link weights to optimize TE objectives under conventional link-state (shortest path) routing paradigm? Key Insight: traffic engineering optimization is closely related to optimal link weight assignment using “shortest path routing” (with some caveats!) –The relationship comes from duality properties of linear programming optimal link weight assignment problem is a dual problem to the optimal traffic engineering problem! For materials in slides 53-62, see [WWZ01] CSci5221: Intra-Domain Traffic Engineering

15. 15 Duality of Linear Programming Primal Dual Y’s are Lagrange multipliers for equality constraints Ax=b; z ≥ 0 Lagrange multipliers for inequality constraints x ≥ 0 CSci5221: Intra-Domain Traffic Engineering

16. 16 Complementary Slackness. Let x and y be feasible solutions. A necessary and sufficient condition for them to be optimal is that for all i 1.x i > 0  y T A i = c i 2.x i = 0  y T A i < c i Here A i is i-th column of A CSci5221: Intra-Domain Traffic Engineering

17. 17 Example: Primal (P-SP) topology G = (V,E), link weights CSci5221: Intra-Domain Traffic Engineering

18. 18 Example: Dual (D-SP) CSci5221: Intra-Domain Traffic Engineering

19. 19 Dual Solution Interpretation optimal solution to dual problem length of shortest path from s k to j length of shortest path from s k to t k CSci5221: Intra-Domain Traffic Engineering

20. 20 Duality (More General Form) Primal Dual y 1 : Lagrange multipliers for equality constraints Ax=b 1 ; y 2 ≥ 0 : Lagrange multipliers for inequality constraints A’x ≥ b 2 Lagrange dual: g(y 1,y 2 ) :=inf x ≥ 0 {c T x +y T 1 (b 1 -Ax) +y T 2 (b 2 -A’x)} CSci5221: Intra-Domain Traffic Engineering

21. 21 Load Balancing Optimization Problem CSci5221: Intra-Domain Traffic Engineering

22. 22 Re-formulating the Problem Let {X *k ij } be optimal solutions, then d k X *k ij is the load of demand (flow) k placed on link (i,j) Define -- total load of all demands on link (i,j); C * ij b C ij CSci5221: Intra-Domain Traffic Engineering

23. 23 Dual Formulation dual variables CSci5221: Intra-Domain Traffic Engineering

24. 24 Properties of Primal-Dual Solutions optimal solution to primal problem dual problem if can think of as shortest path distance from s k to j when link weights are Therfore: solution to TE problem is also solution to shortest path problem with CSci5221: Intra-Domain Traffic Engineering

25. 25 Link Weight Assignment: Generalization works for rich set of cost functions example: where  ij are piecewise linear CSci5221: Intra-Domain Traffic Engineering

26. 26 Issues solutions are flow specific - need destination specific solutions –not a big deal, can reformulate to account for this solutions may not support equal split rule of OSPF –accounting for this yields NP-hard problem –modify IP routing CSci5221: Intra-Domain Traffic Engineering

27. 27 One approach to overcome the “splitting problem” current routing tables have thousands of routing prefixes instead of routing each prefix on all equal cost paths, selectively assign next hops to (each) prefix –i.e., remove some equal cost next hops assigned to prefixes goal: to approximate optimal link load see [FT00], [FRT02] and [SDG05] CSci5221: Intra-Domain Traffic Engineering

28. 28 Example : EQUAL-SUBSET-SPLIT i j k l Prefix A : 5 Prefix B : 1 Prefix C : 8 Prefix D : 10 9 3 12 Prefixes: D C Prefixes: A B Prefixes: D C B A 5 + 4 = 9 2.5 + 0.5 = 3 5 + 4 + 2.5 + 0.5 = 12 Prefix A: Hops k,l Prefix B : Hops k,l Prefix C: Hops j,l Prefix D: Hops j,l CSci5221: Intra-Domain Traffic Engineering

