Traffic Engineering in the presence of Tunneling and Diversity Constraints: Formulation and Lagrangean Decomposition Approach

We present a mixed integer linear programming (MIP) formulation for a traffic engineering problem where we address the restricted number of active tunnels on each link in the presence of diversity requirements. The design has significance in networks such as multi-protocol-label-switching (MPLS)based networks where such conditions can be applicable. For large networks, we present the solution approach using Lagrangean decomposition algorithm by considering the dual problem and using subgradient optimization. The dual subproblems are shown to have integral solutions for continuous relaxed versions. Such a construction gives us the benefit of solving the MIP problem with a series of continuous problems. We present numerical results for fairly large networks generated randomly using a topology and traffic generator. We also present computational results to show the influence of tunnel restriction and diversity parameter on traffic engineering of a network.