A mean field model for a class of garbage collection algorithms in flash-based solid state drives

Garbage collection (GC) algorithms play a key role in reducing the write amplification in flash-based solid state drives, where the write amplification affects the lifespan and speed of the drive. This paper introduces a mean field model to assess the write amplification and the distribution of the number of valid pages per block for a class C of GC algorithms. Apart from the Random GC algorithm, class C includes two novel GC algorithms: the d-Choices GC algorithm, that selects d blocks uniformly at random and erases the block containing the least number of valid pages among the $d$ selected blocks, and the Random++ GC algorithm, that repeatedly selects another block uniformly at random until it finds a block with a lower than average number of valid blocks. Using simulation experiments we show that the proposed mean field model is highly accurate in predicting the write amplification (for drives with $N=50000$ blocks). We further show that the d-Choices GC algorithm has a write amplification close to that of the Greedy GC algorithm even for small d values, e.g., d = 10, and offers a more attractive trade-off between its simplicity and its performance than the Windowed GC algorithm introduced and analyzed in earlier studies. The Random++ algorithm is shown to be less effective as it is even inferior to the FIFO algorithm when the number of pages $b$ per block is large (e.g., for b ≥ 64).