The stable paths problem and interdomain routing
IEEE/ACM Transactions on Networking (TON)
BGP4: Inter-Domain Routing in the Internet
BGP4: Inter-Domain Routing in the Internet
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How effective are interdomain routing protocols, such as the Border Gateway Protocol, at routing packets? Theoretical analyses have attempted to answer this question by ignoring the packets and instead focusing upon protocol stability. To study stability, it suffices to model only the control plane (which determines the routing graph) --- an approach taken in the Stable Paths Problem. To analyse packet routing, it requires modelling the interactions between the control plane and the forwarding plane (which determines when packets are forwarded), and our first contribution is to introduce such a model. We then examine the effectiveness of packet routing in this model for the broad class next-hop preferences with filtering. Here each node v has a filtering list$\mathcal{D}(v)$ consisting of nodes it does not want its packets to route through. Acceptable paths (those that avoid nodes in the filtering list) are ranked according to the next-hop, that is, the neighbour of v that the path begins with. On the negative side, we present a strong inapproximability result. For filtering lists of cardinality at most one, given a network in which an equilibrium is guaranteed to exist, it is NP-hard to approximate the maximum number of packets that can be routed to within a factor of O(n1−ε), for any constant ε0. On the positive side, we give algorithms to show that in two fundamental cases every packet will eventually route with probability one. The first case is when each node's filtering list contains only itself, that is, $\mathcal{D}(v)=\{v\}$. Moreover, with positive probability every packet will be routed before the control plane reaches an equilibrium. The second case is when all the filtering lists are empty, that is, $\mathcal{D}(v)=\emptyset$. Thus, with probability one packets will route even when the nodes don't care if their packets cycle! Furthermore, with probability one every packet will route even when the control plane has no equilibrium at all. To our knowledge, these are the first results to guarantee the possibility that all packets get routed without stability. These positive results are tight --- for the general case of filtering lists of cardinality one, it is not possible to ensure that every packet will eventually route.