Many telecommunication networks use the open shortest path first (OSPF) protocol for the routing of traffic. In such networks, each router sends the traffic on the shortest paths to the destination, with respect to the link weights assigned. An interesting question is whether or not a set of desired routing patterns can be obtained in an OSPF network by assigning appropriate weights. If not, we wish to find the source of the infeasibility. We study these issues by formulating a mathematical model and investigating its feasibility. A certain structure, called valid cycle, is found to be present in most infeasible instances. This yields new necessary conditions, stronger than those previously known, for the existence of weights yielding a set of given desired shortest path graphs. A valid cycle indicates which parts of the routing patterns are in conflict and can be used for changing the routing patterns to make the problem feasible. A polynomial algorithm for finding valid cycles is presented, the method is illustrated by a numerical example, and computational tests are reported.

We consider network design and routing for Internet Protocol (IP) traffic. The design problem concerns capacity dimensioning of communication links, where the design cost consists of fixed charges and linear capacity expansion costs. The optimization problem also concerns determining the amount of traffic demand to be carried by the network and the metric used by a shortest path routing protocol. We present a novel linear mixed-integer mathematical formulation and two heuristic solution procedures. The first heuristic uses mixed-integer programming to generate a sequence of routing solutions. The second solution approach is a simulated annealing meta heuristic. Computational experiments for synthesized and real-life networks show that high-quality solutions can be obtained by both approaches.