Quantifying routing asymmetry in the Internet at the AS level

Our objective is to quantify the extent of routing asymmetry in the Internet: the measure of the difference between the forward and backward paths between two end points. Routing asymmetry has not been studied extensively. Most previous studies only consider asymmetry in terms of length and there is a lack of a systematic approach for quantifying asymmetry. One of the challenges in quantifying asymmetry is the formulation of an appropriate set of metrics that can effectively capture various notions of asymmetry. We point out that asymmetry could be of various types. We propose a framework to quantify the routing asymmetry between end hosts and propose two new metrics: absolute asymmetry and length-based normalized asymmetry. Our metrics capture the differences in router/AS identities, their appearing sequences and path lengths in a seamless way. We apply our framework to real Internet measurement data and examine routing asymmetry at the autonomous system (AS) level. We deduce the routing asymmetry distribution based on our framework, and we find that about 14% of pairs of routes considered display AS level routing asymmetry. Furthermore, our studies demonstrate that the routing asymmetry exhibits a skewed distribution, since a few end-points are consistently members of asymmetric pairs.