Cloudonomics: The Business Value of Cloud Computing, + Website

Linear Growth

We’ve looked at uniform, normal, and triangular demand distributions, but suppose we are fortunate in that our customer demand growth is steady, that is, demand is linear, of the form ax + b. If the growth is definitely steady and we can ratchet up capacity, we are in good shape. If we are running a rental car service and the first day of operation we have one customer, the second day of operation we have two, and so on, we just need to buy cars at a rate of one per day, and we will have perfect capacity. Even if it takes a month to order and receive a car, it’s no problem if we can forecast accurately; we just order cars one month ahead of time, and we still have perfect capacity.

If, however, we are more conservative, there is a problem. Suppose we don’t really trust our forecast, and we wait until there is proof of demand before increasing capacity. Then, there is a direct relationship between the time it takes to acquire a car—that is, to provision capacity—and the penalty we will pay for insufficient capacity. If we are always one day behind, we will always be one car short. If we are always two days behind, we will always be two cars short. If we are always n days behind, we will always be n cars short.

As shown in Exhibit 14.2, since we are always short, we always pay a penalty proportional to cd. Consequently, the total penalty is proportional to the length of the delay, the size of the penalty, and the duration for which we pay the penalty:

EXHIBIT 14.2 ...