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In a two-level virtual memory, the memory access time for main memory, $t_M=10^{−8}$ sec, and the memory access time for the secondary memory, $t_D=10^{−3}$ sec. What must be the hit ratio, $H$ such that the access efficiency is within $80$ percent of its maximum value? $\tag {GATE-CS-1990}$

I came across the problem above. I have read textbooks on operating systems like Operating Systems Concepts by Galvin et. al, Modern Operating Systems by Andrew S Tanenbaum. But while studying them, I never encountered the term "access efficiency". Hence I cannot possibly figure out how to proceed.

Here few of my peers tried to explain the thing based on their logic or intuition... But there is no formal support to their concept. Moreover I am not satisfied with what they actually say in the page.

All I could figure out from the problem is, if $h$ is the hit ratio, to find a page in the main memory, the estimated memory access time (EMAT) is:

$$\text{EMAT}= \text{2 memory access for two page table levels}\\ \text{ + 1 memory access for the page}+(1-h)[\text{Time to access secondary memory}]$$

$$\implies \text{EMAT}=3\times 10^{-8} s+ (1-h)\times{10^{-3}} s$$

if $h=1$ then the best EMAT is :

$$\text{EMAT}_\text{BEST}=3\times 10^{-8}s$$


After this I do not know how to proceed.

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  • $\begingroup$ Unfortunately I would assume that "access efficiency" means whatever the author wants it to mean. $\endgroup$
    – gnasher729
    Commented Jan 24, 2022 at 15:28
  • $\begingroup$ Please can you give more examples @gnasher729. Because this term as such I havn't encountered in any book. Is it a standard term? You say that "whatever the author wants to mean". Going by the literal meaning of the words I could say a statement : "We use cache in memory systems for access efficiency", with that being said, I would normally think of the statement in the "speedup" point of view, With cache, effective memory access time reduces compared to the situation when we have no cache in the system. But I am converting the statement to finding "speedup", $\endgroup$ Commented Jan 24, 2022 at 15:44
  • $\begingroup$ But what could be hardcore mathematics behind the term "access efficiency"? in general or in context to this question. Since you say that the author (here in case the question maker) could mean anything, how to possibly analyze what he is thinking... Please can you help me... By sharing whatever you know or feel regarding this... $\endgroup$ Commented Jan 24, 2022 at 15:46
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    $\begingroup$ Unfortunately, we don't know and we can't know what the author means. It's not a term that is well defined or that I have seen defined anywhere. $\endgroup$
    – gnasher729
    Commented Jan 24, 2022 at 17:12

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