Using submodularity in solving the robust bandwidth packing problem with queuing delay guarantees

Abstract

This paper addresses the robust bandwidth packing problem with queuing delay guarantees. The queuing delays are approximated using the M/G/1 model. The problem involves nonlinear constraints that aim to limit the total queuing delays and satisfy edge capacities. We present two types of reformulations for this intractable problem. The first type consists of conic quadratically constrained or linear programs with integer variables, which can be implemented using commercial solvers. The second type is mixed-integer linear programs with an exponential number of constraints. To address the nonlinear constraints, we reformulate them into multiple linear constraints by combining polymatroid or submodular inequalities with the supporting hyperplanes of a concave function. The computational results demonstrate the effectiveness of the proposed formulations.