Analytical reproduction / no device measurements
SSD over-provisioning: analytical model values
Seven computed reserve-to-write-amplification cases with explicit logical and physical capacity denominators. Analytical model evaluation, not SSD measurements.
Download CSV7 rows / 6 columnsJSON and provenance / Evaluator code / Research explanation
Method
Evaluate Xiang and Kurkoski arXiv:1110.4245v1 equation 12 by solving A*log(1-1/A)+(1+rho)=0 for finite A>1. Bisection uses log1p, an expanding upper bracket and at most 100 steps, stopping at floating-point resolution. rho=(P-L)/L; supported domain 0.01 to 1. Capacity units are identical. No random sampling or device I/O.
| Reserve / logical | Reserve / physical | Write amplification | Victim pages reclaimed |
|---|---|---|---|
| 7% | 6.54% | 7.817 | 12.79% |
| 10% | 9.09% | 5.677 | 17.61% |
| 20% | 16.67% | 3.188 | 31.37% |
| 25% | 20.00% | 2.693 | 37.14% |
| 30% | 23.08% | 2.364 | 42.30% |
| 50% | 33.33% | 1.716 | 58.28% |
| 100% | 50.00% | 1.255 | 79.68% |
Interpretation
A 20% physical-capacity reserve is a 25% logical-capacity reserve. WAF is physical page writes per host page write in the stated model. It is not IOPS, bytes per second, a guarantee, or a recommendation to change a drive's capacity.
Reproduce
The linked module prints the exact CSV with Node.js and no external packages. Provenance JSON records SHA-256 hashes of code and CSV. This command performs no drive I/O:
node --input-type=module -e 'import { toCsv } from "./ssd-overprovisioning.mjs"; process.stdout.write(toCsv())'Limits
- Uniform independent page writes and stationary simplified cleaning behavior; not commercial firmware.
- An asymptotic approximation to the paper's greedy model, not an exact finite-block greedy formula.
- No reproduction of either paper's simulator, trace evaluation or physical-device experiment.
- No metadata, parity, compression, wear-leveling or cache-folding traffic; no latency or lifetime prediction.
- No confidence interval: deterministic arithmetic uncertainty is distinct from model applicability.
- P denotes physical capacity available to this model, not all installed NAND including unavailable overhead.
Column definitions
- opUserPercent
- 100*(P-L)/L; reserve divided by logical capacity.
- sparePhysicalPercent
- 100*(P-L)/P; the same reserve divided by physical capacity.
- physicalPerLogical
- P/L = 1 + rho; dimensionless.
- waf
- Model physical page writes per host page write; dimensionless, not measured.
- reclaimedFraction
- Fraction q of victim pages freed for new host writes; 1/waf.
- validFraction
- Fraction of victim pages relocated; 1-q.
Sources and license
CC0-1.0 for Hesela's original implementation and computed rows; source papers retain their rights.
- Luojie Xiang and Brian M. Kurkoski. An Improved Analytic Expression for Write Amplification in NAND Flash. arXiv:1110.4245v1 (19 October 2011), sections II-IV, equation 12 and Table I.
- Peter Desnoyers. Analytic Modeling of SSD Write Performance. SYSTOR 2012, sections 2-6, Tables 1-2. DOI: 10.1145/2367589.2367603.
Corpus: over-provisioning, greedy garbage collection and hot/cold data separation.