This study investigates the Internet's resilience to instabilities caused by the mismatch of its topological state and routing information. A first numerical analysis proves that the Internet possesses unused path diversity which could be employed to strengthen its resilience to failures. Therefore, a new routing framework called Chain Routing, which takes advantage of such path diversity, is proposed. This novel idea is based in the mathematical concept of complete order, which is a binary relation that is irreflexive, asymmetric, transitive and complete. More important is the fact that complete orders, when represented as a graph, are the most connected digraph that does not contain any cycles. Consequently, a complete order could be applied to route information from a source to a destination with the guarantee that cycles will not develop in a path. A second numerical analysis demonstrates the feasibility of implementing Chain Routing as part of a routing protocol. Finally, an analysis is presented on how network stability could be maintained if a routing protocol integrates complete orders in time and topology.
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