Non-binary information propagation: Modeling BGP routing churn

In this work, we generalize the commonly-used “binary” (or categorical) information propagation model to describe the propagation of a continuous-value node-property in a network. Most efforts so far focus on discrete states for nodes (i.e. healthy, sick). Here, we extend the above model to describe the propagation of a node property that is characterized by a real value. As a case study, we focus on routing messages at the Internet backbone (BGP level), which we refer to as routing instability or churn. Our goal is to develop the simplest possible model that can characterize the propagation of routing instability. To capture an important routing property (routing policies), we enrich the model in a non-trivial way. Varying our small set of model parameters, we show that our model can exhibit a wide range of behaviors, from fast “die-out” to non-zero steady-state and oscillations. To the best of our knowledge, this is the first work that casts routing as a network-wide propagation problem and sets the stage for a theoretical analysis of routing instability, and the propagation of non-binary node properties in general.