Lecture 6 Virtual Memory Management

Outline

1. Definition of Global Page Replacement Algorithm

2. Working Set Page Replacement Algorithm
3. Page Fault Frequency Algorithm

Local Replacement Algorithm ignores memory access pattern differences of different processes

FIFO: Assume initial order is a->b->c
Number of physical pages: 3 -> Number of page faults: 9

Local Replacement Algorithm ignores memory access pattern differences of different processes

FIFO page replacement algorithm: assume initial order a->b->c
Number of physical pages: 4 -> Number of page faults: 1

How Global Replacement Algorithms work

• Ideas
  • Allocate a variable number of physical pages for a process
• Problems in Global Replacement Algorithms
  • Memory demand of a process varies at different stages
  • The memory allocated to the process should adapt
    at different stages
  • The global replacement algorithm should determine the number of physical pages allocated to the process

CPU Utilization with different number of running programs

• There is a mutual promotion and restriction relationship between CPU utilization and the number of programs running
  • When there are few running programs, we can increase CPU utilization by increasing the number of running programs
  • Large number of running programs will increase memory access frequency and reduces the locality of memory access
    -Lower locality leads to higher page fault rate and lower CPU utilization

Outline

1. Definition of Global Page Replacement Algorithm

2. Working Set Page Replacement Algorithm

3. Page Fault Frequency Algorithm

Working Set

The set of logical pages currently used by a process, it can be expressed as a binary function W(t, $\Delta$)

• Current execution time $t$
• Working-set window $\Delta$: A fixed-length page access time window
• working set window $\Delta$ size $\tau$
  • The length of the time window, represented by the memory accesses before the current time $t$
• working set W(t, $\Delta$)
  • The set of all pages accessed within the time window $\Delta$ before the current time $t$
• working set size | W(t, $\Delta$) |: Number of pages

Working set example of a process

Page access record:
W(t, $\Delta$) ={1,2,5,6,7} , working set window size $\tau=10$, current time $t=t_1$

Working set example of a process

Page access record:
W(t, $\Delta$) ={1,2,3,4,5,6,7} , working set window size $\tau=10$, current time $t=t_1$

Working set example of a process

Page access record:
W(t, $\Delta$) ={3,4}, working set window size $\tau=10$, current time $t=t_2$

Changes of Working Set

• After a process starts to execute, its working set is gradually established by accessing new pages
• When the locality area of memory accesses is roughly stable, the working set size is also roughly stable
• When the locality area changes, the working set quickly expands and contracts until it transitions to the next stable value.

Resident Set

The set of pages that are actually present in the memory of a process at the current time.

• Relationship between working set and resident set
  • The working set is an inherent property of a process during its execution.
  • The resident set is determined by the number of physical pages allocated to the process and the page replacement algorithm, which depends on the system
• Relationship between page fault rate and resident set
  • When the resident set $\supseteq$ working set, the page fault rate is relatively low.
  • When the working set changes dramatically (transition), the page fault rate is relatively high.
  • After the process resident set size reaches a certain number, the page fault rate will not decrease significantly

Working Set Page Replacement Algorithm

• Idea

  • Swap out pages not in the working set

• Working set window size $\tau$

  • The set of pages accessed in the previous $\tau$ memory accesses before the current time form the working set

• Implementation

  • Memory Access Record linkedlist: Maintains a list of accessed pages within the window
  • When a page is accessed, swap out pages not in the working set and update the Memory Access Record list
  • When a page fault occurs, swap in the page and update the list.

Example of Working Set Replacement Algorithm

$\tau=4$

Example of Working Set Replacement Algorithm

$\tau=4$

Example of Working Set Replacement Algorithm

$\tau=4$

Example of Working Set Replacement Algorithm

$\tau=4$

Example of Working Set Replacement Algorithm

$\tau=4$

Example of Working Set Replacement Algorithm

$\tau=4$

Example of Working Set Replacement Algorithm

$\tau=4$

Example of Working Set Replacement Algorithm

$\tau=4$

Example of Working Set Replacement Algorithm

$\tau=4$

Outline

1. Definition of Global Page Replacement Algorithm
2. Working Set Page Replacement Algorithm

3. Page Fault Frequency Algorithm

Page-Fault-Frequency (Page Fault Rate)

The number of page faults / the number of memory accesses or the reciprocal of the average time interval between page faults.

• Factors Affecting Page Fault Rate
  • Page replacement algorithm
  • Number of physical pages allocated to the process
  • Page size
  • The coding method of a program

Page Fault Frequency Replacement Algorithm

By adjusting the resident set size, the page fault frequency of each process keeps in a reasonable range.

• If the process's page fault frequency is too high, increase the resident set to allocate more physical pages.
• If the process's page fault frequency is too low, decrease the resident set to reduce its number of physical pages.

Page Fault Frequency Replacement Algorithm

• When accessing memory, set the reference bit flag
• When there is a page fault, calculate the time interval from the last page fault time $t_{last}$ to the current time $t_{current}$
  • If $t_{current} – t_{last}>T$ (tolerated page fault window), then replace all pages that have not been visited during the time interval $[t_{last} , t_{current} ]$
  • If $t_{current} – t_{last} \le T$, then add missing pages to the resident set

Example of Page Fault Frequency Algorithm

Assuming the window size is 2

Example of Page Fault Frequency Algorithm

Assuming the window size is 2

Example of Page Fault Frequency Algorithm

Assuming the window size is 2

Example of Page Fault Frequency Algorithm

Assuming the window size is 2

Example of Page Fault Frequency Algorithm

Assuming the window size is 2

Example of Page Fault Frequency Algorithm

Assuming the window size is 2

Example of Page Fault Frequency Algorithm

Assuming the window size is 2

Example of Page Fault Frequency Algorithm

Assuming the window size is 2

Example of Page Fault Frequency Algorithm

Assuming the window size is 2

Example of Page Fault Frequency Algorithm

Assuming the window size is 2

Thrashing

• Thrashing

  • Physical pages are not enough to contain all working sets
  • Lead to a large number of page faults, frequent page replacement
  • Lead to slow execution of the process

• Cause of thrashing

  • As the number of processes residing in memory increases, the number of physical pages allocated to each process decreases, and the page fault frequency keeps increasing

• The OS needs to balance the concurrency level and page fault frequency

  • Select an appropriate number of processes and the demanding number of physical pages for each process

Course Lab 2

• Chapter 4: Address Space -> Chapter4 Exercises ->
  • rCore
  • uCore
• Lab tasks
  • Rewrite the kernel function for obtaining system time and process control block
  • Implement system calls for mapping and unmapping virtual memory
• Submission requirements
  • April 9, 2023

Lecture 5 Summary of Virtual Memory

• Section 1 Concepts of Virtual Memory
  • Demanding Paging, Overlay, Swapping, Concept of Virtual Memory, Page Fault
• Section 2 Local Page Replacement Algorithms
  • Concepts of page replacement algorithm, OPT, FIFO, LRU, Clock, Improved Clock Page Replacement Algorithm, LFU, Belady Phenomenon
• Section 3 Global Page Replacement Algorithms
  • Global page replacement algorithm, Working Set Replacement Algorithm, Page Fault Frequency Algorithm