Consider a demand paging system with four page frames (initially empty) and LRU page replacement policy. For the following page reference string $$7, 2, 7, 3, 2, 5, 3, 4, 6, 7, 7, 1, 5, 6, 1$$ the page fault rate, defined as the ratio of number of page faults to the number of memory accesses (rounded off to one decimal place) is ________.

We simulate the LRU replacement policy with 4 page frames for the reference string of length 15:

1. Ref 7: Page Fault (PF 1), Frames: $[7]$

2. Ref 2: Page Fault (PF 2), Frames: $[7, 2]$

3. Ref 7: Hit, Frames: $[2, 7]$

4. Ref 3: Page Fault (PF 3), Frames: $[2, 7, 3]$

5. Ref 2: Hit, Frames: $[7, 3, 2]$

6. Ref 5: Page Fault (PF 4), Frames: $[7, 3, 2, 5]$

7. Ref 3: Hit, Frames: $[7, 2, 5, 3]$

8. Ref 4: Page Fault (PF 5), Evict 7 (LRU), Frames: $[2, 5, 3, 4]$

9. Ref 6: Page Fault (PF 6), Evict 2 (LRU), Frames: $[5, 3, 4, 6]$

10. Ref 7: Page Fault (PF 7), Evict 5 (LRU), Frames: $[3, 4, 6, 7]$

11. Ref 7: Hit, Frames: $[3, 4, 6, 7]$

12. Ref 1: Page Fault (PF 8), Evict 3 (LRU), Frames: $[4, 6, 7, 1]$

13. Ref 5: Page Fault (PF 9), Evict 4 (LRU), Frames: $[6, 7, 1, 5]$

14. Ref 6: Hit, Frames: $[7, 1, 5, 6]$

15. Ref 1: Hit, Frames: $[7, 5, 6, 1]$

• Total memory accesses = $15$

• Total page faults = $9$