A new linear path pair availability constraint for network design

It is essential for network operators to guarantee required levels of availability in the network without incurring in excessive costs. We address the optimization problem of upgrading links at a given cost, to achieve end-to-end availability guarantees in the network, via pairs of working and backup paths. These guarantees are expressed as nonlinear path pair availability constraints which cannot be readily linearized. For this reason, most works have only considered the working path availability or disaggregated models where availability guarantees are considered separately for the working and backup paths. We show that the aggregated models which jointly consider the availabilities of the working and backup paths can provide better solutions than the disaggregated models. Moreover, we present a more efficient aggregated model based on a novel strategy to linearize the path pair availability constraints, and show that it further improves previous results. It is usual to impose that the upgraded links belong to a spanning tree subgraph. We further compare the solutions with and without this imposition and show that relaxing the tree condition can provide better solutions.