Thursday, April 25, 2013

Moore, Kryder vs. SAW

Ashish Sood et al's paper Predicting the Path of Technological Innovation: SAW vs. Moore, Bass, Gompertz, and Kryder is very interesting. They propose a discontinuous model in which technology evolves in steps, separated by periods of stasis they call waits, leading them to dub the model SAW (Step And Wait). They show that it models the evolution of a wide range of technologies better than continuous models such as Moore's and Kryder's laws. Our work on the economics of long-term storage is based on Kryder's law, a continuous model. Below the fold I ask whether we need to change models.

Sood et al. Figure 1
First, Sood et al's Figure 1(a) is a log-linear plot of the performance of the desktop storage market from 1971 to 2009. The black line is magnetic disk, the dominant storage medium. It is close to a straight line, showing that the difference between a continuous exponential and SAW is small. But note that their plot ends before the recent disruptions caused by the Thai floods and the difficulties of the transition to Heat-Assisted Magnetic Recording.

Second, in Sood et al's Table 6 their model predicts a mean time between steps of 1.25 years and a mean step size of 0.35 for magnetic disk. This leads them to predict an overall performance growth rate of 0.31 as against their version of Kryder's law at 0.28, not a large deviation compared to other technologies in their study.

Sood et al. Figure 3
These two observations are summarized in Sood et al's Figure 3, which makes it clear that magnetic disk is an outlier among the technologies they studied, having by far the shortest wait time and among the smallest step sizes. Thus the difference between continuous and discontinuous models for this technology is small.

Third, Sood et al's definition of performance for the desktop memory market is bytes per square inch (Table 2). Our definition of performance for long-term storage is bytes per dollar. My colleague Daniel Rosenthal has studied the relationship between these two metrics. It appears that about 3/4 of the decrease in $/GB can be attributed to the increase in bits/in2. But for the purpose of this discussion the important observation is that the price per byte of a new generation of disk technology typically starts out higher than that of its predecessor and decreases gradually until it drops from the market some considerable time after the introduction of its successor. On the shelves at Fry's we have:
  • 4TB drives at $267
  • 3TB drives at $140, $230, $130, $190, $150, $150
  • 2TB drives at $190, $240, $120, $110, $110, $160, $130, $160, $105, $100, $180
  • 1TB drives at $100, $80, $80, $80, $280, $80, $80, $100, $130, $80, $80, $70, $90
The variation in price for a single disk size is because some are enterprise drives. Taking the cheapest drive, which in each technology is a "green" consumer drive, we have:
Capacity (TB) Cost ($/GB)
4 0.067
3 0.043
2 0.05
1 0.07

Note that the latest technology (4TB) is still more expensive than its two most recent predecessors (3TB & 2TB). The previous technology (3TB) is now cheaper than its predecessors. This price evolution during the market life of each technology means that, despite Sood et al's conclusions, a continuous model would still be appropriate for our purposes even if the first two points are discounted.

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