# Multi-Commodity Flow Traffic Engineering with Hybrid MPLS/OSPF Routing

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2 2 and their traffic demands. Section IV reviews related work and Section V concludes the paper. II. PROBLEM FORMULATION We assume that a network runs a link-state routing protocol such as and also is capable of setting up MPLS paths throughout the network. The TE problem is that given the network topology, traffic matrix (i.e., traffic demand between any ingress-egress pair), and routing, which MPLS paths need to be configured and how to split the traffic between and MPLS so that the maximal link utilization in the network is minimized. We formulate this problem using multi-commodity flows as follows. The network is represented by a directed graph, G = (N, A). Each arc l has capacity c(l). Two binary parameters I and O are defined. Il v denotes whether arc l s head is connected to node v, and Ol v denotes whether arc l s tail is connected to node v. In the traffic matrix D, each D(s, t) represents the traffic volume that flows from the ingress router s to the egress router t. According to the theory of MCF, D(t, t) = s N,s t D(s, t). A binary parameter P s,t l represents whether the route from s to t goes through l. A flow variable fl t denotes the amount of the MPLS traffic from all the other nodes to t that goes through link l. Variable u(l) is the utilization of link l. Variable L (l) represents the traffic that is routed according to on link l while variable L MPLS (l) is the traffic that is routed according to MPLS. Variable α(s, t) represents the percentage of D(s, t) that is routed by MPLS. The traffic engineering problem then can be formulated as the following Linear Programming (LP) problem. min U (1) s.t. l A f t l Os l l A f t l Is l = α(s, t)d(s, t) s, t N (2) L MPLS (l) = t N f t l l A (3) L (l) = s,t N P s,t l (1 α(s, t))d(s, t) l A (4) u(l) = L (l) + L MPLS (l) l A () c(l) fl t l A; t N (6) α(s, t) 1 s, t N (7) u(l) U l A (8) The solution to the above problem will give the optimal LSPs and their required bandwidths in variable L MPLS (l). The constraint in Equation (4) is our contribution, and no previous work has done this [1]. This constraint guides the LP solver to search for the solution that includes the routes, so that fewer number of MPLS paths will be needed. In a typical case of our evaluation scenarios, only needs four LSPs, while classical MCF without Equation (4) needs 43 LSPs. Detailed evaluations will be presented in the next section. can be much more responsive than other TE methods since its input and output can be obtained very quickly and its impact to the network is incremental. The input information to includes the network topology, traffic matrix, and link weights. Among them, network topology and link weights are available in s link-state database. Traffic matrix can be computed from measured link utilization data. According to Zhang et al. [11], a backbone-router to backbonerouter traffic matrix for a tier-1 ISP network can be computed in seconds on a 336MHz Ultrasparc-II machine back in 22. The output of is the LSPs that need to be configured and the traffic amount that these LSPs will carry. As we will show in the evaluation, solving problem takes no more than a few tens of seconds. does not change link weights, therefore the drawbacks of network convergence and large traffic shift are avoided. When the traffic demand changes over time, must change LSP setup to adjust the traffic distribution. Such adjustments are incremental in that they only impacts a small number of routers and a small amount of traffic that are involved in the LSPs that need to be changed. Overall, when traffic demand changes, is able to quickly recompute the optimal solution, set up the LSPs, and only affect the network where it is necessary. Therefore it is possible to run much more frequently (e.g., every few minutes) than other TE methods to be responsive to changing traffic. III. EVALUATION We use several real network topologies and their traffic matrices to evaluate. Internet2 topology is configured according to the data from [12]. Abilene, GEANT and AT&T topologies come from the TOTEM toolbox [13]. All the topologies contain link weights, which are used to generate the routes. To obtain the traffic matrix for Internet2, we take the netflow data from [12], and generate one week traffic matrix using TOTEM. The measured traffic matrices of Abilene and GEANT are available from TOTEM project [14], while estimated traffic matrices of Abilene is downloaded from []. AT&T s traffic matrix is not publicly available. In measuring s computation time, we use a randomly generated traffic matrix with AT&T s topology. All the evaluation is done by the open source LP solver GLPK on a Linux machine with a 3.GHz Intel Pentium 4 CPU and 1 GB memory. A. The Number of LSPs achieves optimal traffic engineering with only a small number of LSPs. Figure 1 compares the number of LSPs under and traditional MCF using three different topologies and traffic matrices on different days in a week. The number of routes is shown for reference, which is the same as n (n 1) where n is the number of routers in the network. In theory traditional MCF would require full-mesh LSPs, but since we use hybrid routing and some LSPs are the same as paths, the traditional MCF does not need to set up full-mesh LSPs in the evaluation. requires much fewer paths than traditional MCF, which demonstrates

