GATE CS 2018 Q.20 (CS Q.10): Memory Management and Virtual Memory

Consider a process executing on an operating system that uses demand paging. The average time for a memory access in the system is M units if the corresponding memory page is available in memory, and D units if the memory access causes a page fault. It has been experimentally measured that the average time taken for a memory access in the process is X units.

Which one of the following is the correct expression for the page fault rate experienced by the process?

(D - M) / (X - M)

(X - M) / (D - M)

(D - X) / (D - M)

(X - M) / (D - X)

Official answer and solution

Official answer: B
From: Official GATE 2018 answer key

Solution

Express effective memory access time as a weighted average and solve for page fault rate.

Let $p$ denote the page fault rate. Then $1 - p$ is the probability that a memory access hits in memory without a fault.

The expected access time $X$ is given by:

X = (1 - p)M + pD

Expand and rearrange:

X = M - pM + pD = M + p(D - M)

X - M = p(D - M)

p = \frac{X - M}{D - M}

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2018 Computer Science and Information Technology (CS)
Question: 20 of 65, printed as CS Q.10
Section: Computer Science and Information Technology

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