# AMAT using Local miss rate, global miss rate, local hit rate, global hit rate

Consider the following scenario as shown in image:

I have summarized the above Memory layout in terms of Miss rates and hit rates:

.---.----------------.------------.------------.------------.--------.
|   |                |     0      |     1      |     2      |   3    |
:---+----------------+------------+------------+------------+--------:
|   |                | LMR        | GMR        | LHR        | GHR    |
:---+----------------+------------+------------+------------+--------:
| 0 | L1 cache       | 10/100     | 10/100     | 90/100     | 90/100 |
:---+----------------+------------+------------+------------+--------:
| 1 | L2 cache       | 3/10       | 3/100      | 7/10       | 7/100  |
:---+----------------+------------+------------+------------+--------:
| 2 | Main Memory    | 0/3        | 0/100      | 3/3        | 3/100  |
:---+----------------+------------+------------+------------+--------:
| 3 | Sum of columns | Not useful | Not useful | Not useful | 1      |
'---'----------------'------------'------------'------------'--------'


Here LMR - local miss rate, GMR - global miss rate, LHR - local hit rate, GHR - global hit rate. From the above table I deduced the following insights:

1. Sum of the Global Hit rates (GHR) of all caches and Main Memory is 1.
2. The formula for AMAT(Average Memory Access Time) can be interpreted as follows:

AMAT = t1 + m1t2 + m1m2t3

(or)

AMAT = t1 + M1t2 + M2t3

. where m1,m2 are local miss rates of Level 1 and Level 2 caches respectively. M1,M2 are global miss rates of Level 1 and Level 2 caches respectively. t1, t2, t3 are access times for level 1 cache, level 2 cache and Main Memory. For the given example,

AMAT = t1 + 10/100t2 + 3/100t3

1. From point 2 it can be said that

M1 = m1; M2 = m1*m2; and so on

1. Local Hit rate of Main Memory (or final level cache) is always 1. Here it is assumed that required word is surely found in Main Memory ( or final level cache).
• Local Hit rate of level 1 cache = Global Hit rate of level 1 cache.

• Local Miss rate of level 1 cache = Global Miss rate of level 1 cache.

Now my question is "Are these points correct?". I did not find any information relevant to the above points. Also are there any more insights I can get from the table? Like relation between GHR and lmr, lhr.