An Improved Analytical Expression for Write Amplification in NAND Flash

TL;DR

This paper presents an improved analytical model for write amplification in NAND flash memory, utilizing the Lambert W function and focusing on the invalid page probability during garbage collection, resulting in more accurate predictions.

Contribution

It introduces a refined expression for write amplification based on invalid page probability, improving accuracy over previous models by incorporating Lambert W function.

Findings

The new model predicts write amplification with higher accuracy.

Asymptotic analysis confirms dependence on overprovisioning factor only.

Comparison shows closer alignment with numerical simulations.

Abstract

Agarwal et al. gave an closed-form expression for write amplification in NAND flash memory by finding the probability of a page being valid over the whole flash memory. This paper gives an improved analytic expression for write amplification in NAND flash memory by finding the probability of a page being invalid over the block selected for garbage collection. The improved expression uses Lambert W function. Through asymptotic analysis, write amplification is shown to depend on overprovisioning factor only, consistent with the previous work. Comparison with numerical simulations shows that the improved expression achieves a more accurate prediction of write amplification. For example, when the overprovisioning factor is 0.3, the expression proposed by this paper gives a write amplification of 2.36 whereas that of the previous work gives 2.17, when the actual value is 2.35.