Modeling a policy-capable path-vector routing protocol using Jacobi iteration over a path algebra

Several computer network design and analysis activities either require or benefit from having knowledge of the sets of paths possible between the network's nodes. Often these activities utilize path sets containing those network paths of shortest length due to the availability of shortest path algorithms. However, in large operational IP networks (including the whole public Internet), user data may be forwarded along network paths which are not of shortest length due to the effects of inter-domain routing policies. To determine these policy-influenced network paths, two path algebras are developed which model a baseline and enhanced policy-capable path-vector routing protocol respectively. The enhanced model extends the capability of the baseline by including support for local preferencing and selective export filtering of network paths to support common Internet routing policies. Although both new path algebras can be considered "weak" in that they lack a few specific algebraic properties (such as being right distributive over multiplication), it is shown that both models can use Jacobi iteration to converge to sets of paths that form a (routing) in-tree. These sets of network paths are equivalent to that output by a path-vector routing protocol operating over a user-supplied topology. For large network topologies, the baseline routing protocol model is shown to require an order of magnitude less run-time and memory to calculate the same path sets as the de facto approach of discrete-event network simulation.