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Economies and Diseconomies of Scale

Consider a sy...

Question

Consider a system with 2 - level caches. Access times of Level 1 cache, Level 2 cache, and main memory are 1 ns, 10 ns and 500 ns, respectively. The hit rates of Level 1 and Level 2 caches are 0.8 and 0.9, respectively. What is the average access time of the system ignoring the search time within the cache?

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Solution

\(Access~ time ~(Hierarchical)\)

\(\Rightarrow\,\,H_1T_1+(1-H_1)H_2(T_2+T_1)+(1-H_1)\)
\((1-H_2)\,(T_3+T_2+T_1)\)

\(=0.8+1.8+10=12.6\,ns\)

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