A write back cache basically performs four types of accesses, namely a cache read access (read hit), a cache update (write hit), a line fill, and a write back of a dirty line. Let a cache line...

A write back cache basically performs four types of accesses, namely a cache read access (read hit), a cache update (write hit), a line fill, and a write back of a dirty line. Let a cache line comprise S sectors. The read hit then takes one cycle, the write hit two cycles, and the line fill and the write back take W + S cycles each.

Show that the write back cache achieves a better CPI ratio than the write through cache if the number of dirty misses and the number of writes (stores) obey: