On the distribution of valid pages with greedy garbage collection for NAND flash

Flash memory uses relocate-on-write, also called out-of-place write for performance reasons. Relocate-on-write requires a garbage-collection process, which results in additional write operations referred to as write-amplification. The reclaiming policy that selects the blocks to garbage-collect is greedy if it is based only on the amount of free space to be gained-Write amplification is a critical factor limiting the write performance and endurance in solid-state drives and the greedy garbage collection policy minimizes it. In this paper, we derive an expression for the steady-state distribution of valid-pages using a novel probabilistic model for flash-based SSDs for a greedy reclaiming policy. This distribution lends itself directly to evaluation of write-amplification and gives insight into designing newer garbage collection policies, which would further reduce write-amplification. Numerical evaluation of the derived expression matches the distribution obtained via Monte-Carlo simulation for several different drive configurations, thereby validating the derivation.