The behavior of the cache in the presence of update transactions is more complicated than for retrievals.
There is still an initial period during which the cache fills. Then, because cache pages are being modified, there is a point at which the cache must begin writing those pages to disk before it can load other pages. Over time, the amount of writing and reading stabilizes, and subsequent transactions have a given probability of requiring a disk read and another probability of causing a disk write.
The steady-state period is interrupted by checkpoints, which cause the cache to write all dirty pages to disk.