29. 29 Advantages requires no change in data path can leverage existing routing protocols current routers have 10,000s of routes in routing tables –provides large degree of flexibility in next hop allocation to match optimal allocation CSci5221: Intra-Domain Traffic Engineering

30. CSci5221: Intra-Domain Routing and TE 30 Performance CSci5221: Intra-Domain Traffic Engineering

31. 31 Traffic Engineering Summary can use OSPF/ISIS to support traffic engineering objectives performance objectives link weights –Further considerations: Link weight assignment under multiple traffic matrices, and/or under multiple topologies (under link failures) equal splitting rule complicates problem –heuristics provide good performance – small changes to IP routing provide in better performance MPLS suffers none of these problems, but protocol more complex! CSci5221: Intra-Domain Traffic Engineering

32. 32 Traffic Demands & Traffic Matrices How to measure and model the traffic demands? –Know where the traffic is coming from and going to Why do we care about traffic demands? –Traffic engineering utilizes traffic demand matrices in balancing traffic loads and managing network congestion –Support what-if questions about topology and routing changes –Handle the large fraction of traffic crossing multiple domains Understanding traffic demand matrices are critical inputs to network design, capacity planning and business planning! How to populate the demand model? –Typical measurements show only the impact of traffic demands Active probing of delay, loss, and throughput between hosts Passive monitoring of link utilization and packet loss –Need network-wide direct measurements of traffic demands How to characterize the traffic dynamics? –User behavior, time-of-day effects, and new applications –Topology and routing changes within or outside your network CSci5221: Intra-Domain Traffic Engineering

33. 33 Traffic Demands Big Internet Web Site User Site CSci5221: Intra-Domain Traffic Engineering

34. 34 Traffic Demands Interdomain Traffic What path will be taken between AS’s to get to the User site? Next: What path will be taken within an AS to get to the User site? AS 4, AS 3, U Web Site User Site AS 1 AS 2 AS 3 AS 4 U AS 3, U CSci5221: Intra-Domain Traffic Engineering

35. 35 Traffic Demands Web Site User Site Zoom in on one AS 200 110 10 110 300 25 75 50 300 IN OUT 3 OUT 2 OUT 1 110 Change in internal routing configuration changes flow exit point! 110 CSci5221: Intra-Domain Traffic Engineering

36. 36 Defining Traffic Demand Matrices Granularity and time scale: –Source/destination network prefix pairs, source/destination AS pairs – ingress/egress routers, or ingress/egress PoP pairs? –Finer granularity: traffic demands likely unstable or fluctuate too widely! 36 CSci5221: Intra-Domain Traffic Engineering

37. Traffic Matrix (TM) Point-to-Point Model: T: = [T i,j ], where T i,j from an ingress point i to an egress point j over a given time interval –ingress/egress points: routers or PoPs –an ingress-egress pair is often referred to as an O-D pair Point-to-Multipoint Model: –Sometimes it may be difficult to determine egress points due to uncertainty in routing or route changes Definition: V(in, {out}, t) Entry link (in) Set of possible exit links ({out}) Time period (t) Volume of traffic (V(in,{out},t)) 37 CSci5221: Intra-Domain Traffic Engineering

38. 38 (Ideal) Measurement Methodology Measure traffic where it enters the network –Input link, destination address, # bytes, and time Determine where traffic can leave the network –Set of egress links associated with each network address (forwarding tables) Compute traffic demands –Associate each measurement with a set of egress links Even at PoP-level, direct measurement can be too expensive! –We either need to tap all ingress/egress links, or collect netflow records at all ingress/egress routers May lead to reduced performance at routers large amount of data: limited router disk space, export Netflow records consumes bandwidth! Either packet-level or flow-level data, need to map to ingress/egress points, and a lot of processing to generate TM! In practice: a combination of sampled flow measurements, link loads & estimation/inference techniques 38 CSci5221: Intra-Domain Traffic Engineering