In the memory access time formula for the hierarchical cache - which is given as :$Emat = H1\times T1 + (1-H1)(H2\times (T1+T2) + (1-H2)\times (T1+T2+T3))$ (where Hi = Hit Ratio for the i-th level cache and Ti = Access time for i-th level cache. T3 = MM access time
I think, this formula assumes that the Cache used is Load through cache since we consider the initial search time for level 1 cache (T1) in the case that a miss may occur in level 1 cache, but we do not consider the access time for level1 after the required block has been transferred into the cache.
Is my intuition correct? If yes, then what should be the Emat formula for Load Back cache ? Should we add extra Ti values?