1. Operating Systems CMPSC 473 Virtual Memory Management (3) November 16 2010 – Lecture 20 Instructor: Bhuvan Urgaonkar

2. Exam 1 grades

3. Demand Paging Example Memory access time = 200 nanoseconds Average page-fault service time = 8 milliseconds EAT = (1 – p) x 200 + p (8 milliseconds) = (1 – p x 200 + p x 8,000,000 = 200 + p x 7,999,800 If one access out of 1,000 causes a page fault, then EAT = 8.2 microseconds. This is a slowdown by a factor of 40!!

4. What happens if there is no free frame? Page replacement – find some page in memory, but not really in use, swap it out –algorithm –performance – want an algorithm which will result in minimum number of page faults Same page may be brought into memory several times

5. Page Replacement Prevent over-allocation of memory by modifying page-fault service routine to include page replacement Use modify (dirty) bit to reduce overhead of page transfers – only modified pages are written to disk Page replacement completes separation between logical memory and physical memory – large virtual memory can be provided on a smaller physical memory

6. Need For Page Replacement OS

7. Basic Page Replacement 1. Find the location of the desired page on disk 2. Find a free frame: - If there is a free frame, use it - If there is no free frame, use a page replacement algorithm to select a victim frame 3. Bring the desired page into the (newly) free frame; update the page and frame tables 4. Restart the process

8. Page Replacement

9. Page Replacement Algorithms Want lowest page-fault rate Evaluate algorithm by running it on a particular string of memory references (reference string) and computing the number of page faults on that string In all our examples, the reference string is 1, 2, 3, 4, 1, 2, 5, 1, 2, 3, 4, 5

10. Graph of Page Faults Versus The Number of Frames

11. First-In-First-Out (FIFO) Algorithm Reference string: 1, 2, 3, 4, 1, 2, 5, 1, 2, 3, 4, 5 3 frames (3 pages can be in memory at a time per process) 4 frames Belady’s Anomaly: more frames cause more page faults!!! 1 2 3 1 2 3 4 1 2 5 3 4 9 page faults 1 2 3 1 2 3 5 1 2 4 5 10 page faults 4 43

12. FIFO Page Replacement

13. FIFO Illustrating Belady’s Anomaly

14. Optimal Algorithm Replace page that will not be used for longest period of time 4 frames example 1, 2, 3, 4, 1, 2, 5, 1, 2, 3, 4, 5 How do you know this? Used for measuring how well your algorithm performs 1 2 3 4 6 page faults 4 5

15. Optimal Page Replacement

16. Least Recently Used (LRU) Algorithm Reference string: 1, 2, 3, 4, 1, 2, 5, 1, 2, 3, 4, 5 Counter implementation –Every page entry has a counter; every time page is referenced through this entry, copy the clock into the counter –When a page needs to be changed, look at the counters to determine which are to change 5 2 4 3 1 2 3 4 1 2 5 4 1 2 5 3 1 2 4 3

17. LRU Page Replacement

18. LRU Algorithm (Cont.) Could keep pages in order –Priority queue: Update = O(log n), eviction = O(log n) Optimize for common case –Common case: hits, not misses! –Hash table Update = O(1), eviction = O(n)

19. Cost of Maintaining Exact LRU Hash tables: too expensive –On every reference: Compute hash of page address Update time stamp –Unfortunately: 10x - 100x more expensive!

20. Cost of Maintaining Exact LRU Alternative: doubly-linked lists –Move items to front when referened –LRU items at end of list –Still too expensive 4-6 pointer updates per reference Can we do better?

21. LRU Approximation Algorithms: Hardware Support Reference bit –With each page associate a bit, initially = 0 –When page is referenced bit set to 1 –Replace the one which is 0 (if one exists) We do not know the order, however Second chance –Need reference bit –Clock replacement –If page to be replaced (in clock order) has reference bit = 1 then: set reference bit 0 leave page in memory replace next page (in clock order), subject to same rules

22. Hardware Support Maintain reference bits for every page –On each access, set reference bit to 1 –Page replacement algorithm periodically resets reference bits A0A0 B0B0 C0C0 A, B, C, B, C, C, D Reset reference bits

23. Hardware Support Maintain reference bits for every page –On each access, set reference bit to 1 –Page replacement algorithm periodically resets reference bits A0A0 B1B1 C0C0 A, B, C, B, C, C, D

24. Hardware Support Maintain reference bits for every page –On each access, set reference bit to 1 –Page replacement algorithm periodically resets reference bits A0A0 B1B1 C1C1 A, B, C, B, C, C, D

25. Hardware Support Maintain reference bits for every page –On each access, set reference bit to 1 –Page replacement algorithm periodically resets reference bits A0A0 B1B1 C1C1 A, B, C, B, C, C, D

26. Hardware Support Maintain reference bits for every page –On each access, set reference bit to 1 –Page replacement algorithm periodically resets reference bits –Evict page with reference bit = 0 D1D1 B1B1 C1C1 A, B, C, B, C, C, D Cost per miss = O(n)

27. The Clock Algorithm Variant of FIFO and LRU Keep frames in circle On page fault, OS: –Checks reference bit of next frame –If bit = 0, replace page, set bit to 1 –If bit = 1, set bit to 0, advance pointer to next frame A, B, C, D, B, C, E, F, C, G A1A1 C1C1 D1D1 B1B1

28. The Clock Algorithm Variant of FIFO and LRU Keep frames in circle On page fault, OS: –Checks reference bit of next frame –If bit = 0, replace page, set bit to 1 –If bit = 1, set bit to 0, advance pointer to next frame A, B, C, D, B, C, E, F, C, G A1A1 C1C1 D1D1 B1B1

