Probability-based routing symmetry metrics

Abstract

In communication networks, if streams between two endpoints follow the same physical paths for both forward and reverse direction, they are symmetric. Routing asymmetry affects several protocols, and impacts part of traffic analysis techniques. We propose two routing symmetry metrics to express different meanings when talking about routing symmetry, namely, (1) the forward and reverse flows coming from one node to another are exactly the same, and (2) one single node is visited by both flows. The two metrics are termed as identity symmetry and cross symmetry, respectively. Then, we build a model to link the macroscopic symmetry with the microscopic routing behavior, and present some analysis results, thus make it possible to design a routing algorithm with some desired symmetry. The simulation and dataset study show that routing algorithms that generate next hop randomly will lead to a symmetric network, but it is not the case for Internet. Because the paths of Internet are heavily dominated by a small number of prevalent routes, Internet is highly asymmetry.