1. Memory Management Virtual Memory Page replacement algorithms
Chapter 4
Sec. 4.4

2. Structure of a page table entry

3. Issues with page tables
They can be very large
It takes more time to access a memory location
Virtual page first has to be mapped to its corresponding physical frame
The spectrum of solutions
High speed registers to implement the table
Put entire page table in main memory

4. Page swapping
What to do if the memory reference is to a page that is not in main memory?
This is called a page fault
“Swap” a page out of main memory and “swap” the needed page in its place
The decision about which page to swap out is made by a page replacement algorithm

5. When a page fault occurs…
Page fault forces choice about which page should be overwritten
Modified page may first have to be saved to the hard drive
But if is unmodified, it can just be overwritten
Best not to choose “popular” page
It will probably need to be brought back in soon

6. Page replacement algorithms
Choosing the page that gets swapped out
Optimal
NRU
FIFO
Second Chance
Clock
LRU
NFU
Working Set
WSClock

7. Optimal Page Replacement Algorithm
Replace page that will be needed at the farthest point in future
Optimal but unrealizable
Can estimate by logging page use on previous runs of a given process
Impractical

8. Optimal algorithm example Using 3 page frames
7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Total number of page faults is ___ . This algorithm (although the best) is implausible to implement since it requires future knowledge. It is used mainly for comparison studies.

9. Not Recently Used (NRU)
Each page has reference and modified bits
bits are set when page is referenced, modified
Pages are classified
not referenced, not modified: 0 0
not referenced, modified: how can it be?
referenced, not modified: 1 0
referenced, modified: 1 1
Removes page at random from the lowest numbered non-empty class

10. FIFO Maintain a linked list of all pages
in order in which they came into memory
The page at the head of the list swapped out
Disadvantage?
Advantage?

11. FIFO example Using 3 frames
7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Total of ___ faults.
Suppose we had 4 frames instead of 3, would there be fewer page faults?

12. Another FIFO example Consider the reference string
1, 2, 3, 4, 1, 2, 5, 1, 2, 3, 4, 5
With three frames there are faults
With four frames there are faults.
This is an example of Belady's Anomaly.

13. P's show which page references show page faults
Belady's Anomaly?!?
FIFO with 3 page frames
FIFO with 4 page frames
P's show which page references show page faults

14. Second Chance FIFO modification
A FIFO linked list is maintained, as before.
The page at the head of the list is chosen to be swapped out unless its R bit is 0
In that case, it goes to the end of the list
And the next process on the list is examined for swapping…

15. Clock Variation of second chance

16. Least Recently Used (LRU)
Rationale is that pages used recently will be used again soon
replace pages that have been unused for longest time
If implemented with a linked list of pages
the list must be updated with every memory reference
Other techniques require hardware support
Counter is maintained
When a page is referenced, it receives the counter’s value
LRU matrix

17. LRU using a matrix – pages referenced in order 0,1,2,3,2,1,0,3,2,3
LRU matrix
LRU using a matrix – pages referenced in order 0,1,2,3,2,1,0,3,2,3

18. LRU example
7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Total number of page faults is _____.
This is often the best page-replacement algorithm that we can use.

19. Additional reference bits (LRU enhancement )
Instead of just clearing the bits every so often, we can keep extra information by having a reference byte
At regular intervals (100 ms, e.g.) a clock interrupt occurs
OS shifts the reference bit into the high order position of the reference byte, and shifts all other bits down to the right

20. Additional reference bits example
For example, the reference byte is and the reference bit is 1 when the timer expires.
The reference byte now becomes , and the reference bit is set back to 0
Interpreting these bytes as unsigned integers, the least recently referenced page is the one with the smallest reference byte.

21. Not frequently used (NFU)
Counter in each page table entry is initialized to 0
At each clock interrupt, the value of the reference bit is added to the counter, and then set back to 0.
At a page fault, the page with the smallest counter is swapped out.
Not very useful, but a variation of it accounts for the aging of pages.
This is a simulation of LRU
See pp

22. Working Set / Locality Model
The working-set strategy starts by looking at how many frames a process is actually using.
This approach defines the locality model of process execution
As a process executes, it moves from one locality to another.
A locality is a set of pages actively used together
A program is composed of several (possibly overlapping) localities

23. What is locality?
For example, when a procedure is called, it defines a new locality. When the procedure is exited, the locality changes
If we allocate enough frames to accommodate the process’ current locality
it will fault for the pages in its current locality until they are all in memory.
it will not fault again until it changes its locality.

24. Working-Set Model
This model uses a parameter, kto define the working-set window
The idea is to examine the most recent kpage references. The set of pages in the most recent kpage references is the working set
If a page is in active use, it will be in the working set
If it is no longer being used, it will drop from the working set kunits after its last reference

25. Example A page reference string, withk= 10 t1 t2
At time t1 the working set is {1,2,5,6,7}
At time t2 the working set is {3, 4}
The accuracy of the working set depends upon the selection of k.
if it is too small, it may not encompass the working set
if it is too large, it may overlap several localities

26. Implementation
The OS monitors the working-set of each process and allocates to that working-set enough frames to provide it with its working-set size
If there are any extra frames, another process can be started.
If the sum of the working-sets increases, exceeding the total number of frames, a process is suspended. That process’ pages are written out and its frames reallocated.

27. Working Set

28. WSClock

29. Summary