Queueing Systems

, Volume 77, Issue 2, pp 149–176 | Cite as

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

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Abstract

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 \(\mathcal {C}\) of GC algorithms. Apart from the Random GC algorithm, class \(\mathcal {C}\) 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 \(N=50{,}000\) 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 \(b \ge 64\)).

Keywords

Mean field model Garbage collection Flash-based solid state drives Write amplification \(d\)-Choices 

Mathematics Subject Classification

60K30 68W20 68M20 68P20 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of Antwerp - iMindsAntwerpBelgium

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