3 3 Number of Paths MCF Number of Paths 2 1 MCF Number of Paths MCF (a) At each h on Internet2 from to (b) At each h on Abilene from to (c) At each h on GEANT from -- to --11 Fig. 1. The number of LSPs that need to be established to optimize the objective of traffic engineering TABLE I CPU TIME OF Topology #Nodes #Links totem alone Internet ms 1. ms Abilene ms 2. ms GEANT ms 9. ms AT&T s s TABLE II CPU TIME OF DIFFERENT TE METHODS Method Internet2 Abilene GEANT 6.33 s s 12.4 s 16.2 s s s ms ms ms Original MAX MEAN Fig. 3. Link utilization of Internet2 from to Original MAX MEAN Original MAX MEAN Fig. 2. Link utilization of Abilene from to the effectiveness of Equation (4) in the problem formulation. The number of LSPs required by is only a small fraction of the full-mesh. We also run a test with AT&T topology, which contains 4 nodes and 364 links with a randomly generated traffic matrix, and only needs 31 LSPs. B. CPU Time We measure the CPU time by on different topologies and compare it with other TE methods. As Table I shows, computation is generally fast. totem is the CPU time when is implemented within the TOTEM toolbox, and alone is the CPU time when is implemented standalone without the overhead of the toolbox. In Fig. 4. Link utilization of GEANT from -- to --11 both cases, it takes sub-second for small to medium topologies, and for the large AT&T topology it still just takes a couple tens of seconds. Table II compares the CPU time between, (a previously proposed hybrid routing TE solution), and (IGP Weight Optimization). The other two methods are part of the TOTEM toolbox. The result shows that is about two orders of magnitude faster than and. C. Maximal Link Utilization The objective of the traffic engineering problem is to minimize the maximal link utilization. is supposed to provide the optimal solution to the TE problem. We use three topologies and real traffic matrices to evaluate and other TE methods regarding the maximal link utilization.

5 U() U U(real) 1 2 Fig. 7. The robustness of against the inaccuracy in the traffic matrices of Abilene. U = U(estimated) U(real) traffic matrix estimates. In other words, even if the actual traffic demand is somewhat different from the traffic matrix used in the TE computation, the resulting routing paths should still have reasonably low link utilization. For instance, Roughan et al. [1] have demonstrated that weight optimization is robust. In this subsection, we evaluate s robustness. For the purpose of evaluation, we need a traffic matrix estimate and actual traffic demand in order to compare s performance using them. For Abilene, we get the estimated traffic matrices from []. For Internet2, we simply use the traffic matrix measured in the previous -minute interval as the estimate for the next -minute interval. Similarly, for GEANT, we use the traffic matrix measured in the previous -minute interval as the estimate for the next -minute interval. We use U(real) to denote the maximal link utilization when the TE method uses the real traffic demand, U(estimated) the maximal link utilization when the TE method uses traffic matrix estimate, and U() the maximal link utilization under. The normalized inaccuracy of is defined in Equation (9): Inaccuracy = U(estimated U(real) U() U(real) 1% (9) When Inaccuracy =, using the estimated traffic matrix performs the same as using the real traffic matrix. When Inaccuracy = 1%, with the estimated traffic matrix performs the same as pure routing. When Inaccuracy > 1%, is worse than the pure routing. Figure 7 shows a typical result using Abilene data at each hour on It is clear that is robust in that the reduction of maximal link utilization is still significant when estimated traffic matrices are used. To compare the robustness of with and, we plot the CDF (Cumulative Distribution Function) of Inaccuracy in Figure 8. In the sub-figures, for Internet2 and Abilene, we also draw the parts of the CDF curves where the TE method improves the traffic distribution (Inaccuracy < 1%). For Internet2 (Figure 8(a)), the traffic matrices of every five minutes from through are considered, and improves 94.24% of all the cases. For Abilene (Figure 8(b)), improves for all the cases. For GEANT (Figure 8(c)), all the three TE methods improve the traffic distribution in all cases, and the majority of them are improved significantly. It has been observed [14] that the traffic in GEANT network has certain stability in that the link with the maximal link utilization does not change very often. The same links with the low capacity often gets the highest utilization which helps three TE methods to reduce maximal link utilization. Except that in Figure 8(a) shows comparable robustness, is in general more robust than the other TE methods. For example, 97.42% points are under 1% Inaccuracy in on GEANT, while for this number is 88.69% and for only 33.93%. The has the worst robustness among the three. For example, in Abilene, there are only 4.61% percent of points that improve the traffic distribution. IV. RELATED WORK Weight optimization was first proposed by Fortz and Thorup [3] [2]. The problem was proved to be NP-hard and heuristic methods were used to search for solutions. Roughan et al. examined the robustness of weight optimization using the real topology and traffic matrices from a tier-1 ISP [1], where the traffic matrices were derived from link load data using techniques developed by Zhang et al. [11]. Wang et al. [7] proved that the optimal routing with respect to the objective of traffic engineering can always be achieved by shortest path routing under appropriate link weights. PEFT [17] is a scheme that sets link weights so that all the multi-commodity flows will follow the shortest paths. However, the change of the link weights still leads to network-wide routing convergence and traffic shift. MATE [4] and TeXCP [] work in similar fashion by splitting the traffic load among multiple MPLS paths, but they do not deal with how to establish these paths. They also need to frequently probe each paths for its congestion state. As a comparison, gives both the LSPs need to be established and the split ratio between MPLS paths and paths. does not need to explicitly probe the paths, but it needs the traffic matrix, which can be derived from link utilization data reported by -TE [18]. Hybrid routing uses both and MPLS to achieve traffic engineering goals and avoids the drawbacks of the both. It has been proposed and explored in previous work such as [6] [8] [9], but they all resorted to heuristics to find solutions. As we demonstrated in this paper, the problem actually can be formulated and solved through linear programming. gives the optimal solution and runs faster than previous heuristics. V. CONCLUSION formulates the traffic engineering problem as a linear programming multi-commodity flow problem, solves it for optimal solutions, and realizes it via hybrid /MPLS routing. It avoids network convergence and traffic shift caused by weight optimization, as well as the full-mesh tunnels required by pure MPLS approach. Compared with other hybrid routing schemes, provides the optimal solution,

