OSPF Routing with Optimal Oblivious Performance Ratio Under Polyhedral Demand Uncertainty

We study the best OSPF style routing problem in telecommunication networks, where weight management is employed to get a routing configuration with the minimum oblivious ratio. We consider polyhedral demand uncertainty: the set of traffic matrices is a polyhedron defined by a set of linear constraints, and the performance of each routing is assessed on its worst case congestion ratio for any feasible traffic matrix in the polyhedron. The problem is an accurate reflection of real world IP networks, not only because it considers the likelihood of having inaccurate demand estimates but also because it models one of the main currently viable traffic forwarding technologies, i.e., Open Shortest Path First (OSPF) routing with equal load sharing. This is an NP-hard problem even for a fixed demand matrix, so the problem considered in the paper is also NP-hard. First, we prove that the optimal oblivious routing under polyhedral traffic uncertainty on a non-OSPF network can be obtained in polynomial time using a duality-based reformulation. Then we consider the OSPF routing with equal load sharing under polyhedral traffic uncertainty, and present a compact mixed-integer linear programming formulation with flow variables. We propose an alternative tree formulation and a branch-and-price algorithm. Finally, we report and discuss test results for several network instances.