Virtual Memory: Page Replacement

Realizing Virtual Memory Hardware support

Memory Management Unit (MMU): address translation, bits, interrupts

Operating system supportPage replacement policyResident set managementLoad control degree of multiprogramming

Page Replacement Policy Resident set maintenance

Fixed or variable allocation Per-process or global replacement

Page replacement problemA fixed number of frames, M, is used to map the process virtual memory pagesWhich page should be replaced when a page fault occurs and all M frames are occupied?

Requirements and Metrics Workload: a sequence of virtual

memory references (page numbers) Page fault rate =

#page faults/#memory references Minimize the page fault rate for

workloads obeying the principle of locality

Keep hardware/software overhead as small as possible

Algorithms Optimal (OPT) Least Recently Used (LRU) First-In-First-Out (FIFO) Clock

Optimal Policy (OPT) Replace the page which will be

referenced again in the most remote future

Impossible to implementWhy?

Serves as a baseline for other algorithms

Least Recently Used (LRU) Replace the page that has not been

referenced for the longest time The best approximation of OPT for

the locality constrained workloads Possible to implement Infeasible as the overhead is high

Why?

First-In-First-Out (FIFO) Page frames are organized in a circular

buffer with a roving pointer Pages are replaced in round-robin style

When page fault occur, replace the page to which the pointer points to

Simple to implement, low overhead High page fault rate, prone to

anomalous behavior

Clock (second chance) Similar to FIFO but takes page usage

into accountCircular buffer + page use bitWhen a page is referenced: set use_bit=1When a page fault occur: For each page:

if use_bit==1: give page a second chance: use_bit=0; continue scan;

if use_bit==0: replace the page

Example: Page 727 is needed

0

1

2

3

4

56

7

8

n

.

.

.

Page 9use = 1

Page 19use = 1

Page 1use = 0

Page 45use = 1

Page 191use = 1

Page 556use = 0

Page 13use = 0

Page 67use = 1

Page 33use = 1

Page 222use = 0

next frame pointer

After replacement0

1

2

3

4

56

7

8

n

.

.

.

Page 9use = 1

Page 19use = 1

Page 1use = 0

Page 45use = 0

Page 191use = 0

Page 727use = 0

Page 13use = 0

Page 67use = 1

Page 33use = 1

Page 222use = 0

next frame pointer

Example of all algorithms

LRU and non-local workloads Workload: 1 2 3 4 5 1 2 3 4 5…

Typical for array based applications What is the page fault rate for M=1,

…,5? A possible alternative is to use a

Most Recently Use (MRU) replacement policy

Belady’s Anomaly It is reasonable to expect that regardless

of a workload, the number of page faults should not increase if we add more frames: not true for the FIFO policy:

1, 2, 3, 4, 1, 2, 5, 1, 2, 3, 4, 5

1

2

3

1

2

3

4

1

2

5

3

4

1

2

3

1

2

3

5

1

2

4

5

44 3

Algorithm comparison

Clock algorithm with 2 bits Use “modified” bit to evict unmodified

(clean) pages in preference over modified (dirty) pages

Four classes:u=0; m=0: not recently used, cleanu=0; m=1: not recently used, dirtyu=1; m=0: recently used, cleanu=1; m=1: recently used, dirty

First scan: look for (0,0) frame, do not change the use bit

If (0,0) frame is found, replace it Second scan: look for (0,1) frame, set

use bit to 0 in each frame bypassedIf (0,1) frame is found, replace it

If all failed, repeat the above procedure

this time we will certainly find something

Clock algorithm with 2 bits

Page buffering Evicted pages are kept on two lists:

free and modified page lists Pages are read into the frames on the

free page list Pages are written to disk in large

chunks from the modified page list If an evicted page is referenced, and it

is still on one of the lists, it is made valid at a very low cost

Page BufferingB

B

B

B

B36N21N3N78N2N47N22N39N4N8N

55N

B

B

B

B36N21N3N78N2N47N22B39N4N8N

Page fault:55 is needed22 is evicted

Bufferedframes(B)

Normalframes(N)

Resident set management With multiprogramming, a fixed

number of memory frames are shared among multiple processes

How should the frames be partitioned among the active processes?

Resident set is the set of process pages currently allocated to the memory frames

Global page replacement All memory frames are candidates

for page evictionA faulting process may evict a page of other process

Automatically adjusts process sizes to their current needs

Problem: can steal frames from “wrong” processes

Leads to thrashing

Local page replacement Only the memory frames of a

faulting process are candidates for replacement

Dynamically adjust the process allocation

Working set modelPage-Fault Frequency (PFF) algorithm

The working set model [Denning’68] Working set is the set of pages in

the most recent page references

Working set is an approximation of the program locality

The working set strategy Monitor the working set for each

currently active process Adjust the number of pages

assigned to each process according to its working set size

Monitoring working set is impractical The optimal value of is unknown

and would vary

Page-Fault Frequency (PFF) Approximate the page-fault frequency:

Count all memory references for each active processWhen a page fault occurs, compare the current counter value with the previous page fault counter value for the faulting processIf < F, expand the WS; Otherwise, shrink the WS by discarding pages with use_bit==0

Swapping If a faulting process cannot expand its

working set (all frames are occupied), some process should be swapped out

The decision to swap processes in/out is the responsibility of the long/medium term scheduler

Another reason: not enough memory to run a new process

Long (medium) term scheduling Controls multiprogramming level Decision of which processes to swap

out/in is based onCPU usage (I/O bound vs. CPU bound)Page fault ratePrioritySizeBlocked vs. running

UNIX process statesrunning

user

runningkernel

readyuser

readykernel blocked

zombie

sys. callinterrupt

schedule

created

return

terminated

wait for event

event done

schedule

preempt

interrupt

readyswapped

blockedswapped

Swap out

event done

Swap outSwap in

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