6 6 Percentage of Points (%) Inaccuracy (%) Percentage of Points (%) Inaccuracy (%) Percentage of Points (%) Inaccuracy (%) (a) Internet2 (b) Abilene (c) GEANT Fig. 8. The CDFs of Inaccuracy runs about two orders of magnitude faster, and is robust to measurement inaccuracy in traffic matrices. could be deployed at multiple places in a network and invoked relatively frequently to respond to changes in traffic demand. Therefore provides a good candidate for distributed, responsive traffic engineering solution in today s networks. ACKNOWLEDGMENTS We thank the anonymous reviewers for their comments. This work was supported by NSFC (6621, 6873), the Specialized Research Fund for the Doctoral Program of Higher Education of China (2638) and 863 high-tech project (27AA1Z216, 27AA1Z468). This work was done during Mingui Zhang s visit at the University of Arizona when he was supported by the China Scholarship Council (28626) and partially by NSF award CNS [14] S. Uhlig, B. Quoitin, J. Lepropre, and S. Balon, Providing Public Intradomain Traffic Matrices to the Research Community, ACM SIGCOMM Computer Communication Review, vol. 36, no. 1, pp , January 26. [] Traffic Matrices of Abilene. [Online]. Available: yzhang/research/abilenetm/ [16] Y. Zhang, M. Roughan, C. Lund, and D. L. Donoho, Estimating Point-to- Point and Point-to-Multipoint Traffic Matrices: An Information-Theoretic Approach, IEEE/ACM Trans. Netw., vol. 13, no., pp ,. [17] D. Xu, M. Chiang, and J. Rexford, Link-State Routing with Hop-by-Hop Forwarding Can Achieve Optimal Traffic Engineering, in Proceedings of IEEE INFOCOM, 28. [18] D. Katz, K. Kompella, and D. Yeung, RFC 363: Traffic Engineering (TE) Extensions to Version 2, Sept 23. [Online]. Available: REFERENCES [1] M. Roughan, M. Thorup, and Y. Zhang, Traffic Engineering with Estimated Traffic Matrices, in Proceedings of ACM IMC, 23. [2] B. Fortz and M. Thorup, Optimizing /IS-IS Weights in a Changing World, IEEE Journal On Selected Areas In Communications, vol. 2, no. 4, pp , May 22. [3], Internet Traffic Engineering by Optimizing Weights, in Proceedings of IEEE INFOCOM, 2. [4] A. Elwalid, C. Jin, S. Low, and I. Widjaja, MATE: MPLS Adaptive Traffic Engineering, in Proceedings of IEEE INFOCOM, 21. [] S. Kandula, D. Katabi, B. Davie, and A. Charny, Walking the Tightrope: Responsive Yet Stable Traffic Engineering, in Proceedings of ACM SIGCOMM,. [6] F. Skivée, S. Balon, and G. Leduc, A Scalable Heuristic for Hybrid IGP/MPLS Traffic Engineering - Case Study on an Operational Network, in Proceedings of IEEE ICON, 26. [7] Y. Wang, Z. Wang, and L. Zhang, Internet Traffic Engineering without Full Mesh Overlaying, in Proceedings of IEEE INFOCOM, 21. [8] H. Pham and B. Lavery, Hybrid Routing for Scalable IP/MPLS Traffic Engineering, in Proceedings of IEEE ICC, 23. [9] E. Mulyana and U. Killat, An Offline Hybrid IGP/MPLS Traffic Engineering Approach under LSP Constraints, in Proceedings of the 1st International Network Optimization Conference, INOC, 23. [1] H. Eiselt and C.-L. Sandblom, Integer Programming and Network Models. Germany: Springer, 2. [11] Y. Zhang, M. Roughan, N. Duffield, and A. Greenberg, Fast Accurate Computation of Large-Scale IP Traffic Matrices from Link Loads, in Proceedings of ACM SIGMETRICS, 23. [12] Internet2 Netflow Data. [Online]. Available: [13] TOolbox for Traffic Engineering Methods (TOTEM). [Online]. Available:

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