Non-convex Optimization in Internet Routing: Protocol, Formulation, and Computation

Network operators control the flow of traffic through their networks by adapting the configuration of the underlying routing protocols. For example, they tune the integer link weights that routing protocols like OSPF use to do distributed forwarding of packets. The resulting optimization problem by the operator—to find the best link weights for a given topology and traffic matrix—is well-known to be computationally intractable even for the simplest objective functions, forcing the use of local-search techniques. This is a difficult optimization in part because these protocols split traffic evenly along shortest paths and in part because of the specific representation of the optimization problem. In this paper, we propose a readily implementable routing protocol called Distributed Exponentially-weighted Flow SpliTting (DEFT), where the routers can direct traffic on non-shortest paths, with an exponential penalty on longer paths. It leads to a cost function for the operator that is provably not worse than OSPF, and verified to be almost optimal in experiments based on various network topologies. One of the innovations in solving link weight optimization for DEFT is on problem representation: both link weights and traffic flows are integrated as optimization variables, and another is the computational method of two-stage iterative relaxation, which is much more efficient than state-of-the-art local search heuristics. DEFT retains the simplicity of having routers compute paths based on configurable link weights, while approaching the performance of more complex routing protocols that can split traffic arbitrarily over any paths.