Network synthesis under survivability constraints

Telecommunication networks are subject to link and equipment failures. Since failures cannot be entirely avoided, networks have to be designed so as to survive failure situations. In this paper, we are interested in designing low cost survivable networks. Given point-to-point traffic demands and a cost/capacity function for each link, we aim at finding the minimum cost capacities satisfying the given demands and survivability requirements. A survivability model that reroutes interrupted traffic using all the available capacities on the network is presented and studied. In the proposed model, capacity and flow assignments for each network operating state are jointly optimized. We prove the NP-hardness of the optimisation problem defined by dual constraints. Then, we propose a polynomial relaxation along with a fast heuristic to compute a feasible solution of the problem from its relaxed optimal solution. Our solution approaches are tested on a set of problem instances.