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Effective Access Time using Hit ratio and Miss ratio

Before this read chapter please follow the previous chapter first:  Calculate Effective Access Time (EMAT)

The percentage of times that the required page number is found in the TLB is called the hit ratio.

For example, if we have 80% TLB hit ratio, for example, means that we find the desire page number in the TLB 80% percent of the time. And only one memory access is required.

If we fail to find the page number in the TLB, then we must first access memory for the page table and get the frame number and then access the desired byte in the memory. So, here we access memory two times.

So, the percentage of time to fail to find the page number in the TLB is called miss ratio.

So, if hit ratio = 80% then miss ratio=20%

To find the Effective Memory-Access Time (EMAT), we weight the case by its probability: We can write EMAT or EAT.

Where, 

Note: The above formula of EMAT is for single-level paging with TLB.

Effective Access time when multi-level paging is used:

In the case of the multi-level paging concept of TLB hit ratio and miss ratio are the same.

Where TLB hit ratio is same single level paging because here no need access any page table, we get page number directly from TLB.

But in case of TLB miss when the page number is not present at TLB, we have to access the page table and if it is a multi-level page table, we require to access multi-level page tables for the page number. 

So, how many times it requires to access the main memory for the page table depends on how many page tables we used. For each page table, we have to access one main memory reference. 

Let us use k-level paging i.e. k number of page tables are present, and then we have to access an additional k number of main memory access for the page table.

 [for any confusion about  (k x m + m) please follow: Problem of paging and solution]

Note: This two formula of EMAT (or EAT) is very important for examination.

EMAT for single-level paging with TLB hit and miss ratio:

We can write EMAT formula in another way:

Let, miss ratio = h, hit ration = (1 - h), memory access time = m and TLB access time = t.

So, we can write

Note: We can also use this formula to calculate EMAT but keep in your mind that here h is miss ratio.

EMAT for Multi-level paging with TLB hit and miss ratio:

Same way we can write EMAT formula for multi-level paging in another way:

Let, miss ratio = h, hit ration = (1 - h), memory access time = m, TLB access time = t and page-level = k.

So, we can write

Note: We can also use this formula to calculate EMAT but keep in your mind that here h is miss ratio.

Conclusion:

Effective memory Access Time (EMAT) for single level paging with TLB hit and miss ratio:

Or, 

EMAT for Multi level paging with TLB hit and miss ratio:

Or,