Cloudonomics: The Business Value of Cloud Computing, + Website

Random Walks

Rather than the simplicity of flat demand or linear growth or the monotonicity of exponential growth, often demand variation is more like the stock market. Up a little, flat, up a little more, down a little, up a lot, flat again, . . . In the same way that stocks fluctuate as buyers and sellers enter and leave the market, the aggregate level of demand for some applications can be modeled as users arriving at a site, engaging in some activity—say, searching or shopping—and then moving on to do something else.

Albert Einstein is known for the theory of relativity. But in 1905, he not only developed the special theory of relativity, explained the photoelectric effect, and equated matter with energy, he also managed to explain Brownian motion, first observed by Scottish botanist Robert Brown, where particles suspended in the air or a liquid tend to bounce about. One of the key things that Einstein showed was that the “displacement” of a particle (i.e., how far it moved) was proportional to the square root of the elapsed time.

In Brownian motion, a particle can be jostled in any direction. In a one-dimensional random walk, picture a particle that can move either left or right. In some variations, the particle can move exactly one step either way; in others there is some distribution of potential distances, say, uniform, or perhaps normal.

In general, though, here’s what happens. It is certainly possible that a particle moves to the left continuously, say, L—L—L—L—L—L . ...