GATE CS 2011 Q20 — Memory Management and Virtual Memory

The effective memory access time ($EAT$) in a demand-paging system is calculated using the formula:

Where:

• $p$ is the page fault rate (probability of a page fault).
• $T_m$ is the memory access time when no page fault occurs.
• $T_{pf}$ is the page fault service time.

Step-by-step Calculation:

1. Identify the given values and unify the units to nanoseconds ($\text{ns}$):
   • Memory access time ($T_m$) = $20\text{ ns}$
   • Page fault service time ($T_{pf}$) = $10\text{ ms} = 10 \times 10^6\text{ ns} = 10^7\text{ ns}$
   • Page fault rate ($p$) = $\frac{1}{10^6} = 10^{-6}$
2. Substitute the values into the formula: $$EAT = (1 - 10^{-6}) \times 20\text{ ns} + 10^{-6} \times 10^7\text{ ns}$$
3. Simplify the expression: $$EAT = \left(20 - 20 \times 10^{-6}\right)\text{ ns} + 10\text{ ns}$$ $$EAT = 20\text{ ns} - 0.00002\text{ ns} + 10\text{ ns}$$ $$EAT = 29.99998\text{ ns} \approx 30\text{ ns}$$

Thus, the effective memory access time is approximately $30\text{ ns}$.