When a CPU writes to the cache, both the item in the cache and the corresponding item in the memory must be updated. If data is not in the cache, it must be fetched from memory and loaded in the cache. If tl is the time taken to reload the cache on a miss, show that the effective average access time of the memory system is given by:

tave = htc + (1 ? h)tm + (1 ? h)tl.


If a memory access occurs, the access may be to cached data (a hit), or to data not in the cache (a miss).
The average time spent accessing cached data is h?tc (the hit ratio multiplied by the cache access time).
If the data is not in the cache, the probability is 1 ? h (an access is a hit or miss and both probabilities add up to 1).
The average time devoted to misses is (1 ? h)tm where tm is the memory access time.
When a miss occurs, the cache has to be reloaded from memory. The time for this is the probability of a miss
multiplied by the time to load a line; that is (1 ? h) tl. The total time is:
tave = htc + (1 ? h)tm + (1 ? h)tl.
Note that the (1 ? h)tm term is redundant if the loading of the data into the CPU is carried out in parallel with the
refilling of a cache line.

Computer Science & Information Technology

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