Virtual Memory and Page Replacement Algorithms

1. Virtual Memory (b)

2. Basic Page Replacement • Find the location of the desired page on disk. • 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. • Read the desired page into the (newly) free frame. Update the page and frame tables. • Restart the process.

3. Page Replacement

4. 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.

5. Graph of Page Faults Versus The Number of Frames

6. 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 1 1 4 5 2 2 1 3 9 page faults 3 3 2 4 1 1 5 4 2 2 1 10 page faults 5 3 3 2 4 4 3

7. FIFO Page Replacement

8. Replacement Algorithms FIFO page replacement • Assign time stamp with each page • time created • Replace oldest page • Advantages • easy • Disadvantages • could replace frequently used page • Can we improve the performance by adding more frames? • FIFO Replacement – Belady’s Anomaly • more frames  less page faults?

9. FIFO Illustrating Belady’s Anomaly What is going on here? Belady’s Anomaly

10. 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 4 2 6 page faults 3 4 5

11. Optimal Page Replacement

12. 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. 1 5 2 3 5 4 4 3

13. LRU Page Replacement

14. LRU Algorithm (Cont.) • Stack implementation – keep a stack of page numbers in a double link form: • Page referenced: • move it to the top • requires 6 pointers to be changed • No search for replacement

15. Use Of A Stack to Record The Most Recent Page References

16. LRU Approximation Algorithms • 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.

17. Second-Chance (clock) Page-Replacement Algorithm

18. Clock Algorithm Clock Algorithm Enhancements • Consider reference bit and dirty bit • 4 possible cases • (0,0) neither modified or referenced • (0,1) not recently used but modified • (1,0) recently used but clean • (1,1) recently used and modified • Still use “clock algorithm” • clear only reference bit upon consideration • Macintosh uses this scheme

19. Clock Algorithm Clock Algorithm Enhancements • Add additional reference bits • At regular intervals • record the reference bits • clear the reference bits • Record the reference bits in a shift register • 8 bits • shift in the new reference bit value • Replace page with lowest reference value

20. 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.

21. Allocation of Frames • Each process needs minimum number of pages. • Example: IBM 370 – 6 pages to handle SS MOVE instruction: • instruction is 6 bytes, might span 2 pages. • 2 pages to handle from. • 2 pages to handle to. • Two major allocation schemes. • fixed allocation • priority allocation

22. Fixed Allocation • Equal allocation – e.g., if 100 frames and 5 processes, give each 20 pages. • Proportional allocation – Allocate according to the size of process.

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

24. 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.

25. 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.

26. Thrashing • Why does paging work?Locality model • Process migrates from one locality to another. • Localities may overlap. • Why does thrashing occur? size of locality > total memory size

27. Locality In A Memory-Reference Pattern

28. Working Set of a Process • W(t, x): The set of pages accessed over the last x instructions at time t. • Principle of locality ensures that the working set changes slowly.

29. Working-Set Model •   working-set window  a fixed number of page references Example: 10,000 instruction • WSSi (working set of Process Pi) =total number of pages referenced in the most recent  (varies in time) • if  too small will not encompass entire locality. • if  too large will encompass several localities. • if  =   will encompass entire program. • D =  WSSi  total demand frames • if D > m  Thrashing • Policy if D > m, then suspend one of the processes.

30. Working-set model

31. Working Sets • Processes go through phases • Stable  stays within stable working set • Transient  working set is rapidly changing • A study in 1971 revealed • Stable phases account for ~ 98% of time • Half of the page faults occur during other 2% • Fault rates during transitions were 100 to 1000 times higher than during stable phases • Stable phases were relatively insensitive to the time delta chosen.

32. Working Set Policy • Working set Policy • Compute working set size for all processes • Only admit a process if total working set size leaves free frames • Don’t allow a working set page to be replaced • When a process is blocked (I/O, etc.) • Prepage in its working set upon return. • How do we keep track of working set?

33. 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.

34. Page-Fault Frequency Scheme • Establish “acceptable” page-fault rate. • If actual rate too low, process loses frame. • If actual rate too high, process gains frame.

35. Other Considerations • Prepaging • Page size selection • fragmentation • table size • I/O overhead • locality

36. Other Considerations (Cont.) • TLB Reach - The amount of memory accessible from the TLB. • TLB Reach = (TLB Size) X (Page Size) • Ideally, the working set of each process is stored in the TLB. Otherwise there is a high degree of page faults.

