Exponential Growth

Suppose instead of a linear growth environment there is exponential growth, as many hot start-ups and even some companies that are no longer quite start-ups seem to have. At first glance, the situation—as illustrated in Exhibit 14.3—seems identical to the linear growth case; after all, the curves are following each other.

EXHIBIT 14.3 Exponential Demand Growth with Constant Resourcing Delay

image

However, there is something very different going on. The horizontal distance stays the same—at any “altitude,” the demand curve and the resource curve are separated by the same horizontal distance. But, over time, as we move farther to the right, the vertical drop increases. In other words, rather than always being one server or one car short or two cars short, we start off one car short then we are a few cars short then we are dozens and then thousands and then millions. The difference over time, rather than being constant, is exponential.

When the demand function is exponential—that is, D(t) = et—any fixed provisioning interval for deploying resources in accordance with the current demand level (i.e., there is no forecasting) will fall exponentially farther behind. This is easy to show. Let the fixed provisioning interval be p. Then, in chasing the demand function D(t), we set resources R(t) = etp. Thus, the difference between the two is:

where k = 1 − ep and thus ...

Get Cloudonomics: The Business Value of Cloud Computing, + Website now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.