GATE CS 2014 Set 3 Q33 — Memory Management and Virtual Memory

To find the effective memory access time (EMAT), we analyze the two possible scenarios based on the TLB hit ratio:

• TLB Hit (Probability $h = 0.6$):
  The TLB is searched first, and the physical address translation is found. Then, physical memory is accessed to retrieve the data.
  $\text{Time} = t_{TLB} + t_m = 10\text{ ms} + 80\text{ ms} = 90\text{ ms}$
• TLB Miss (Probability $1 - h = 0.4$):
  The TLB is searched first and results in a miss. Then, the page table in physical memory is accessed to get the frame number, followed by a second physical memory access to retrieve the actual data.
  $\text{Time} = t_{TLB} + 2 \times t_m = 10\text{ ms} + 2 \times 80\text{ ms} = 170\text{ ms}$

Using these values, we calculate the Effective Memory Access Time (EMAT):

$$\text{EMAT} = h \times (t_{TLB} + t_m) + (1 - h) \times (t_{TLB} + 2 \times t_m)$$

Substituting the given values:

$$\text{EMAT} = 0.6 \times 90 + 0.4 \times 170$$

$$\text{EMAT} = 54 + 68 = 122\text{ ms}$$

Thus, the effective memory access time is 122 milliseconds.