Minimizing Backup Capacity Considering Routings in Primary and Backup Networks for Random Multiple Link Failures

This paper proposes an optimization approach with providing of the probabilistic survivability guarantees to minimize the total capacity in a backup network by determining both routings in primary and backup networks, simultaneously. The backup network is designed to protect the primary network from the random multiple link failures with the probability of link failure. In a conventional approach, the routing in the primary network is not considered to be variable to minimize the total capacity in the backup network. Considering the primary routing as a variable to decide the backup network can reduce the total capacity in the backup network compared to that of the conventional approach. In the proposed approach, both routings in the primary and backup networks are considered as decision variables. Robust optimization is employed in our optimization problem to provide the probabilistic survivability guarantees for different link capacities in the primary network. Numerical results show that the proposed approach achieves lower total capacity in the backup network than that of the conventional approach.