GATE CS 2015 Set 1 Q.57 (CS Q.47): Memory Management and Virtual Memory

Consider a main memory with five page frames and the following sequence of page references: $3, 8, 2, 3, 9, 1, 6, 3, 8, 9, 3, 6, 2, 1, 3$ . Which one of the following is true with respect to page replacement policies First In First Out (FIFO) and Least Recently Used (LRU)?

Both incur the same number of page faults

FIFO incurs 2 more page faults than LRU

LRU incurs 2 more page faults than FIFO

FIFO incurs 1 more page faults than LRU

Official answer and solution

Official answer: A
From: Official GATE 2015 answer key

Solution

Simulate FIFO and LRU page replacement policies step by step over the 15-page reference string with 5 frames.

Given 5 frames and page references: $3, 8, 2, 3, 9, 1, 6, 3, 8, 9, 3, 6, 2, 1, 3$ .

FIFO Simulation:
- Ref 3: [3] -> Fault 1
- Ref 8: [3, 8] -> Fault 2
- Ref 2: [3, 8, 2] -> Fault 3
- Ref 3: [3, 8, 2] -> Hit
- Ref 9: [3, 8, 2, 9] -> Fault 4
- Ref 1: [3, 8, 2, 9, 1] -> Fault 5 (frames full)
- Ref 6: Replace oldest (3) -> [6, 8, 2, 9, 1] -> Fault 6
- Ref 3: Replace oldest (8) -> [6, 3, 2, 9, 1] -> Fault 7
- Ref 8: Replace oldest (2) -> [6, 3, 8, 9, 1] -> Fault 8
- Ref 9: Hit
- Ref 3: Hit
- Ref 6: Hit
- Ref 2: Replace oldest (9) -> [6, 3, 8, 2, 1] -> Fault 9
- Ref 1: Hit
- Ref 3: Hit
  Total FIFO faults = $9$ .
LRU Simulation:
- Ref 3: [3] -> Fault 1
- Ref 8: [3, 8] -> Fault 2
- Ref 2: [3, 8, 2] -> Fault 3
- Ref 3: [8, 2, 3] -> Hit
- Ref 9: [8, 2, 3, 9] -> Fault 4
- Ref 1: [8, 2, 3, 9, 1] -> Fault 5
- Ref 6: LRU is 8, replace with 6 -> [2, 3, 9, 1, 6] -> Fault 6
- Ref 3: [2, 9, 1, 6, 3] -> Hit
- Ref 8: LRU is 2, replace with 8 -> [9, 1, 6, 3, 8] -> Fault 7
- Ref 9: [1, 6, 3, 8, 9] -> Hit
- Ref 3: [1, 6, 8, 9, 3] -> Hit
- Ref 6: [1, 8, 9, 3, 6] -> Hit
- Ref 2: LRU is 1, replace with 2 -> [8, 9, 3, 6, 2] -> Fault 8
- Ref 1: LRU is 8, replace with 1 -> [9, 3, 6, 2, 1] -> Fault 9
- Ref 3: [9, 6, 2, 1, 3] -> Hit
  Total LRU faults = $9$ .

Both policies incur the same number of page faults ( $9$ ). This corresponds to option A.

Final answer

Common trap

Assuming LRU must strictly outperform FIFO on any reference sequence.

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

Source

Paper: GATE 2015 Computer Science and Information Technology (CS) Session 1
Question: 57 of 65, printed as CS Q.47
Section: Computer Science and Information Technology

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