Consider the following page-reference string:1, 2, 3, 4, 2, 1, 5, 6, 2, 1, 2, 3, 7, 6, 3, 2, 1, 2, 3, 6How many page faults would occur for the following replacement algorithms, assuming three frames? Remember all frames are initially empty. A. FIFO replacement b. LRU replacement c. Optimal Mention the merits and demerits of each of the above algorithms.

Let’s analyze each replacement algorithm for the given page-reference string:

FIFO (First In, First Out):

FIFO replacement algorithm replaces the oldest page in the memory. It doesn’t consider how frequently or recently a page was accessed.

Page Faults:

1. 1, 2, 3 -> (Page Fault)
2. 4 -> (Page Fault)
3. 2 -> (Page Fault)
4. 1 -> (Page Fault)
5. 5 -> (Page Fault)
6. 6 -> (Page Fault)
7. 2 (Page already in memory)
8. 1 (Page already in memory)
9. 2 (Page already in memory)
10. 3 (Page Fault)
11. 7 -> (Page Fault)

Total Page Faults: 7

Merits:

• Simple to implement.
• Performs well for real-time systems where predictability is more important than optimization.

Demerits:

• May not always result in the minimum number of page faults.
• Doesn’t consider the frequency or recency of page accesses.

LRU (Least Recently Used):

LRU replacement algorithm replaces the page that has not been used for the longest period of time.

Page Faults:

1. 1, 2, 3 -> (Page Fault)
2. 4 -> (Page Fault)
3. 2 -> (Page Fault)
4. 1 -> (Page Fault)
5. 5 -> (Page Fault)
6. 6 -> (Page Fault)
7. 2 (Page already in memory)
8. 1 (Page already in memory)
9. 2 (Page already in memory)
10. 3 (Page Fault)
11. 7 -> (Page Fault)

Total Page Faults: 7

Merits:

• Guarantees optimal page replacement in theory.
• Better performance than FIFO in most cases.

Demerits:

• Complex to implement efficiently.
• Requires additional bookkeeping to track the recency of page accesses.
• Can suffer from “thrashing” when implemented inefficiently.

Optimal:

The Optimal replacement algorithm replaces the page that will not be used for the longest period of time in the future. This algorithm is theoretical because it’s not possible to know future page accesses.

Page Faults:

1. 1, 2, 3 -> (Page Fault)
2. 4 -> (Page Fault)
3. 2 -> (Page Fault)
4. 1 -> (Page Fault)
5. 5 -> (Page Fault)
6. 6 -> (Page Fault)
7. 2 (Page already in memory)
8. 1 (Page already in memory)
9. 2 (Page already in memory)
10. 3 (Page Fault)
11. 7 -> (Page Fault)

Total Page Faults: 7

Merits:

• Theoretically provides the minimum number of page faults.
• Useful for benchmarking other algorithms.

Demerits:

• Impossible to implement in practice since future page accesses are unknown.
• Often used as a benchmark for comparison rather than practical implementation.

In this particular example, all three algorithms resulted in the same number of page faults, but in other cases, they may differ.