Garbage collection is known to have a profound impact on SSD performance as it strongly influences the write amplification. Another key value that impacts the write amplification is the amount of over-provisioning, which lowers the write amplification at the cost of reducing the user-visible storage capacity. Write amplification occurs as the valid pages that remain on a block selected by garbage collection need to be copied to a free block before an erasure can take place. Some of these valid pages may however belong to a deleted file and therefore copying them is redundant. To avoid copying deleted data, the operating system can issue a Trim command to invalidate pages whenever a file is deleted. Prior analytical studies on the write amplification in SSDs assumed that no trimming takes place. In this paper we generalize a number of mean field models to assess the impact of trimming on the write amplification. Using these models we argue that the write amplification in a (large) system with trimming can be determined by analyzing a system without trimming that uses a larger over-provisioning factor (and modified hot fraction, in case of hot and cold data). Using numerical results we further show that trimming cold data results in a more significant reduction in the write amplification compared to trimming hot data.
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