A mathematical model of the trim command in NAND-flash SSDs

Use of the Trim command is known to result in improvement in NAND-flash based solid state drive (SSD) performance. In this paper, we analytically model the amount of improvement in terms of effective overprovisioning, as measured by the effective spare factor. We show the effective spare factor is Gaussian with mean and variance dependent on the percentage of Trim requests in the workload and the manufacturer-specified spare factor, and the variance also dependent on the total storage capacity of the SSD.