GATE CS 2020 Q53 — Memory Management and Virtual Memory

To find the Average Memory Access Time ($\text{AMAT}$), we analyze the two primary cases based on the $\text{TLB}$ hit ratio ($h = 0.95$):

1. Case 1: TLB Hit (Probability = $0.95$)
   The translation is found in the $\text{TLB}$, and then the main memory is accessed for the data.
   $$\text{Time}_{\text{hit}} = T_{\text{tlb}} + T_m = 20 + 100 = 120\text{ ns}$$
2. Case 2: TLB Miss (Probability = $0.05$)
   The page table in main memory must be accessed first ($T_{\text{tlb}} + T_m = 120\text{ ns}$). Then, we check if the page is present in main memory:
   • Page Hit (Probability = $0.90$): The page is in memory. We access the data directly.
     $$\text{Time}_{\text{miss, hit}} = (T_{\text{tlb}} + T_m) + T_m = 120 + 100 = 220\text{ ns}$$
   • Page Fault (Probability = $0.10$): The page must be fetched from disk.
     • With $20\%$ probability, a dirty page is written back and the new page is read: $5000 + 5000 = 10000\text{ ns}$.
     • With $80\%$ probability, only the new page is read: $5000\text{ ns}$.
     • Average Page Fault Service Time ($T_{pf}$) = $0.20 \times 10000 + 0.80 \times 5000 = 6000\text{ ns}$.
     After servicing the fault, the data is accessed in memory ($T_m = 100\text{ ns}$).
     $$\text{Time}_{\text{miss, fault}} = (T_{\text{tlb}} + T_m) + T_{pf} + T_m = 120 + 6000 + 100 = 6220\text{ ns}$$
   $$\text{Average Time}_{\text{miss}} = 0.90 \times 220 + 0.10 \times 6220 = 198 + 622 = 820\text{ ns}$$

Now, we calculate the overall $\text{AMAT}$:

Thus, the average memory access time is 155 ns (which lies in the range 155 to 156).