Browsing by Subject "Oblivious routing"
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Item Open Access Optimal oblivious routing under linear and ellipsoidal uncertainty(Springer, 2008) Belotti, P.; Pınar, M. Ç.In telecommunication networks, a common measure is the maximum congestion (i.e., utilization) on edge capacity. As traffic demands are often known with a degree of uncertainty, network management techniques must take into account traffic variability. The oblivious performance of a routing is a measure of how congested the network may get, in the worst case, for one of a set of possible traffic demands. We present two models to compute, in polynomial time, the optimal oblivious routing: a linear model to deal with demands bounded by box constraints, and a second-order conic program to deal with ellipsoidal uncertainty, i.e., when a mean-variance description of the traffic demand is given. A comparison between the optimal oblivious routing and the well-known OSPF routing technique on a set of real-world networks shows that, for different levels of uncertainty, optimal oblivious routing has a substantially better performance than OSPF routing.Item Open Access OSPF routing with optimal oblivious performance ratio under polyhedral demand uncertainty(Springer, 2010) Altın, A.; Belotti, P.; Pınar, M. Ç.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 a routing is sought with a fair performance for any feasible traffic matrix in the polyhedron. The problem accurately reflects real world networks, where demands can only be estimated, and models one of the main traffic forwarding technologies, Open Shortest Path First (OSPF) routing with equal load sharing. This is an NP-hard problem as it generalizes the problem with a fixed demand matrix, which is also NP-hard. We prove that the optimal oblivious routing under polyhedral traffic uncertainty on a non-OSPF network can be obtained in polynomial time through Linear Programming. 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 formulation and a branch-and-price algorithm. Finally, we report and discuss test results for several network instances.