Cloudonomics: The Business Value of Cloud Computing, + Website

Inverse Square Root Law

It should be clear that regardless of the approach that we use—packing or covering—the area, A, that is covered is proportional to the number of circles, n, and is also based on the radius of each circle, r. Specifically, A ∝ nr2, where the constant of proportionality depends on the packing strategy that we use and thus what is referred to as the packing density, η (eta). And we’ve stipulated that latency is proportional to distance. But this means that for a given area A, , or, in other words, on a plane, the average latency and therefore also the worst-case latency are both proportional to the inverse square root of the number of nodes.

This is very powerful for small n but rapidly leads to diminishing returns. If global round-trip response times are, say, 160 milliseconds, by using a couple of dozen or so nodes, we can get round-trip latencies way down, say, to 10 or 20 milliseconds. However, it becomes increasingly difficult to reduce latencies through node build-outs: At some point, for example, reducing latency by a microsecond or so might require billions of service nodes. This is too many even for McDonald’s or Starbucks.