1

Virtual Memory (b)

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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. Read the desired page into the (newly) free frame. Update the page and frame tables.

4. Restart the process.

3

Page Replacement

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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.

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Graph of Page Faults Versus The Number of Frames

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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

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

44 3

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FIFO Page Replacement

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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?

Replacement Algorithms

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FIFO Illustrating Belady’s Anomaly

What is going on here?Belady’s Anomaly

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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

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Optimal Page Replacement

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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

2

3

5

4

4 3

5

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LRU Page Replacement

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LRU Algorithm (Cont.)

Stack implementation – keep a stack of page numbers in a double link form: Page referenced:

move it to the toprequires 6 pointers to be changed

No search for replacement

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Use Of A Stack to Record The Most Recent Page References

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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.

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Second-Chance (clock) Page-Replacement Algorithm

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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

Clock Algorithm

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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

Clock Algorithm

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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.

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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

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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.

mSs

pa

m

sS

ps

iii

i

ii

for allocation

frames of number total

process of size

5964137

127

564137

10

127

10

64

2

1

2

1

a

a

s

s

m

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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.

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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.

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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.

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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

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Locality In A Memory-Reference Pattern

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Working Set of a Process

Time, t

W(t, x)

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.

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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.

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Working-set model

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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.

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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?

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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.

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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.

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Other Considerations

Prepaging

Page size selection fragmentation table size I/O overhead locality

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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.

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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.

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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

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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.

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

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Operating System Examples

Unix SVR4 Solaris 2 Linux Win 2K Windows NT

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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?

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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

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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 basedon free memory

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SVR4 Kernel Allocation Used for structures < size of a page Lazy buddy system

Don’t split/coalesce blocks as oftenFrequently 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

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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.

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Solar Page Scanner

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Linux Memory Management Virtual Memory Addressing

Supports 3-level page tablesPage Directory - One page in size (must be in

memory)Page Middle Directory - Can span multiple

pages, Will have size=1 on PentiumPage Table - Points to individual pages

Page Allocation Uses a buddy system with 1-32 page block

sizes

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Linux Memory Management Page Replacement

Based on clock algorithm Uses age variable

Incremented when page is accessedDecremented as it scans memoryWhen 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

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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)

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W2k Resident Set Management Uses variable allocation, local scope When a page fault occurs, a page is selected

from the local set of pages If main memory is plentiful, allow the resident

set to grow as pages are brought into memory

If main memory is scarce, remove less recently accessed pages from the resident set

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W2k Paging Page Faults

Page marked as not present CPU (H/W) determines page isn’t in memory Interrupts the program, starts O.S. page fault handler O.S. verifies the reference is valid but not in memory

(Otherwise reports illegal address) Swap out a page if needed Read referenced page from disk Update page table entry Resume interrupted process (or switch to another

process) Page Size

Smaller has more frames, less internal fragmentation, but larger tables

Common sizes: Table 8.2, page 348

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Windows NT

Uses demand paging with clustering. Clustering brings in pages surrounding the faulting page.

Processes are assigned working set minimum and working set maximum.

Working set minimum is the minimum number of pages the process is guaranteed to have in memory.

A process may be assigned as many pages up to its working set maximum.

When the amount of free memory in the system falls below a threshold, automatic working set trimming is performed to restore the amount of free memory.

Working set trimming removes pages from processes that have pages in excess of their working set minimum.