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Cache Average Access Time

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$H$ is the hit rate of cache level $L_i$
$T_i$ is the access time of level

Backlinks2

221104 Translation Look-aside Buffers

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L_i

L_{i}

R_i

is the burst rate per word of level

L_i

(after startup access time)

B

is the block size

$T_\text{average}$ with $L_1$ cache

Then there are two possible cases.

We have a hit and only pay $L_1$ cache time.
We miss and read the whole block to $L_1$

Therefore, Average Access Time $T_\text{average}$ is (Hit Time) $T_1$ + (Miss Ratio) $(1-H_1)$ × (Miss Penalty) $(T_\text{main memory} + B \times R_\text{main memory})$

T_\text{average} =T_1 + (1-H_1) \times [T_\text{main memory} + B \times R_\text{main memory}]

$T_\text{average}$ with $L_2$ cache

Hit at $L_1$ cache
Hit at $L_2$ cache
We miss and read the whole block from memory

Similarly,

T_\text{average} =T_1 + (1-H_1) \times H_2 \times [T_2 + B \times R_2] + (1-H_1) \times (1-H_2) \times [T_2 + T_\text{main memory} + B \times R_\text{main memory}]

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Cache Average Access Time

TaverageT_\text{average}Taverage​ with L1L_1L1​ cache

TaverageT_\text{average}Taverage​ with L2L_2L2​ cache

$T_\text{average}$ with $L_1$ cache

$T_\text{average}$ with $L_2$ cache