An Improved Analytical Expression for Write Amplification in NAND Flash
  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. 
Luojie Xiang, Brian Kurkoski
cs.PF