4.4 Page replacement algorithms
Page replacement algorithms
Also seen in:CPU cacheWeb server cache of web pagesBuffered I/O (file) caches
Optimal page replacement
1. Page fault occurs.2. Scan all pages currently in memory.3. Determine which page won’t be needed
(referenced) until furthest in the future.4. Replace that page.
Not really possible. (But useful as a benchmark.)
Depends on code as well as data.
Algorithms we will discuss:
1. Optimal2. NRU3. FIFO4. Second chance5. Clock6. LRU7. NFU8. Aging9. Working set10. WSClock
NRU (not recently used)
Bits set by hardware after every memory reference
Cleared only by software (OS) R bits – set when page is referenced (read
or write) M bits – set when page is modified (written) Periodically (after k clock interrupts), R bits
are cleared
NRU page categories
1. Not referenced, not modified
2. Not referenced, modified (only occurs when #4’s R bit is cleared
during clock interrupt)
3. Referenced, not modified
4. Referenced, modified
NRU algorithm: remove random page from lowest numbered non empty category
NRU algorithm evaluation
Simple Efficient Not optimal but adequate
FIFO page replacement
Queue pages as they are requested. Remove page at head (front) of queue.
Oldest page is removed first
+ simple/efficient
- might remove a heavily used page
Second chance page replacement Inspect R bit of oldest page
Recall: R bits are set when page is referenced (read or write); periodically (after k clock interrupts), R bits are cleared.
If R==0 then• page is old & unused so replace it
Else• Clear R bit• Move page from head to tail of FIFO
• (treating it as a newly loaded page)
• Try a different page
Second chance page replacement load time
page
Clock page replacement
Circular list instead of queue Clock hand points to oldest page If (R==0) then
Page is unused so replace it Else
Clear RAdvance clock hand
(very similar to second chance – queue instead of list)
Clock page replacement
LRU (least recently used) page replacement A page recently used is likely to be used in
the near future. A page not used in ages is not likely to be
used in the near future. Algorithm:
“age” the pages• Maintain a queue of pages in memory.
• Recently used at front; oldest at rear.
• Every time a page is referenced, it is removed from the queue and placed at the front of the queue.
• This is slow!
LRU in hardware
Implementation #1:64 bit counter, C, incremented after
every instructionEach page also has a 64 bit counterWhen a page is referenced, C is
copied to its counter.Page with lowest counter is oldest.
LRU in hardware
Implementation #2:Given n page frames, let M be a nxn
matrix of bits initially all 0.Reference to page frame k occurs.Set all bits in row k of M to 1.Set all bits in column k of M to 0.Row with lowest binary value is least
recently used.
LRU in hardware: implementation #2 example
oldest
NFU (Not Frequently Used)
Hardware doesn’t often support LRU. Software counter associated w/ each
page initially set to 0. At each clock interrupt:
Add R bit (either 0 or 1) to the counter for each page.
Page with lowest counter is NFU.
NFU problem
It never forgets! So pages that were frequently referenced
(during initialization for example) but are no longer needed appear to be FU.
Solution (called “aging”): Shift all counters to right 1 bit before R bit is
added in. Then R bit is added to MSb (leftmost bit)
instead of LSb (rightmost bit). Page w/ lowest value is chosen for removal.
NFU w/ aging
1. Shift to right
2. MSb = R
00010000
Differences between LRU and NFU LRU updated after every instruction so it’s
resolution is very fine. NFU is coarse (updated after n instructions
execute between clock interrupts). A given page referenced by n-1 instruction is
given equal weight to a page referenced by only 1 instruction (between clock interrupts).
n/2 references to a given page at the beginning of the interval are given equal weight with n/2 references to another page at the end of the interval.
Working set page replacement algorithm Demand paging = start up processes with 0
pages and only load what’s needed. Locality of reference = during any phase of
execution, the process references only a relatively small fraction of its pages.
Working set = set of pages that a process is currently using.
Thrashing = causing a page fault every few instructions.
Working sets
Working set model = make sure a page is in memory before the process needs it.a.k.a. prepaging
w.s. = set of pages used in the k most recent memory references.
Working set algorithm
Uses current virtual time (CVT) = amount of CPU time a process has actually used since it started.
T is a threshold on CVT R and M bits as before; clock interrupt
Working set algorithm
(greatest age/least virtual time) and choose that one if no better candidate exists.
age = current virtual time (i.e., time of last use)
If no suitable candidate exists, pick one at random.
WSClock page replacement
Previous WS algorithm requires entire page table be scanned at each page fault.
WSClock:Simple, efficient, widely used.Uses circular list of page frames.
WSClock page replacementAt each page fault…
Loop once through page table:Examine PTE pointed to by clock hand.If r bit == 1 then
clear r bit; advance clock hand; goto loopelse
If age>tIf page is clean then use this page!Else write dirty page to disk; advance clock hand; goto loop
If write scheduled, wait for completion and used that page.Else pick a victim at random.
WSClock page replacement
clear r bit and advance clock
hand.
Replace old and advance.
Summary of page replacement algorithms
In practice, random page replace typically performs better than FIFO but worse than LRU.