  A new framework to perform routing at the Autonomous System level is proposed
in this paper. This mechanism, called Chain Routing, uses complete orders as
its main topological unit. Since complete orders are acyclic digraphs that
possess a known topology, it is possible to define an acyclic structure to
route packets between a group of Autonomous Systems. The adoption of complete
orders also allows easy identification and avoidance of persistent route
oscillations, eliminates the possibility of developing transient loops in
paths, and provides a structure that facilitates the implementation of traffic
engineering. Moreover, by combining Chain Routing with other mechanisms that
implement complete orders in time, we suggest that it is possible to design a
new routing protocol which could be more reliable and stable than BGP's current
implementation. Although Chain Routing will require an increase of the message
overhead and greater coordination between network administrators, the rewards
in stability and resilience should more than compensate for this effort.