29. The Clock Algorithm Variant of FIFO and LRU Keep frames in circle On page fault, OS: –Checks reference bit of next frame –If bit = 0, replace page, set bit to 1 –If bit = 1, set bit to 0, advance pointer to next frame A, B, C, D, B, C, E, F, C, G A1A1 C1C1 D1D1 B1B1

30. The Clock Algorithm Variant of FIFO and LRU Keep frames in circle On page fault, OS: –Checks reference bit of next frame –If bit = 0, replace page, set bit to 1 –If bit = 1, set bit to 0, advance pointer to next frame A, B, C, D, B, C, E, F, C, G A0A0 C1C1 D1D1 B1B1

31. The Clock Algorithm Variant of FIFO and LRU Keep frames in circle On page fault, OS: –Checks reference bit of next frame –If bit = 0, replace page, set bit to 1 –If bit = 1, set bit to 0, advance pointer to next frame A, B, C, D, B, C, E, F, C, G A0A0 C1C1 D1D1 B1B1

32. The Clock Algorithm Variant of FIFO and LRU Keep frames in circle On page fault, OS: –Checks reference bit of next frame –If bit = 0, replace page, set bit to 1 –If bit = 1, set bit to 0, advance pointer to next frame A, B, C, D, B, C, E, F, C, G A0A0 C1C1 D1D1 B0B0

33. The Clock Algorithm Variant of FIFO and LRU Keep frames in circle On page fault, OS: –Checks reference bit of next frame –If bit = 0, replace page, set bit to 1 –If bit = 1, set bit to 0, advance pointer to next frame A, B, C, D, B, C, E, F, C, G A0A0 C1C1 D1D1 B0B0

34. The Clock Algorithm Variant of FIFO and LRU Keep frames in circle On page fault, OS: –Checks reference bit of next frame –If bit = 0, replace page, set bit to 1 –If bit = 1, set bit to 0, advance pointer to next frame A, B, C, D, B, C, E, F, C, G A0A0 C0C0 D0D0 B0B0

35. The Clock Algorithm Variant of FIFO and LRU Keep frames in circle On page fault, OS: –Checks reference bit of next frame –If bit = 0, replace page, set bit to 1 –If bit = 1, set bit to 0, advance pointer to next frame A, B, C, D, B, C, E, F, C, G E1E1 C0C0 D0D0 B0B0

36. The Clock Algorithm Variant of FIFO and LRU Keep frames in circle On page fault, OS: –Checks reference bit of next frame –If bit = 0, replace page, set bit to 1 –If bit = 1, set bit to 0, advance pointer to next frame A, B, C, D, B, C, E, F, C, G E0E0 C0C0 D0D0 F1F1

37. The Clock Algorithm Variant of FIFO and LRU Keep frames in circle On page fault, OS: –Checks reference bit of next frame –If bit = 0, replace page, set bit to 1 –If bit = 1, set bit to 0, advance pointer to next frame A, B, C, D, B, C, E, F, C, G E0E0 C1C1 D0D0 F0F0

38. The Clock Algorithm Variant of FIFO and LRU Keep frames in circle On page fault, OS: –Checks reference bit of next frame –If bit = 0, replace page, set bit to 1 –If bit = 1, set bit to 0, advance pointer to next frame A, B, C, D, B, C, E, F, C, G E0E0 C0C0 D0D0 F0F0

39. The Clock Algorithm Variant of FIFO and LRU Keep frames in circle On page fault, OS: –Checks reference bit of next frame –If bit = 0, replace page, set bit to 1 –If bit = 1, set bit to 0, advance pointer to next frame A, B, C, D, B, C, E, F, C, G E0E0 C0C0 G1G1 F0F0

40. Segmented Queue Real systems: segment queue into two parts –Approximate for frequently-referenced pages E.g., first 1/3 page frames - fast –Exact LRU for infrequently-referenced pages How do we move between segments?

41. Counting Algorithms Keep a counter of the number of references that have been made to each page LFU Algorithm: replaces page with smallest count MFU Algorithm: based on the argument that the page with the smallest count was probably just brought in and has yet to be used

42. Fixed Allocation Equal allocation – For example, if there are 100 frames and 5 processes, give each process 20 frames. Proportional allocation – Allocate according to the size of process

43. Priority Allocation Use a proportional allocation scheme using priorities rather than size If process P i generates a page fault, –select for replacement one of its frames –select for replacement a frame from a process with lower priority number

44. Global vs. Local Allocation Global replacement – process selects a replacement frame from the set of all frames; one process can take a frame from another Local replacement – each process selects from only its own set of allocated frames

45. Thrashing If a process does not have “enough” pages, the page-fault rate is very high. This leads to: –low CPU utilization –operating system thinks that it needs to increase the degree of multiprogramming –another process added to the system Thrashing: a process is busy swapping pages in and out

46. Thrashing (Cont.)

47. Demand Paging and Thrashing Why does demand paging work? Locality model –Process migrates from one locality to another –Localities may overlap Why does thrashing occur?  size of locality > total memory size

48. Locality In A Memory-Reference Pattern

49. Working-set model

50. Keeping Track of the Working Set Approximate with interval timer + a reference bit Example: ∆ = 10,000 –Timer interrupts after every 5000 time units –Keep in memory 2 bits for each page –Whenever a timer interrupts copy and sets the values of all reference bits to 0 –If one of the bits in memory = 1 => page in working set Why is this not completely accurate? Improvement = 10 bits and interrupt every 1000 time units