37. Increasing the Size of the TLB • Increase the Page Size. This may lead to an increase in fragmentation as not all applications require a large page size. • Provide Multiple Page Sizes. This allows applications that require larger page sizes the opportunity to use them without an increase in fragmentation.

38. Other Considerations (Cont.) • Program structure • int A[][] = new int[1024][1024]; • Each row is stored in one page • Program 1 for (j = 0; j < A.length; j++) for (i = 0; i < A.length; i++) A[i,j] = 0;1024 x 1024 page faults • Program 2 for (i = 0; i < A.length; i++) for (j = 0; j < A.length; j++) A[i,j] = 0; 1024 page faults

39. Other Considerations (Cont.) • I/O Interlock– Pages must sometimes be locked into memory. • Consider I/O. Pages that are used for copying a file from a device must be locked from being selected for eviction by a page replacement algorithm.

40. Reason Why Frames Used For I/O Must Be In Memory

41. Operating System Examples • Unix SVR4 • Solaris 2 • Linux • Win 2K • Windows NT

42. Memory Management • Two separate memory management schemes in Unix SVR4 and Solaris • Paging System – Allocate page frames • Kernel Memory Allocator – Allocate memory for the kernel • Paging System Data Structures • Page Table – One entry for each page of virtual memory for that process • Page Frame Number – physical frame # • Age – how long in memory w/o reference • Copy on Write – 2 processes sharing page: after fork(), waiting for exec() • Modify – page modified? • Reference – set when page accessed • Valid – page is in main memory • Protect – are we allowed to write to this page?

43. Paging Data Structures • Disk Block Descriptor • Swap Device Number – Logical device • Device Block Number – Block location • Type of storage – Swap or executable • Page Frame Data Table • Page State – Available, in use, in executable, in transfer • Reference Count – # processes using page • Logical Device – Device holding copy • Block Number – Location on device • Pfdata pointer – For linked list of pages • Swap-use Table • Reference Count – # references to page on a storage device • Page/storage unit number – Page ID

44. SVR4 Page Replacement • Clock algorithm variant (Fig 8.23) • Fronthand– Clear Use bits • Backhand– Check Use bits, if use=0 prepare to swap page out • Scanrate– How fast hands move • Faster rate frees pages faster • Handspread– Gap between hands • Smaller gap frees pages faster • System adjusts values based on free memory

45. SVR4 Kernel Allocation • Used for structures < size of a page • Lazy buddy system • Don’t split/coalesce blocks as often • Frequently allocate/release memory, but the amount of blocks is use tends to remain steady • Locally free – Not coalesced • Globally free – Coalesce if possible • Want: # locally free £ # in use

46. Solaris 2 • Maintains a list of free pages to assign faulting processes. • Lotsfree– threshold parameter to begin paging. • Paging is peformed by pageout process. • Pageout scans pages using modified clock algorithm. • Scanrate is the rate at which pages are scanned. This ranged from slowscan to fastscan. • Pageout is called more frequently depending upon the amount of free memory available.

47. Solar Page Scanner

48. Linux Memory Management • Virtual Memory Addressing • Supports 3-level page tables • Page Directory - One page in size (must be in memory) • Page Middle Directory - Can span multiple pages, Will have size=1 on Pentium • Page Table - Points to individual pages • Page Allocation • Uses a buddy system with 1-32 page block sizes

49. Linux Memory Management • Page Replacement • Based on clock algorithm • Uses age variable • Incremented when page is accessed • Decremented as it scans memory • When age=0, page may be replaced • Has effect of least frequently used method • Kernel Memory Allocation • Uses scheme called slab allocation • Blocks of size 32 through 4080 bytes

50. Win 2K Memory Management • Virtual Address Map • 00000000 to 00000FFF – Reserved (Catch NULL pointers) • 00001000 to 7FFFEFFF – User space • 7FFFEFFF to 7FFFFFFF – Reserved (Catch wild pointers) • 80000000 to FFFFFFFF – System • Page States • Available – Not currently used • Reserved – Set aside, but not counted against memory quota (not in use) • No disk swap space allocated yet • Process can declare memory that can be quickly allocated when it is needed • Committed: space set aside in paging file (in use)