1. Traffic Matrix Estimation for Traffic Engineering Mehmet Umut Demircin

2. Traffic Engineering (TE) Tasks  Load balancing  Routing protocols configuration  Dimensioning  Provisioning  Failover strategies

3. Particular TE Problem Optimizing routes in a backbone network in order to avoid congestions and failures.  Minimize the max-utilization.  MPLS (Multi-Protocol Label Switching) Linear programming solution to a multi-commodity flow problem.  Traditional shortest path routing (OSPF, IS-IS) Compute set of link weights that minimize congestion.

4. Traffic Matrix (TM) A traffic matrix provides, for every ingress point i into the network and every egress point j out of the network, the volume of traffic T i,j from i to j over a given time interval. TE utilizes traffic matrices in diagnosis and management of network congestion. Traffic matrices are critical inputs to network design, capacity planning and business planning.

5. Traffic Matrix (cont’d) Ingress and egress points can be routers or PoPs.

6. Determining the Traffic Matrix Direct Measurement: TM is computed directly by collecting flow- level measurements at ingress points. Additional infrastructure needed at routers. (Expensive!) May reduce forwarding performance at routers. Terabytes of data per day. Solution = Estimation

7. TM Estimation Available information:  Link counts from SNMP data.  Routing information. (Weights of links)  Additional topological information. ( Peerings, access links)  Assumption on the distribution of demands.

8. Traffic Matrix Estimation: Existing Techniques and New Directions A. Madina, N. Taft, K. Salamatian, S. Bhattacharyya, C. Diot Sigcomm 2003

9. Three Existing Techniques Linear Programming (LP) approach.  O. Goldschmidt - ISMA Workshop 2000 Bayesian estimation.  C. Tebaldi, M. West - J. of American Statistical Association, June 1998. Expectation Maximization (EM) approach.  J. Cao, D. Davis, S. Vander Weil, B. Yu - J. of American Statistical Association, 2000.

10. Terminology c=n*(n-1) origin-destination (OD) pairs. X: Traffic matrix. (X j data transmitted by OD pair j) Y=(y 1,y 2,…,y r ) : vector of link counts. A: r-by-c routing matrix (a ij =1, if link i belongs to the path associated to OD pair j) Y=AX r Infinitely many solutions!

11. Linear Programming Objective: Constraints:

12. Statistical Approaches

13. Bayesian Approach Assumes P(X j ) follows a Poisson distribution with mean λ j. (independently dist.) needs to be estimated. (a prior is needed) Conditioning on link counts: P(X,Λ|Y) Uses Markov Chain Monte Carlo (MCMC) simulation method to get posterior distributions. Ultimate goal: compute P(X|Y)

14. Expectation Maximization (EM) Assumes Xj are ind. dist. Gaussian. Y=AX implies: Requires a prior for initialization. Incorporates multiple sets of link measurements. Uses EM algorithm to compute MLE.

15. Comparison of Methodologies Considers PoP-PoP traffic demands. Two different topologies (4-node, 14-node). Synthetic TMs. (constant, Poisson, Gaussian, Uniform, Bimodal) Comparison criteria:  Estimation errors yielded.  Sensitivity to prior.  Sensitivity to distribution assumptions.

16. 4-node topology

17. 4-node topology results

18. 14-node topology

19. 14-node topology results

20. Marginal Gains of Known Rows

21. New Directions Lessons learned:  Model assumptions do not reflect the true nature of traffic. (multimodal behavior)  Dependence on priors  Link count is not sufficient (Generally more data is available to network operators.) Proposed Solutions:  Use choice models to incorporate additional information.  Generate a good prior solution.

22. New statement of the problem X ij = O i.α ij  O i : outflow from node (PoP) i.  α ij : fraction O i going to PoP j. Equivalent problem: estimating α ij. Solution via Discrete Choice Models (DCM).  User choices.  ISP choices.

23. Choice Models Decision makers: PoPs Set of alternatives: egress PoPs. Attributes of decision makers and alternatives: attractiveness (capacity, number of attached customers, peering links). Utility maximization with random utility models.

24. Random Utility Model U i j = V i j + ε i j : Utility of PoP i choosing to send packet to PoP j. Choice problem: Deterministic component: Random component: mlogit model used.

25. Results Two different models (Model 1:attractiveness, Model 2: attractiveness + repulsion )

26. Fast Accurate Computation of Large-Scale IP Traffic Matrices from Link Loads Y. Zhang, M. Roughan, N. Duffield, A. Greenberg Sigmetrics 2003

27. Highlights Router to router traffic matrix is computed instead of PoP to PoP. Performance evaluation with real traffic matrices. Tomogravity method (Gravity + Tomography)

28. Tomogravity Two step modeling.  Gravity Model: Initial solution obtained using edge link load data and ISP routing policy.  Tomographic Estimation: Initial solution is refined by applying quadratic programming to minimize distance to initial solution subject to tomographic constraints (link counts).

29. Gravity Modeling General formula: Simple gravity model: Try to estimate the amount of traffic between edge links.

30. Generalized Gravity Model Four traffic categories  Transit  Outbound  Inbound  Internal Peers: P 1, P 2, … Access links: a 1, a 2,... Peering links: p 1,p 2,…

31. Generalized Gravity Model

33. Tomography Solution should be consistent with the link counts.

34. Reducing the computational complexity Hundreds of backbone routers, ten thousands of unknowns. Observations: Some elements of the BR to BR matrix are empty. (Multiple BRs in each PoP, shortest paths) Topological equivalence. (Reduce the number of IGP simulations)

35. Quadratic Programming Problem Definition: Use SVD to solve the inverse problem. Use Iterative Proportional Fitting (IPF) to ensure non-negativity.

36. Evaluation of Gravity Models

37. Performance of proposed algorithm

38. Comparison

39. Robustness Measurement errors x=At+ε ε=x*N(0,σ)

40. Questions?