Topology Discovery on Unicast Networks: A Hierarchical Approach Based on End-to-End Measurements

In this paper we address the problem of topology discovery in unicast logical tree networks using endto-end measurements. Without any cooperation from the internal routers, topology estimation can be formulated as hierarchical clustering of the leaf nodes based on pair-wise correlations as similarity metrics. We investigate three types of similarity metrics: queueing delay measured by sandwich probes, delay variance measured by packet pairs, and loss rate measured also by packet pairs. Unlike previous work which first assumes the network topology is a binary tree and then tries to generalize to a non-binary tree, we provide a framework which directly deals with general logical tree topologies. Based on our proposed finite mixture model for the set of similarity measurements we develop a penalized hierarchical topology likelihood that leads to a natural clustering of the leaf nodes level by level. A hierarchical algorithm to estimate the topology is developed in a similar manner by finding the best partitions of the leaf nodes. Our simulations show that the algorithm is more robust than binary-tree based methods. The three types of similarity metrics are also evaluated under various network load conditions using ns-2.