An Empirical Study of Routing Bias in Variable-Degree Networks

Recent work on Internet measurement and topology characterization has revealed a feature sharply distinct from the early Erdős-Rényi random graph model: highly variable degree distributions which arguably follow power-laws. Such properties may significantly affect various network algorithms and protocols. This paper explores whether and how degree variability causes routing bias, a phenomenon that routing algorithms may strongly favor nodes with better connectivity. This paper demonstrates that in variable-degree networks, including both synthetic networks and measured Internet topologies, there is a super-linear preference for routing algorithms to choose high-degree nodes in routing decision; in addition, the level of such preference remarkably depends on the degree variability of the network. Empirical study shows that the probability of routing through a node with degree d is approximately proportional to d, where 1 < θ < 2 and its value is larger when degree variability is lower. These findings are important to various network practices, including traffic provisioning, routing algorithm design, and network measurement. In particular, this paper illustrates that in traceroute-based topology discovery, routing bias implies that links associated to less well-connected nodes are less likely to be discovered. Hence, routing bias can become an important contributor to the incompleteness of measured router-level topologies.