4.4 Page replacement algorithms

Page replacement algorithms Also seen in: CPU cache Web server cache of web pages Buffered I/O (file) caches

Optimal page replacement Page fault occurs Scan all pages currently in memory Determine which page won’t be needed (referenced) until furthest in the future Replace that page Not really possible. (But useful as a benchmark.) Depends on code as well as data.

Algorithms we will discuss: Optimal NRU FIFO Second chance Clock LRU NFU Aging Working set 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 Not referenced, not modified Not referenced, modified Occurs when #4’s R bit is cleared during clock interrupt Referenced, not modified Referenced, modified NRU algorithm: remove random page from lowest numbered non empty class

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 If R==0 then page is old & unused Replace it Else Clear R bit Move page to from head to tail of FIFO Treating it as a newly loaded page Try another 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 Replace it Else Clear R Advance clock hand

Clock page replacement

LRU (least recently used) page replacement Page recently used is likely to be used in the near future; 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 instruction Each page also has a 64 bit counter When 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 Shift to right 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 = 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 age = current virtual time – time of last use  (greatest age/least virtual time) and choose that one if no better candidate exists. 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 replacement At 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 loop else If age>t If 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. WSClock page replacement Replace old and advance.

Summary of page replacement algorithms