In flash-based solid-state drives (SSD) and log-structured file systems, new data is written out-of-place, which over time exhausts the available free space. New free space is created by the garbage-collection process, which reclaims the space occupied by invalidated data. The write amplification, incurred because of the additional write operations performed by the garbage-collection mechanism is a critical factor that negatively affects the lifetime and endurance of SSDs. We develop two complementary theoretical models of the SSD operation for uniformly-distributed random small user writes: a Markov chain model, which is useful to explore the performance characteristics of small and medium-sized systems, and a second model that captures the behavior of large systems. The combination of both models allows us to comprehensively characterize the system operation and behavior. Results of theoretical and practical importance are analytically derived and confirmed by means of simulation. Our results demonstrate that (i) as the system occupancy increases, the write amplification increases; (ii) as the number of blocks increases, the write amplification decreases and approaches a lower bound; and (iii) as the number of pages contained in a block increases, the write amplification increases and approaches an upper bound. They also show that, for large systems, the number of free pages reclaimed by the greedy garbagecollection mechanism after each block recycling takes one of two successive values, which provides a quasi-deterministic performance guarantee.