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Consider the virtual page reference string
1, 2, 3, 2, 4, 1, 3, 2, 4, 1
on a demand paged virtual memory system running on a computer system that has main memory
size of 3 page frames which are initially empty. Let LRU, FIFO and OPTIMAL denote the number
of page faults under the corresponding page replacement policy. Then
  • a)
    OPTIMAL < LRU < FIFO
  • b)
    OPTIMAL < FIFO < LRU
  • c)
    OPTIMAL = LRU
  • d)
    OPTIMAL = FIFO
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Consider the virtual page reference string1, 2, 3, 2, 4, 1, 3, 2, 4, 1...
FIFO
1 1 1 4 4 4
2 2 2 1 1
3 3 3 2                           → (6) faults
Optimal
1 1 1 1 1
2 2 4 4
3 3 2                               → (5) faults
LRU
1 1 1 4 4 4 2 2 2
2 2 2 2 3 3 3 1
3 3 1 1 1 4 4                    → (9) faults
Optimal < FIFO < LRU
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Most Upvoted Answer
Consider the virtual page reference string1, 2, 3, 2, 4, 1, 3, 2, 4, 1...
The OPTIMAL page replacement policy selects the page that will not be used for the longest period of time in the future. To determine the number of page faults under OPTIMAL, we need to analyze the page reference string and determine which pages will be needed in the future.

The page reference string is:
1, 2, 3, 2, 4, 1, 3, 2, 4, 1

Initially, all page frames are empty. Let's analyze the page reference string step by step:

1. Page 1 is referenced. It is not in memory, so a page fault occurs. The page frame is filled with page 1.

2. Page 2 is referenced. It is not in memory, so a page fault occurs. The page frame is filled with page 2.

3. Page 3 is referenced. It is not in memory, so a page fault occurs. The page frame is filled with page 3.

4. Page 2 is referenced again. It is already in memory, so no page fault occurs.

5. Page 4 is referenced. It is not in memory, so a page fault occurs. The page frame is filled with page 4.

6. Page 1 is referenced again. It is already in memory, so no page fault occurs.

7. Page 3 is referenced again. It is already in memory, so no page fault occurs.

8. Page 2 is referenced again. It is already in memory, so no page fault occurs.

9. Page 4 is referenced again. It is already in memory, so no page fault occurs.

10. Page 1 is referenced again. It is already in memory, so no page fault occurs.

In total, there are 3 page faults under the OPTIMAL page replacement policy.
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Consider the virtual page reference string1, 2, 3, 2, 4, 1, 3, 2, 4, 1on a demand paged virtual memory system running on a computer system that has main memorysize of 3 page frames which are initially empty. Let LRU, FIFO and OPTIMAL denote the numberof page faults under the corresponding page replacement policy. Thena)OPTIMAL < LRU < FIFOb)OPTIMAL < FIFO < LRUc)OPTIMAL = LRUd)OPTIMAL = FIFOCorrect answer is option 'B'. Can you explain this answer?
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