On the Optimality of the Greedy Garbage Collection Strategy for SSDs

Solid State Drives (SSDs) have replaced magnetic disks in many application areas, as they provide very high performance for arbitrary access patterns. Nevertheless, data written to a physical page has to be erased before a page can be rewritten. The corresponding garbage collection (GC) process can only be performed on a block granularity, where a block includes many pages, impacting both the performance and lifetime of an SSD. The cost of a GC process is typically measured in terms of its write amplification, i.e., the number of blocks internally written by the SSD divided by the number of write requests of the host.Several GC heuristics have been proposed to optimize the write amplification of SSDs. These heuristics have been mostly empirically evaluated, while no thorough theoretical results are available on the optimality of GC algorithms even for seemingly simple cases like uniform and independent access distributions.In this work, we theoretically investigate the GREEDY GC strategy for uniformly independently distributed write accesses. We therefore model the garbage collection process on SSDs as a stochastic process and prove that the expected write amplification incurred by the GREEDY GC strategy is at most that of any other online GC strategy.