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1 Riikka Susitaival and Samuli Aalto. Adaptive load balancing with OSPF. In Proceedings of the Second International Working Conference on Performance Modelling and Evaluation of Heterogeneous Networks (HET NETs 2004), pages P9/1 P9/10, Networks UK Publishers Reprinted with permission.

9 Figure 3: The maximum link utilization as a function of the number of iterations, when there are no traffic fluctuations, δ = 0. Left-hand-side: 10-node network. Right-hand-side: 20-node network Figure 4: The maximum link utilization as a function of the number of iterations, when there are random traffic fluctuations in a shorter time-scale, δ = 0.1. Left-hand-side: 10-node network. Right-hand-side: 20-node network. the optimal value in the 20-node network. Note that in the 10-node network in the iteration rounds from 500 to 1000 the result of heuristics and the sub-optimal value are equal. Then we assumed that the link weights and the splitting ratios of each router can be optimized in a longer time scale (hours to days). The shortest paths needed for the adaptive algorithm are thus first calculated using the optimal link weights corresponding to the original traffic demands d k and determined from the dual problem (3) and the splitting ratios from the solution of the primal problem (2) and formula (4). After that the link weights remain unchanged. Figure 6 shows the resulting maximum link utilization for the 10-node and 20-node networks as a function of the number of iterations for granularity parameters g = 20 and g = 50. Now the sub-optimal values in the 10-node network are close to the optimal values and thus heuristics can yield to the results close to the optimal solution. In the 20-node network the results are similar to the previous case in Figure 5, except the first iterations where the results are now immediately close to the optimal one. As a conclusion, the optimization of the link weights in the longer time-scale improves the performance of the network. In the 20-node network also the unit weights provide a good result. An explanation is that, in the 10-node network, the number of shortest paths related to the unit link weights is 116 whereas it is 153 in the case of the optimal link weights. Thus the number of φ-parameters is greater in the latter case and also the results are better. In the 20-node network, the corresponding numbers of the shortest paths are 782 and 785. Also the results are quite similar. P9/8

10 Figure 5: The maximum link utilization as a function of the number of iterations, when there are traffic fluctuations in a longer time-scale. Left-hand-side: 10-node network. Right-hand-side: 20-node network Figure 6: The maximum link utilization as a function of the number of iterations. Left-hand-side: 10-node network. Righthand-side: 20-node network. 5 Conclusion In this paper we studied how load can be balanced adaptively in OSPF-networks using a distributed approach. We also considered the procedure of optimizing the OSPF-weights by primal-dual methods and how this can be combined to adaptive heuristics. The results show that the optimization of traffic splitting ratios improves the performance of the network when compared to equal splitting. When the set of shortest paths is small also the changing of OSPF-weights is worthwhile. In the future the approach which combines the shorter and longer time-scale optimization has to be developed further. Also the actual converge time of the adaptive algorithm has to be studied carefully in realistic traffic scenarios. In addition, we have to study if the disorder of packets is really a problem and how this problem can be solved. Acknowledgements. This work was financially supported by the Academy of Finland (grant n:o 74524). P9/9

11 References [1] J. MOY, OSPF Version 2, IETF RFC2328, April [2] E. ROSEN, A. VISWANATHAN AND R. CALLON, Multiprotocol Label Switching Architecture IETF RFC3031, January [3] B. FORTZ, M. THORUP, Internet Traffic Engineering by Optimizing OSPF Weights, in Proc. of IEEE Infocom [4] B. FORTZ AND M. THORUP Optimizing OSPF/IS-IS Weights in a Changing World, IEEE Journal on Selected Areas in Communications, Vol. 20, No. 4, pp , [5] Y. WANG, Z. WANG AND L. ZHANG Internet Traffic Engineering without Full Mesh Overlaying, Proc. of IEEE Infocom [6] A. SRIDHARAN, R. GUÉRIN AND C. DIOT, Achieving Near- Traffic Engineering Solutions for Current OSPF-IS-IS Networks, in Proc. of IEEE Infocom [7] R. SUSITAIVAL, S. AALTO AND J. VIRTAMO, Adaptive load balancing using MPLS, accepted for publication in Proc. of MMB&PGTS, [8] C. VILLAMIZAR, OSPF Optimized Multipath (OSPF-OMP), IETF Internet-draft, draft-ietf-ospf-omp-02, February P9/10

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