Taming the triangle inequality violations with network coordinate system on real internet

Abstract

Network Coordinate (NC) systems are efficient in scalable Internet latency estimation. While most of the focus has been put on how to distort Triangle Inequality Violation (TIV) in metric spaces to relieve the inaccuracy caused by it, TIV is a persistently and widely existing phenomenon on the Internet and thus should be embraced by future NC systems rather than being eliminated. Besides high accuracy, such an NC system can also provide the benefit of reducing the data transmission time by use of proper relay routes. With that in mind, we design an NC system with a hierarchical architecture, which is motivated by the natural idea of partitioning the three TIV links into different autonomous NC systems, in order to make as many as TIVs inherently embeddable in metric space. We implement and deploy our work, named Toread, on real Internet. Evaluation results show that Toread 's metric space can well characterize more than 60% TIVs, thus Toread is highly accurate (0.54 in Toread versus 1.06 in Pyxida at 90th percentile Relative Error) and effective in searching detour paths (succeeds in 58.2% cases).

Reducing TIV interference in network coordinate systems

“…Therefore, several studies have been made to attenuate the impact of TIVs, among which is the two-layer NC systems like Pharos [2]. However, having categorized the TIVs into three categories [1], we find that the twolayer structure can only optimize the first category TIV. What's more, for every triangle with first category TIV, only one edge of it can be estimated more accurately.…”

“…In [1], when dividing the whole network into several clusters, the TIVs can be categorized into three categories ( Figure 1): 1) two of the three nodes lie in the same cluster while the other one does not; 2) all of the three nodes belong to the same cluster 3) each node belongs to a different cluster.…”

Network distance prediction for enabling service-oriented applications over large-scale networks

“…However, the network distance between any two reachable nodes is not necessarily symmetric due to the network structure and routing policy [1,16]. The existing researches [16] have measured the proportion of asymmetric routing: more than 20% of the links have borne the asymmetric flow/packet/byte and more than 14% of the flows in the Internet have shown autonomous system asymmetry. These challenge accurate predictions of network distances.…”

“…However, in such a system the predicted distance always violates the triangle inequality due to routing policies or path inflation. The existing studies show that TIVs are widespread and persistent [6,16]. A TIV occurs among a triple of nodes in the Internet when the latencies between them cannot form a valid triangle, and changes with time.…”

“…Fig. 5 elaborates such a scenario derived from real measurements [16]. A TIV represents a real network path that there exists a closer route to a host through an intermediate host than the direct route, but can not hold for metric space.…”