• Page Fault Handling
• Page Replacement
• Allocation Policies

• The hardware traps to the kernel, saving the program counter on the stack.
• An assembly code routine is started to save the general registers and other volatile information.
• The operating system discovers that a page fault has occurred, and tries to discover which virtual page is needed.
• Once the virtual address that caused the fault is known, the system checks to see if this address is valid and the protection consistent with the access.
• If the page frame selected is dirty, the page is scheduled for transfer to the disk, and a context switch takes place.

• When page frame is clean, operating system looks up the disk address where the needed page is, schedules a disk operation to bring it in.
• When disk interrupt indicates page has arrived, page tables updated to reflect position, frame marked as being in normal state.
• Faulting instruction backed up to state it had when it began and program counter reset to point to that instruction.
• Faulting process scheduled, operating system returns to the (assembly language) routine that called it.
• This routine reloads registers and other state information and returns to user space to continue execution, as if no fault had occurred.

• The operating system tries to keep a certain amount of free memory.
• When the amount of free memory is low, the operating system begins to "steal pages".
• Using special page replacement algorithms, the amount of free memory is restored to an acceptable range.

• Local versus global page replacement. (a) Original configuration. (b) Local page replacement. (c) Global page replacement.

• Page Fault Handling
• Page Replacement
• Allocation Policies

• Optimal page replacement algorithm
• Not recently used page replacement
• First-In, First-Out page replacement
• Second chance page replacement
• Clock page replacement
• Least recently used page replacement
• Working set page replacement
• WSClock page replacement

• Optimal page replacement algorithm
• Not recently used page replacement
• First-In, First-Out page replacement
• Second chance page replacement
• Clock page replacement

• Replace the page that never be used in the future, or will not be used soon.
• Best algorithm ... but is not implementable. It is useful as a benchmark.

Use Referenced and Modified bits to decide.

 R  M  
------
 0  0 
 0  1 
 1  0 
 1  1

• R is set to 0 periodically, especially after a clock tick.
• R = 0 , means this page is not referenced , thus it is less important.
• R = 1 , means this page is important, keep it.
• M = 0 , this page is clean, no need to write to disk.
• M = 1 , this page is dirty, write to disk before replacement.
• Easy to implement.

• Always replacement the oldest pages.
• Might throw out important pages

Operation of second chance.

• (a) Pages sorted in FIFO order.
• (b) Page list if a page fault occurs at time 20 and A has its R bit set. The numbers above the pages are their load times.

• Optimal page replacement algorithm
• Not recently used page replacement
• First-In, First-Out page replacemen
• Second chance page replacement
• Clock page replacement

• Least Recently Used page replacement
• Not Frequently Used page replacemen
• Aging page replacement

• Replace the longest unused page.
• Excellent but difficult to implement exactly.
• Might need special hardware.

• LRU using a matrix when pages are referenced in the order
  0, 1, 2, 3, 2, 1, 0, 3, 2, 3.

• Record R bit in every clock ticks to a counter for each page.
• NFU never forgets.
• So new coming pages are always less important.

• The aging algorithm simulates LRU in software. Shown are six pages for five clock ticks. The five clock ticks are represented by (a) to (e).

• Least Recently Used page replacement
• Not Frequently Used page replacement
• Aging page replacement

• Working Set Page Replacement
• WSClock Page Replacement

• The working set is the set of pages used by the k most recent memory references.
• The function w(k, t) is the size of the working set at time t.

When the hand comes all the way around to its starting point there are two cases to consider:

• At least one write has been scheduled.
• No writes have been scheduled.

• Operation of the WSClock algorithm. (a) and (b) give an example of what happens when R = 1. (c) and (d) give an example of R = 0.

• Working Set Page Replacement
• WSClock Page Replacement

• Summary of Page Replacement Algorithms
• Page fault rate versus page frames
• Belady anomaly

• Page fault rate as a function of the number of page frames assigned.

Bélády's anomaly is the phenomenon in which increasing the number of page frames results in an increase in the number of page faults for certain memory access patterns.
This phenomenon is commonly experienced when using the first-in first-out (FIFO) page replacement algorithm.

Page requests   3   2   1   0   3   2   4   3   2   1   0   4
Newest page     3*  2*  1*  0*  3*  2*  4*  4   4   1*  0*  0
                    3   2   1   0   3   2   2   2   4   1   1
Oldest page             3   2   1   0   3   3   3   2   4   4

Page requests   3   2   1   0   3   2   4   3   2   1   0   4
Newest page     3*  2*  1*  0*  0   0   4*  3*  2*  1*  0*  4*
                    3   2   1   1   1   0   4   3   2   1   0
                        3   2   2   2   1   0   4   3   2   1
Oldest page                 3   3   3   2   1   0   4   3   2

An example of Bélády's anomaly. Using three page frames, nine page faults occur. Increasing to four page frames causes 10 page faults to occur. Page faults are in asterisk(*).

• Summary of Page Replacement Algorithms
• Page fault rate versus page frames
• Belady anomaly

• Chapter 3: Memory management, Modern Operating Systems . Forth Edition, Andrew S. Tanenbaum