Correlation between delay and distance

Finally, we analyze the relationship between geography and the end-to-end delay along a path. Though geography by itself cannot provide any information about many performance characteristics like bandwidth, congestion along a path, the linearized distance of a path does enforce a minimum delay along a path (propagation delay along a path). To study this correlation, we use the TVHosts data set since it represents a wide variety of end-hosts. In our traceroute data, we obtain $3$ RTT samples for every router along the path. Since not all routers in a path are recognizable, we consider the minimum RTT, geographic distance and linearized distance to the last recognizable router along the path. In this analysis, we restrict ourselves to the list of probes in the U.S.

Figure 8: CDF of minimum end-to-end RTT to TVHosts for different ranges of linearized distances and geographic distances of paths

Figure 8 illustrates the correlation of the minimum RTT along a path to the linearized distance of a path and the geographic distance between the end-hosts. We make three important observations. First, at low values of the linearized distance there exists a strong correlation between the delay and linearized distance for a large fraction of end-hosts especially for small values of linearized distances. We expect this correlation to be much stronger as we compute the minimum over a larger number of samples. Second, linearized distance along a path does enforce a minimum end-to-end RTT which is an important performance metric for latency sensitive applications. Third, the minimum RTT between two end-hosts has lesser correlation to the geographic distance between them as compared to the linearized distance of the path connecting them. We observe that for a given range of linearized distance of a path, the RTT variation is much smaller than its variation for the same range of geographic distance between the end-hosts. Hence linearized distance of a path conveys more about the minimum RTT characteristics of a path than merely the geographic distance between the end-hosts. We also verified that these observations hold across the other data sets we collected. The coarse correlation between minimum delay and geographic distance was used in building GeoPing, an IP-to-location mapping service [13].