An optimization model for communication networks resilient to partial multiple link failures

This submission is devoted to optimization of networks that permanently experience fluctuations of the capacity available on their links. This is an important and novel topic since limited link availability is a fundamental feature in wireless networks and yet majority of work in survivable network design is restricted to the total single link failures. We assume a given finite set of network states. Each state is characterized by availability coefficients specifying, for each link, the fraction of its reference capacity available in this state, and by traffic coefficients specifying, for each demand, the proportion of its reference traffic to be realized in the considered state. Our routing strategy allows for thinning/thickening the reference path-flows, with the thickening limited by a given upper bound U of the reference value. Thus, in each state, the value of every path-flow can range from 0 to U times its reference value. For the corresponding link cost minimization problem (where link capacities and state-dependent path-flows are decision variables) we present a non-compact linear programming model together with a solution algorithm based on path generation. We illustrate the effectiveness of the introduced routing strategy by presenting numerical results for a set of representative network examples