A robust optimization approach to network design

Abstract

This thesis addresses the problem of logical topology design for optical backbone networks subject to traffic following a Gaussian distribution. The network design problem is broken into three tasks: traffic routing, capacity allocation, and link placement. The routing and capacity allocation problems are formulated as a convex mathematical program. To extend this formulation to discrete optimization problems, such as the link placement sub-problem, it is reformulated as a mixed integer linear program (MILP) by extending tools from robust optimization to Gaussian variables. Bounds are presented to relate capacity allocation to the probability of traffic overflow on a link. Lastly, the link placement subproblem is formulated as an MILP and network topologies for deterministic traffic are compared with those for stochastic traffic. Additionally, this thesis presents a scheme in which a dedicated backup network is designed to provide protection from random link failures. Upon a link failure in the primary network, traffic is rerouted through a preplanned path in the backup network. We introduce a novel approach for dealing with random link failures, in which probabilistic survivability guarantees are provided to limit capacity over-provisioning. We show that the optimal backup routing strategy in this respect depends on the reliability of the primary network. Specifically, as primary links become less likely to fail, the optimal backup networks employ more resource sharing amongst backup paths. We apply results from the field of robust optimization to formulate an ILP for the design and capacity provisioning of these backup networks. We then propose a simulated annealing heuristic to solve this problem for large-scale networks, and we present simulation results to verify our analysis on optimal backup networks.