Accuracy of path length estimation via network distance based coordinate systems

Network distance estimation via Euclidean coordinate system has been widely studied over the past decade. Basically, each node in the Internet is assigned a set of coordinates and the network distances such as round trip time can be estimated by the Euclidean distances among the nodes. The accuracy of the Euclidean coordinate systems is usually measured with various performance metrics such as relative errors. It is well known that the estimation has intrinsic errors due to the triangle inequality violations among the network distances. Since there have been abundant analysis on the accuracy of the direct distance estimation, i.e., the network distance between two nodes, in this paper, we turn our focus to the path length estimation. Basically, for an overlay path with multiple links, the path length is the sum of the distances of the links along the path. Accurate path length estimation can be exploited for many path selection problems in the peer to peer systems. For example, selecting one hop relay node can be easily implemented via the Euclidean coordinate systems. In this paper, we present a rigorous mathematical analysis on the estimation accuracy especially of the path lengths. We consider the errors as random variables and show that the path length estimation is much more accurate than the direct distance estimation through a rigorous statistical analysis. We also provide simulation results that conform to the mathematical analysis.