Cloud Economics - when demand takes a "random walk"

My previous post was a special case comparison of Amazon's reserved IaaS versus a privately owned data center where server utilization is fixed at 100%. This is a simple comparison super easy to comprehend but also unrealistic because no business has a steady demand all the time. While researching a more generic model I came across a working paper on the economics of cloud under pretty much all conceivable type of demand situations ranging from a linear growth/decline, sawtooth, exponential and even a stochastic "Random Walk".

 The paper at first glance appeared so mathematically rigorous and intense with its use of integral calculus and Monte Carlo simulations (what Joe gracefully calls "simple maths and calculus" in the video below), that I felt compelled to go back and research the author. The author is Joe Weinman who currently leads the communications, media, and entertainment segment for Hewlett-Packard's Worldwide Industry Solutions having moved recently from being the "cloud face" of AT&T's business development initiatives. He is also a prolific inventor (14 patents), frequent global keynote speaker and also author of the pithy "10 laws of cloud computing" on his blog cloudonomics .

Here is a short interview from his AT&T days where he explains why the cloud is not a panacea but a niche solution and his view that Hybrid clouds are likely to be the end state as the market matures.

Quite interesting from a sourcing standpoint are the insights derived from his working paper, some of which co-incide with my special case scenario from my previous post. Hit the jump for these insights:

and I quote from the paper:

"  .. 

1. For flat demand, on-demand provisioning offers no benefit.
2. If demand can be forecasted accurately further out than it takes time to provision, on-demand provisioning also is unnecessary.
3. If on-demand is not an option, and the cost of unserved demand is greater than the cost of resources, it is better to be ―safe than sorry by building in excess capacity ...."

Simple and intuitive so far, and here is where it gets a little involved:

"...However, when there is variability coupled with unpredictability, the following rules hold:

1. For linearly growing or declining demand, a reduction in time (monitoring cycle or resource provisioning) offers a proportional reduction in cost.
2. For exponential demand, the loss associated with even fixed interval provisioning grows exponentially, so on-demand provisioning is essential.
3. If the demand in each time interval is drawn from a random distribution, on demand is far superior to the expected loss from the best fixed capacity strategy.
4. If demand varies as in a Random Walk, time compression offers sub-linear benefits, for example, a two-fold reduction in cost requires a four-fold reduction in time.

Here is the paper for those who are interested. For the less mathematically inclined, you've been warned!  Time is Money: The Value of "On-Demand" (PDF)