Impact of path length on circuitousness

Figure 10: Distance ratio versus the geographic distance between the ends of a path. The median distance ratio is computed over 400 km buckets (0-400 km, 400-800 km, and so on). A minimum distance threshold of 100 km is imposed to prevent the ratio from blowing up, so the first bucket is actually 100-400 km.

One question that arises from the above analysis is whether there is a connection between the circuitousness of a path and its length (i.e., the geographic distance between the two ends of the path). In other words, are longer paths inherently more circuitous, regardless of whether they traverse one ISP or many? If so, the fact that end-to-end paths tend to be longer than intra-ISP paths may explain the greater circuitousness of the former. However, as shown in Figure 10, the trend is quite the opposite. The distance ratio tends to decrease as the geographic distance increases.⁶ The reason is that the impact of a detour is smaller (in relative terms) in the context of a longer path. The distance ratio for the end-to-end path tends to be greater than that for the intra-ISP path, regardless of geographic distance. Thus the greater circuitousness of end-to-end paths is most likely due to the presence of multiple ISP networks in the path.