Open shortest path first routing under random early detection

In this paper we consider a variant of Open Shortest Path First (OSPF) routing that accounts for Random Early Detection (RED), an Active Queue Management method for backbone networks. In the version of OSPF we consider in this paper we only require a single network path be available between each origin and destination, a simplification of the OSPF protocol. We formulate a mixed integer nonlinear program to determine the data paths, referred to as a routing policy. We prove that determining an optimal OSPF routing policy that accounts for RED is NP-Hard. Furthermore, in order for the generated routing policies to be real-world implementable, referred to as realizable, we must determine weights for all arcs in the network such that solving the all-pairs shortest path problem using these weights reproduces the routing policies. We show that determining if a set of all-pairs routes is realizable is also NP-Hard. Fortunately, using traffic data from three real-world backbone networks, we are able to find realizable routing policies for these networks that account for RED, using an off-the-shelf solver, and policies found perform better than those used in each network at the time the data was collected.