Tuesday, August 28, 2012

Re-thinking Storage Technology Replacement Policy

We are now at work on the replacement for our two initial economic models, combining the detailed view of the short-term model with the big picture of the long-term model. As I explained in an earlier post, the policy that determines when storage media are replaced by successors has interesting effects on the outcome. Now I have to implement this policy for the new model, and I'm finding that the additional level of detail from the short-term model makes this a lot more complex. Below the fold is a wonkish discussion of these complexities.

The new algorithm uses two concepts:
  • planning life (PL), defined as the minimum of the device's remaining service life (its entire service life if it is not yet in service), and the planning horizon.
  • cost per byte-tick (CPBT), defined as the net present value at tick 0 of all future expenditures on this device through its planning life.
The steps of the algorithm, which is executed at each simulation tick, are:
  • Unconditionally remove all life-expired devices, paying their move-out cost.
  • Compute the CPBT of each device still in service.
  • Build the "in-service map", a sorted map from the CPBT to the in-service device in decreasing order.
  • Compute the CPBT of each device currently available.
  • Build the "available map", a sorted map from the CPBT to the available device in increasing order.
  • Choose as "cheapest" the first entry in the "available map", which will be the available device with the lowest CPBT.
  • Iterate through the "in-service map". While next entry in the map, the in-service device with the highest CPBT, has a higher CPBT than "cheapest", remove it from the inventory, paying its move-out cost.
  • While the total capacity of the devices in service is less than the demand for storage, add an instance of "cheapest" to the inventory and pay its purchase and move-in costs.
  • For each device in the inventory, pay its running costs for this tick.
Thus, in order to displace a device from the inventory, a new device must have a lower CPBT over its PL than the in-service device does over its PL. Note that the CPBT for the new device includes its purchase and move-in costs, whereas the CPBT for the in-service device excludes them. This is reasonable, since the purchase and move-in costs of the in-service device are sunk costs.

We use the concept of the planning horizon to model the fact that organizations find it difficult to account for costs incurred after some time in the future. This is another way of modeling the "short-termism" identified by Haldane & Davies here (PDF). Different organizations can vary widely in their ability to account for future costs; research grants have very short planning horizons whereas insurance companies have very long planning horizons.

We use the concept of CPBT to put cost comparisons between different storage devices on an apples-to-apples basis. To see why it is needed, consider this example. We have data on 16 4-year old drives, which have only a year of service life left. Should we:
  • Leave the drives in service, paying one year's worth of running costs for 16 drives and, in a year's time, 16 move-out costs?
  • Replace them with 4 of today's drives, which are 4 times as big and would have 5 years of service life left, paying in the first year one year's worth of running costs for 4 drives and the 16 move-out costs and the 4 move-in costs?
Just comparing the money spent in each case during the first year is wrong; it ignores the value of the 4 years of service life that will remain for the new drives at the end of the year.

We compute the net present value at tick zero for each expenditure in order to compare things on the basis of their effect on the overall endowment needed to preserve the collection, which is the overall result of the simulation.

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